id sid tid token lemma pos ejpam-7001 1 1 european european PROPN ejpam-7001 1 2 journal journal PROPN ejpam-7001 1 3 of of ADP ejpam-7001 1 4 pure pure ADJ ejpam-7001 1 5 and and CCONJ ejpam-7001 1 6 applied applied ADJ ejpam-7001 1 7 mathematics mathematic NOUN ejpam-7001 1 8 2025 2025 NUM ejpam-7001 1 9 , , PUNCT ejpam-7001 1 10 vol vol NOUN ejpam-7001 1 11 . . PROPN ejpam-7001 1 12 18 18 NUM ejpam-7001 1 13 , , PUNCT ejpam-7001 1 14 issue issue NOUN ejpam-7001 1 15 4 4 NUM ejpam-7001 1 16 , , PUNCT ejpam-7001 1 17 article article NOUN ejpam-7001 1 18 number number NOUN ejpam-7001 1 19 7001 7001 NUM ejpam-7001 1 20 issn issn PROPN ejpam-7001 1 21 1307 1307 NUM ejpam-7001 1 22 - - SYM ejpam-7001 1 23 5543 5543 NUM ejpam-7001 1 24 – – PUNCT ejpam-7001 1 25 ejpam.com ejpam.com X ejpam-7001 1 26 published publish VERB ejpam-7001 1 27 by by ADP ejpam-7001 1 28 new new PROPN ejpam-7001 1 29 york york PROPN ejpam-7001 1 30 business business PROPN ejpam-7001 1 31 global global PROPN ejpam-7001 1 32 the the DET ejpam-7001 1 33 g g PROPN ejpam-7001 1 34 - - PUNCT ejpam-7001 1 35 rank rank NOUN ejpam-7001 1 36 - - PUNCT ejpam-7001 1 37 mapped map VERB ejpam-7001 1 38 transmuted transmuted ADJ ejpam-7001 1 39 fréchet fréchet NOUN ejpam-7001 1 40 weibull weibull NOUN ejpam-7001 1 41 distribution distribution NOUN ejpam-7001 1 42 under under ADP ejpam-7001 1 43 cubic cubic ADJ ejpam-7001 1 44 model model NOUN ejpam-7001 1 45 : : PUNCT ejpam-7001 1 46 mathematical mathematical ADJ ejpam-7001 1 47 theory theory NOUN ejpam-7001 1 48 , , PUNCT ejpam-7001 1 49 computational computational ADJ ejpam-7001 1 50 statistics statistic NOUN ejpam-7001 1 51 , , PUNCT ejpam-7001 1 52 and and CCONJ ejpam-7001 1 53 sustainability sustainability NOUN ejpam-7001 1 54 data datum NOUN ejpam-7001 1 55 analysis analysis NOUN ejpam-7001 1 56 imliyangba1 imliyangba1 NOUN ejpam-7001 1 57 , , PUNCT ejpam-7001 1 58 mohamed mohamed PROPN ejpam-7001 1 59 f. f. PROPN ejpam-7001 1 60 abouelenein2 abouelenein2 PROPN ejpam-7001 1 61 , , PUNCT ejpam-7001 1 62 bhanita bhanita NOUN ejpam-7001 1 63 das1 das1 NOUN ejpam-7001 1 64 , , PUNCT ejpam-7001 1 65 seema seema PROPN ejpam-7001 1 66 chettri1 chettri1 PROPN ejpam-7001 1 67 , , PUNCT ejpam-7001 1 68 bhupen bhupen ADJ ejpam-7001 1 69 k. k. PROPN ejpam-7001 1 70 baruah3 baruah3 PROPN ejpam-7001 1 71 , , PUNCT ejpam-7001 1 72 partha partha PROPN ejpam-7001 1 73 jyoti jyoti PROPN ejpam-7001 1 74 hazarika4 hazarika4 PROPN ejpam-7001 1 75 , , PUNCT ejpam-7001 1 76 mohamed mohamed PROPN ejpam-7001 1 77 s. s. PROPN ejpam-7001 2 1 eliwa5,6,∗ eliwa5,6,∗ PROPN ejpam-7001 2 2 1 1 NUM ejpam-7001 2 3 department department NOUN ejpam-7001 2 4 of of ADP ejpam-7001 2 5 statistics statistic NOUN ejpam-7001 2 6 , , PUNCT ejpam-7001 2 7 north north NOUN ejpam-7001 2 8 - - PUNCT ejpam-7001 2 9 eastern eastern PROPN ejpam-7001 2 10 hill hill PROPN ejpam-7001 2 11 university university PROPN ejpam-7001 2 12 , , PUNCT ejpam-7001 2 13 shillong shillong PROPN ejpam-7001 2 14 , , PUNCT ejpam-7001 2 15 meghalaya meghalaya PROPN ejpam-7001 2 16 , , PUNCT ejpam-7001 2 17 india india PROPN ejpam-7001 2 18 2 2 NUM ejpam-7001 2 19 department department NOUN ejpam-7001 2 20 of of ADP ejpam-7001 2 21 insurance insurance NOUN ejpam-7001 2 22 and and CCONJ ejpam-7001 2 23 risk risk NOUN ejpam-7001 2 24 management management NOUN ejpam-7001 2 25 , , PUNCT ejpam-7001 2 26 college college NOUN ejpam-7001 2 27 of of ADP ejpam-7001 2 28 business business NOUN ejpam-7001 2 29 , , PUNCT ejpam-7001 2 30 imam imam PROPN ejpam-7001 2 31 mohammad mohammad PROPN ejpam-7001 2 32 ibn ibn PROPN ejpam-7001 2 33 saud saud PROPN ejpam-7001 2 34 islamic islamic PROPN ejpam-7001 2 35 university university PROPN ejpam-7001 2 36 ( ( PUNCT ejpam-7001 2 37 imsiu imsiu PROPN ejpam-7001 2 38 ) ) PUNCT ejpam-7001 2 39 , , PUNCT ejpam-7001 2 40 riyadh riyadh PROPN ejpam-7001 2 41 11432 11432 NUM ejpam-7001 2 42 , , PUNCT ejpam-7001 2 43 riyadh riyadh PROPN ejpam-7001 2 44 , , PUNCT ejpam-7001 2 45 saudi saudi PROPN ejpam-7001 2 46 arabia arabia PROPN ejpam-7001 2 47 3 3 NUM ejpam-7001 2 48 department department NOUN ejpam-7001 2 49 of of ADP ejpam-7001 2 50 chemistry chemistry NOUN ejpam-7001 2 51 , , PUNCT ejpam-7001 2 52 jagannath jagannath PROPN ejpam-7001 2 53 barooah barooah PROPN ejpam-7001 2 54 university university PROPN ejpam-7001 2 55 , , PUNCT ejpam-7001 2 56 india india PROPN ejpam-7001 2 57 4 4 NUM ejpam-7001 2 58 department department NOUN ejpam-7001 2 59 of of ADP ejpam-7001 2 60 statistics statistic NOUN ejpam-7001 2 61 , , PUNCT ejpam-7001 2 62 dibrugarh dibrugarh NOUN ejpam-7001 2 63 university university NOUN ejpam-7001 2 64 , , PUNCT ejpam-7001 2 65 india india PROPN ejpam-7001 2 66 5 5 NUM ejpam-7001 2 67 department department NOUN ejpam-7001 2 68 of of ADP ejpam-7001 2 69 statistics statistic NOUN ejpam-7001 2 70 and and CCONJ ejpam-7001 2 71 operations operation NOUN ejpam-7001 2 72 research research NOUN ejpam-7001 2 73 , , PUNCT ejpam-7001 2 74 college college NOUN ejpam-7001 2 75 of of ADP ejpam-7001 2 76 science science NOUN ejpam-7001 2 77 , , PUNCT ejpam-7001 2 78 qassim qassim PROPN ejpam-7001 2 79 university university PROPN ejpam-7001 2 80 , , PUNCT ejpam-7001 2 81 saudi saudi PROPN ejpam-7001 2 82 arabia arabia PROPN ejpam-7001 2 83 6 6 NUM ejpam-7001 2 84 department department NOUN ejpam-7001 2 85 of of ADP ejpam-7001 2 86 mathematics mathematic NOUN ejpam-7001 2 87 , , PUNCT ejpam-7001 2 88 faculty faculty NOUN ejpam-7001 2 89 of of ADP ejpam-7001 2 90 science science NOUN ejpam-7001 2 91 , , PUNCT ejpam-7001 2 92 mansoura mansoura PROPN ejpam-7001 2 93 university university NOUN ejpam-7001 2 94 , , PUNCT ejpam-7001 2 95 mansoura mansoura PROPN ejpam-7001 2 96 35516 35516 NUM ejpam-7001 2 97 , , PUNCT ejpam-7001 2 98 egypt egypt PROPN ejpam-7001 2 99 abstract abstract PROPN ejpam-7001 2 100 . . PUNCT ejpam-7001 3 1 this this DET ejpam-7001 3 2 work work NOUN ejpam-7001 3 3 introduces introduce NOUN ejpam-7001 3 4 and and CCONJ ejpam-7001 3 5 examines examine VERB ejpam-7001 3 6 a a DET ejpam-7001 3 7 new new ADJ ejpam-7001 3 8 probability probability NOUN ejpam-7001 3 9 distribution distribution NOUN ejpam-7001 3 10 from from ADP ejpam-7001 3 11 the the DET ejpam-7001 3 12 g g NOUN ejpam-7001 3 13 - - PUNCT ejpam-7001 3 14 rankmapped rankmappe VERB ejpam-7001 3 15 transmuted transmuted ADJ ejpam-7001 3 16 fréchet fréchet NOUN ejpam-7001 3 17 - - PUNCT ejpam-7001 3 18 weibull weibull NOUN ejpam-7001 3 19 ( ( PUNCT ejpam-7001 3 20 g g NOUN ejpam-7001 3 21 - - PUNCT ejpam-7001 3 22 rtfw rtfw NOUN ejpam-7001 3 23 ) ) PUNCT ejpam-7001 3 24 family family NOUN ejpam-7001 3 25 , , PUNCT ejpam-7001 3 26 using use VERB ejpam-7001 3 27 both both CCONJ ejpam-7001 3 28 quadratic quadratic ADJ ejpam-7001 3 29 and and CCONJ ejpam-7001 3 30 cubic cubic ADJ ejpam-7001 3 31 models model NOUN ejpam-7001 3 32 . . PUNCT ejpam-7001 4 1 the the DET ejpam-7001 4 2 quadratic quadratic ADJ ejpam-7001 4 3 rank rank NOUN ejpam-7001 4 4 transmuted transmute VERB ejpam-7001 4 5 fréchet fréchet NOUN ejpam-7001 4 6 - - PUNCT ejpam-7001 4 7 weibull weibull NOUN ejpam-7001 4 8 ( ( PUNCT ejpam-7001 4 9 qrtfw qrtfw PROPN ejpam-7001 4 10 ) ) PUNCT ejpam-7001 4 11 and and CCONJ ejpam-7001 4 12 cubic cubic ADJ ejpam-7001 4 13 rank rank NOUN ejpam-7001 4 14 transmuted transmute VERB ejpam-7001 4 15 fréchet fréchet NOUN ejpam-7001 4 16 - - PUNCT ejpam-7001 4 17 weibull weibull NOUN ejpam-7001 4 18 ( ( PUNCT ejpam-7001 4 19 crtfw crtfw NOUN ejpam-7001 4 20 ) ) PUNCT ejpam-7001 4 21 distributions distribution NOUN ejpam-7001 4 22 are be AUX ejpam-7001 4 23 specifically specifically ADV ejpam-7001 4 24 investigated investigate VERB ejpam-7001 4 25 , , PUNCT ejpam-7001 4 26 with with SCONJ ejpam-7001 4 27 the the DET ejpam-7001 4 28 current current ADJ ejpam-7001 4 29 study study NOUN ejpam-7001 4 30 focused focus VERB ejpam-7001 4 31 solely solely ADV ejpam-7001 4 32 on on ADP ejpam-7001 4 33 the the DET ejpam-7001 4 34 crtfw crtfw PROPN ejpam-7001 4 35 model model NOUN ejpam-7001 4 36 . . PUNCT ejpam-7001 5 1 we we PRON ejpam-7001 5 2 calculated calculate VERB ejpam-7001 5 3 and and CCONJ ejpam-7001 5 4 investigated investigate VERB ejpam-7001 5 5 a a DET ejpam-7001 5 6 wide wide ADJ ejpam-7001 5 7 range range NOUN ejpam-7001 5 8 of of ADP ejpam-7001 5 9 statistical statistical ADJ ejpam-7001 5 10 and and CCONJ ejpam-7001 5 11 mathematical mathematical ADJ ejpam-7001 5 12 aspects aspect NOUN ejpam-7001 5 13 of of ADP ejpam-7001 5 14 the the DET ejpam-7001 5 15 crtfw crtfw NOUN ejpam-7001 5 16 distribution distribution NOUN ejpam-7001 5 17 , , PUNCT ejpam-7001 5 18 including include VERB ejpam-7001 5 19 its its PRON ejpam-7001 5 20 moments moment NOUN ejpam-7001 5 21 , , PUNCT ejpam-7001 5 22 moment moment NOUN ejpam-7001 5 23 generating generate VERB ejpam-7001 5 24 function function NOUN ejpam-7001 5 25 , , PUNCT ejpam-7001 5 26 characteristic characteristic ADJ ejpam-7001 5 27 function function NOUN ejpam-7001 5 28 , , PUNCT ejpam-7001 5 29 quantile quantile ADJ ejpam-7001 5 30 function function NOUN ejpam-7001 5 31 , , PUNCT ejpam-7001 5 32 mode mode NOUN ejpam-7001 5 33 , , PUNCT ejpam-7001 5 34 random random ADJ ejpam-7001 5 35 variate variate NOUN ejpam-7001 5 36 generation generation NOUN ejpam-7001 5 37 , , PUNCT ejpam-7001 5 38 hazard hazard NOUN ejpam-7001 5 39 rate rate NOUN ejpam-7001 5 40 function function NOUN ejpam-7001 5 41 , , PUNCT ejpam-7001 5 42 entropy entropy NOUN ejpam-7001 5 43 , , PUNCT ejpam-7001 5 44 and and CCONJ ejpam-7001 5 45 order order NOUN ejpam-7001 5 46 statistics statistic NOUN ejpam-7001 5 47 . . PUNCT ejpam-7001 6 1 the the DET ejpam-7001 6 2 suggested suggest VERB ejpam-7001 6 3 model model NOUN ejpam-7001 6 4 is be AUX ejpam-7001 6 5 highly highly ADV ejpam-7001 6 6 adaptable adaptable ADJ ejpam-7001 6 7 , , PUNCT ejpam-7001 6 8 capable capable ADJ ejpam-7001 6 9 of of ADP ejpam-7001 6 10 simulating simulate VERB ejpam-7001 6 11 both both DET ejpam-7001 6 12 unimodal unimodal ADJ ejpam-7001 6 13 and and CCONJ ejpam-7001 6 14 bimodal bimodal NOUN ejpam-7001 6 15 behaviors behavior NOUN ejpam-7001 6 16 , , PUNCT ejpam-7001 6 17 as as ADV ejpam-7001 6 18 well well ADV ejpam-7001 6 19 as as ADP ejpam-7001 6 20 tolerating tolerate VERB ejpam-7001 6 21 symmetric symmetric ADJ ejpam-7001 6 22 and and CCONJ ejpam-7001 6 23 asymmetric asymmetric ADJ ejpam-7001 6 24 data datum NOUN ejpam-7001 6 25 structures structure NOUN ejpam-7001 6 26 with with ADP ejpam-7001 6 27 variable variable ADJ ejpam-7001 6 28 degrees degree NOUN ejpam-7001 6 29 of of ADP ejpam-7001 6 30 kurtosis kurtosis NOUN ejpam-7001 6 31 . . PUNCT ejpam-7001 7 1 the the DET ejpam-7001 7 2 maximum maximum ADJ ejpam-7001 7 3 likelihood likelihood NOUN ejpam-7001 7 4 method method NOUN ejpam-7001 7 5 was be AUX ejpam-7001 7 6 used use VERB ejpam-7001 7 7 for for ADP ejpam-7001 7 8 parameter parameter NOUN ejpam-7001 7 9 estimation estimation NOUN ejpam-7001 7 10 , , PUNCT ejpam-7001 7 11 and and CCONJ ejpam-7001 7 12 a a DET ejpam-7001 7 13 full full ADJ ejpam-7001 7 14 monte monte PROPN ejpam-7001 7 15 carlo carlo PROPN ejpam-7001 7 16 simulation simulation PROPN ejpam-7001 7 17 study study PROPN ejpam-7001 7 18 was be AUX ejpam-7001 7 19 carried carry VERB ejpam-7001 7 20 out out ADP ejpam-7001 7 21 to to PART ejpam-7001 7 22 assess assess VERB ejpam-7001 7 23 the the DET ejpam-7001 7 24 estimators estimator NOUN ejpam-7001 7 25 ’ ’ PART ejpam-7001 7 26 performance performance NOUN ejpam-7001 7 27 and and CCONJ ejpam-7001 7 28 efficiency efficiency NOUN ejpam-7001 7 29 under under ADP ejpam-7001 7 30 various various ADJ ejpam-7001 7 31 circumstances circumstance NOUN ejpam-7001 7 32 . . PUNCT ejpam-7001 8 1 the the DET ejpam-7001 8 2 simulation simulation NOUN ejpam-7001 8 3 results result NOUN ejpam-7001 8 4 showed show VERB ejpam-7001 8 5 that that SCONJ ejpam-7001 8 6 the the DET ejpam-7001 8 7 estimators estimator NOUN ejpam-7001 8 8 performed perform VERB ejpam-7001 8 9 effectively effectively ADV ejpam-7001 8 10 , , PUNCT ejpam-7001 8 11 with with ADP ejpam-7001 8 12 bias bias NOUN ejpam-7001 8 13 and and CCONJ ejpam-7001 8 14 mean mean VERB ejpam-7001 8 15 square square ADJ ejpam-7001 8 16 error error NOUN ejpam-7001 8 17 reducing reduce VERB ejpam-7001 8 18 as as SCONJ ejpam-7001 8 19 the the DET ejpam-7001 8 20 sample sample NOUN ejpam-7001 8 21 size size NOUN ejpam-7001 8 22 increased increase VERB ejpam-7001 8 23 . . PUNCT ejpam-7001 9 1 to to PART ejpam-7001 9 2 demonstrate demonstrate VERB ejpam-7001 9 3 the the DET ejpam-7001 9 4 crtfw crtfw NOUN ejpam-7001 9 5 distribution distribution NOUN ejpam-7001 9 6 ’s ’s PART ejpam-7001 9 7 practical practical ADJ ejpam-7001 9 8 application application NOUN ejpam-7001 9 9 , , PUNCT ejpam-7001 9 10 two two NUM ejpam-7001 9 11 real real ADJ ejpam-7001 9 12 - - PUNCT ejpam-7001 9 13 world world NOUN ejpam-7001 9 14 sustainability sustainability NOUN ejpam-7001 9 15 - - PUNCT ejpam-7001 9 16 related relate VERB ejpam-7001 9 17 datasets dataset NOUN ejpam-7001 9 18 were be AUX ejpam-7001 9 19 examined examine VERB ejpam-7001 9 20 . . PUNCT ejpam-7001 10 1 the the DET ejpam-7001 10 2 crtfw crtfw PROPN ejpam-7001 10 3 model model NOUN ejpam-7001 10 4 outperformed outperform VERB ejpam-7001 10 5 numerous numerous ADJ ejpam-7001 10 6 wellknown wellknown ADJ ejpam-7001 10 7 lifetime lifetime NOUN ejpam-7001 10 8 and and CCONJ ejpam-7001 10 9 reliability reliability NOUN ejpam-7001 10 10 distributions distribution NOUN ejpam-7001 10 11 in in ADP ejpam-7001 10 12 terms term NOUN ejpam-7001 10 13 of of ADP ejpam-7001 10 14 flexibility flexibility NOUN ejpam-7001 10 15 and and CCONJ ejpam-7001 10 16 goodness goodness NOUN ejpam-7001 10 17 - - PUNCT ejpam-7001 10 18 of of ADP ejpam-7001 10 19 - - PUNCT ejpam-7001 10 20 fit fit NOUN ejpam-7001 10 21 , , PUNCT ejpam-7001 10 22 emphasizing emphasize VERB ejpam-7001 10 23 its its PRON ejpam-7001 10 24 use use NOUN ejpam-7001 10 25 for for ADP ejpam-7001 10 26 both both CCONJ ejpam-7001 10 27 theoretical theoretical ADJ ejpam-7001 10 28 and and CCONJ ejpam-7001 10 29 applied apply VERB ejpam-7001 10 30 data datum NOUN ejpam-7001 10 31 modeling modeling NOUN ejpam-7001 10 32 . . PUNCT ejpam-7001 11 1 2020 2020 NUM ejpam-7001 11 2 mathematics mathematic NOUN ejpam-7001 11 3 subject subject NOUN ejpam-7001 11 4 classifications classification NOUN ejpam-7001 11 5 : : PUNCT ejpam-7001 11 6 62e99 62e99 NUM ejpam-7001 11 7 , , PUNCT ejpam-7001 11 8 62e15 62e15 NUM ejpam-7001 11 9 , , PUNCT ejpam-7001 11 10 62g10 62g10 NUM ejpam-7001 11 11 , , PUNCT ejpam-7001 11 12 62p12 62p12 NUM ejpam-7001 11 13 , , PUNCT ejpam-7001 11 14 62q05 62q05 NUM ejpam-7001 11 15 ∗corresponding ∗corresponde VERB ejpam-7001 11 16 author author NOUN ejpam-7001 11 17 . . PUNCT ejpam-7001 12 1 doi doi NOUN ejpam-7001 12 2 : : PUNCT ejpam-7001 12 3 https://doi.org/10.29020/nybg.ejpam.v18i4.7001 https://doi.org/10.29020/nybg.ejpam.v18i4.7001 PROPN ejpam-7001 12 4 email email NOUN ejpam-7001 12 5 addresses address NOUN ejpam-7001 12 6 : : PUNCT ejpam-7001 12 7 mseliwa@mans.edu.eg mseliwa@mans.edu.eg PROPN ejpam-7001 12 8 ( ( PUNCT ejpam-7001 12 9 m. m. PROPN ejpam-7001 12 10 s. s. PROPN ejpam-7001 12 11 eliwa eliwa PROPN ejpam-7001 12 12 ) ) PUNCT ejpam-7001 12 13 https://www.ejpam.com https://www.ejpam.com X ejpam-7001 12 14 1 1 NUM ejpam-7001 12 15 copyright copyright NOUN ejpam-7001 12 16 : : PUNCT ejpam-7001 13 1 © © PROPN ejpam-7001 13 2 2025 2025 NUM ejpam-7001 13 3 the the DET ejpam-7001 13 4 author(s author(s NOUN ejpam-7001 13 5 ) ) PUNCT ejpam-7001 13 6 . . PUNCT ejpam-7001 14 1 ( ( PUNCT ejpam-7001 14 2 cc cc NOUN ejpam-7001 14 3 by by ADP ejpam-7001 14 4 - - PUNCT ejpam-7001 14 5 nc nc PROPN ejpam-7001 14 6 4.0 4.0 NUM ejpam-7001 14 7 ) ) PUNCT ejpam-7001 14 8 imliyangba imliyangba PROPN ejpam-7001 14 9 et et PROPN ejpam-7001 14 10 al al PROPN ejpam-7001 14 11 . . PUNCT ejpam-7001 14 12 / / SYM ejpam-7001 14 13 eur eur PROPN ejpam-7001 14 14 . . PUNCT ejpam-7001 15 1 j. j. PROPN ejpam-7001 15 2 pure pure PROPN ejpam-7001 15 3 appl appl PROPN ejpam-7001 15 4 . . PROPN ejpam-7001 15 5 math math PROPN ejpam-7001 15 6 , , PUNCT ejpam-7001 15 7 18 18 NUM ejpam-7001 15 8 ( ( PUNCT ejpam-7001 15 9 4 4 NUM ejpam-7001 15 10 ) ) PUNCT ejpam-7001 15 11 ( ( PUNCT ejpam-7001 15 12 2025 2025 NUM ejpam-7001 15 13 ) ) PUNCT ejpam-7001 15 14 , , PUNCT ejpam-7001 15 15 7001 7001 NUM ejpam-7001 15 16 2 2 NUM ejpam-7001 15 17 of of ADP ejpam-7001 15 18 27 27 NUM ejpam-7001 15 19 key key ADJ ejpam-7001 15 20 words word NOUN ejpam-7001 15 21 and and CCONJ ejpam-7001 15 22 phrases phrase NOUN ejpam-7001 15 23 : : PUNCT ejpam-7001 15 24 g g NOUN ejpam-7001 15 25 - - PUNCT ejpam-7001 15 26 rank rank NOUN ejpam-7001 15 27 - - PUNCT ejpam-7001 15 28 mapped map VERB ejpam-7001 15 29 transmuted transmuted ADJ ejpam-7001 15 30 class class NOUN ejpam-7001 15 31 , , PUNCT ejpam-7001 15 32 symmetric symmetric ADJ ejpam-7001 15 33 and and CCONJ ejpam-7001 15 34 asymmetric asymmetric ADJ ejpam-7001 15 35 models model NOUN ejpam-7001 15 36 , , PUNCT ejpam-7001 15 37 failure failure NOUN ejpam-7001 15 38 analysis analysis NOUN ejpam-7001 15 39 , , PUNCT ejpam-7001 15 40 maximum maximum ADJ ejpam-7001 15 41 likelihood likelihood NOUN ejpam-7001 15 42 estimation estimation NOUN ejpam-7001 15 43 , , PUNCT ejpam-7001 15 44 computer computer NOUN ejpam-7001 15 45 simulation simulation NOUN ejpam-7001 15 46 , , PUNCT ejpam-7001 15 47 statistics statistic NOUN ejpam-7001 15 48 and and CCONJ ejpam-7001 15 49 numerical numerical ADJ ejpam-7001 15 50 data datum NOUN ejpam-7001 15 51 1 1 NUM ejpam-7001 15 52 . . PUNCT ejpam-7001 16 1 introduction introduction NOUN ejpam-7001 16 2 recent recent ADJ ejpam-7001 16 3 years year NOUN ejpam-7001 16 4 have have AUX ejpam-7001 16 5 seen see VERB ejpam-7001 16 6 a a DET ejpam-7001 16 7 rise rise NOUN ejpam-7001 16 8 in in ADP ejpam-7001 16 9 interest interest NOUN ejpam-7001 16 10 in in ADP ejpam-7001 16 11 studies study NOUN ejpam-7001 16 12 that that PRON ejpam-7001 16 13 aim aim VERB ejpam-7001 16 14 to to PART ejpam-7001 16 15 either either CCONJ ejpam-7001 16 16 introduce introduce VERB ejpam-7001 16 17 a a DET ejpam-7001 16 18 new new ADJ ejpam-7001 16 19 distribution distribution NOUN ejpam-7001 16 20 or or CCONJ ejpam-7001 16 21 alter alter VERB ejpam-7001 16 22 the the DET ejpam-7001 16 23 baseline baseline ADJ ejpam-7001 16 24 distribution distribution NOUN ejpam-7001 16 25 . . PUNCT ejpam-7001 17 1 because because SCONJ ejpam-7001 17 2 they they PRON ejpam-7001 17 3 can can AUX ejpam-7001 17 4 be be AUX ejpam-7001 17 5 used use VERB ejpam-7001 17 6 to to PART ejpam-7001 17 7 add add VERB ejpam-7001 17 8 parameters parameter NOUN ejpam-7001 17 9 to to ADP ejpam-7001 17 10 any any DET ejpam-7001 17 11 distribution distribution NOUN ejpam-7001 17 12 , , PUNCT ejpam-7001 17 13 making make VERB ejpam-7001 17 14 the the DET ejpam-7001 17 15 final final ADJ ejpam-7001 17 16 distribution distribution NOUN ejpam-7001 17 17 more more ADV ejpam-7001 17 18 flexible flexible ADJ ejpam-7001 17 19 and and CCONJ ejpam-7001 17 20 able able ADJ ejpam-7001 17 21 to to PART ejpam-7001 17 22 represent represent VERB ejpam-7001 17 23 the the DET ejpam-7001 17 24 complexity complexity NOUN ejpam-7001 17 25 of of ADP ejpam-7001 17 26 highly highly ADV ejpam-7001 17 27 skewed skewed ADJ ejpam-7001 17 28 real real ADJ ejpam-7001 17 29 - - PUNCT ejpam-7001 17 30 life life NOUN ejpam-7001 17 31 data data NOUN ejpam-7001 17 32 sets set NOUN ejpam-7001 17 33 , , PUNCT ejpam-7001 17 34 these these DET ejpam-7001 17 35 novel novel ADJ ejpam-7001 17 36 distributions distribution NOUN ejpam-7001 17 37 are be AUX ejpam-7001 17 38 finding find VERB ejpam-7001 17 39 widespread widespread ADJ ejpam-7001 17 40 usage usage NOUN ejpam-7001 17 41 in in ADP ejpam-7001 17 42 many many ADJ ejpam-7001 17 43 real real ADJ ejpam-7001 17 44 - - PUNCT ejpam-7001 17 45 life life NOUN ejpam-7001 17 46 domains domain NOUN ejpam-7001 17 47 [ [ X ejpam-7001 17 48 1 1 NUM ejpam-7001 17 49 ] ] PUNCT ejpam-7001 17 50 . . PUNCT ejpam-7001 18 1 in in ADP ejpam-7001 18 2 the the DET ejpam-7001 18 3 field field NOUN ejpam-7001 18 4 of of ADP ejpam-7001 18 5 statistics statistic NOUN ejpam-7001 18 6 , , PUNCT ejpam-7001 18 7 it it PRON ejpam-7001 18 8 is be AUX ejpam-7001 18 9 common common ADJ ejpam-7001 18 10 practice practice NOUN ejpam-7001 18 11 to to PART ejpam-7001 18 12 generalise generalise VERB ejpam-7001 18 13 probability probability NOUN ejpam-7001 18 14 distributions distribution NOUN ejpam-7001 18 15 . . PUNCT ejpam-7001 19 1 numerous numerous ADJ ejpam-7001 19 2 generalised generalised ADJ ejpam-7001 19 3 distributions distribution NOUN ejpam-7001 19 4 , , PUNCT ejpam-7001 19 5 together together ADV ejpam-7001 19 6 with with ADP ejpam-7001 19 7 their their PRON ejpam-7001 19 8 statistical statistical ADJ ejpam-7001 19 9 features feature NOUN ejpam-7001 19 10 , , PUNCT ejpam-7001 19 11 inferential inferential ADJ ejpam-7001 19 12 problems problem NOUN ejpam-7001 19 13 , , PUNCT ejpam-7001 19 14 and and CCONJ ejpam-7001 19 15 potential potential ADJ ejpam-7001 19 16 applications application NOUN ejpam-7001 19 17 , , PUNCT ejpam-7001 19 18 have have AUX ejpam-7001 19 19 been be AUX ejpam-7001 19 20 introduced introduce VERB ejpam-7001 19 21 in in ADP ejpam-7001 19 22 the the DET ejpam-7001 19 23 literature literature NOUN ejpam-7001 19 24 as as ADP ejpam-7001 19 25 of of ADP ejpam-7001 19 26 late late ADV ejpam-7001 19 27 through through ADP ejpam-7001 19 28 the the DET ejpam-7001 19 29 use use NOUN ejpam-7001 19 30 of of ADP ejpam-7001 19 31 transmutation transmutation NOUN ejpam-7001 19 32 methods method NOUN ejpam-7001 19 33 . . PUNCT ejpam-7001 20 1 a a DET ejpam-7001 20 2 functional functional ADJ ejpam-7001 20 3 composition composition NOUN ejpam-7001 20 4 of of ADP ejpam-7001 20 5 the the DET ejpam-7001 20 6 cumulative cumulative ADJ ejpam-7001 20 7 distribution distribution NOUN ejpam-7001 20 8 functions function NOUN ejpam-7001 20 9 of of ADP ejpam-7001 20 10 two two NUM ejpam-7001 20 11 probability probability NOUN ejpam-7001 20 12 distributions distribution NOUN ejpam-7001 20 13 with with ADP ejpam-7001 20 14 the the DET ejpam-7001 20 15 inverse inverse ADJ ejpam-7001 20 16 cumulative cumulative ADJ ejpam-7001 20 17 distribution distribution NOUN ejpam-7001 20 18 functions function NOUN ejpam-7001 20 19 of of ADP ejpam-7001 20 20 one one NUM ejpam-7001 20 21 and and CCONJ ejpam-7001 20 22 the the DET ejpam-7001 20 23 other other ADJ ejpam-7001 20 24 was be AUX ejpam-7001 20 25 initially initially ADV ejpam-7001 20 26 defined define VERB ejpam-7001 20 27 by by ADP ejpam-7001 20 28 [ [ X ejpam-7001 20 29 2 2 NUM ejpam-7001 20 30 ] ] PUNCT ejpam-7001 20 31 as as ADP ejpam-7001 20 32 the the DET ejpam-7001 20 33 quadratic quadratic ADJ ejpam-7001 20 34 rank rank NOUN ejpam-7001 20 35 transmutation transmutation NOUN ejpam-7001 20 36 map map NOUN ejpam-7001 20 37 ( ( PUNCT ejpam-7001 20 38 qrtmp qrtmp NOUN ejpam-7001 20 39 ) ) PUNCT ejpam-7001 20 40 . . PUNCT ejpam-7001 21 1 in in ADP ejpam-7001 21 2 order order NOUN ejpam-7001 21 3 to to PART ejpam-7001 21 4 study study VERB ejpam-7001 21 5 the the DET ejpam-7001 21 6 mathematical mathematical ADJ ejpam-7001 21 7 features feature NOUN ejpam-7001 21 8 of of ADP ejpam-7001 21 9 the the DET ejpam-7001 21 10 transmuted transmuted ADJ ejpam-7001 21 11 weibull weibull NOUN ejpam-7001 21 12 ( ( PUNCT ejpam-7001 21 13 tw tw NOUN ejpam-7001 21 14 ) ) PUNCT ejpam-7001 21 15 distribution distribution NOUN ejpam-7001 21 16 and and CCONJ ejpam-7001 21 17 the the DET ejpam-7001 21 18 estimates estimate NOUN ejpam-7001 21 19 of of ADP ejpam-7001 21 20 the the DET ejpam-7001 21 21 model model NOUN ejpam-7001 21 22 parameters parameter NOUN ejpam-7001 21 23 , , PUNCT ejpam-7001 21 24 [ [ X ejpam-7001 21 25 3 3 NUM ejpam-7001 21 26 ] ] X ejpam-7001 21 27 utilised utilise VERB ejpam-7001 21 28 the the DET ejpam-7001 21 29 qrtmp qrtmp NOUN ejpam-7001 21 30 to to PART ejpam-7001 21 31 create create VERB ejpam-7001 21 32 a a DET ejpam-7001 21 33 new new ADJ ejpam-7001 21 34 version version NOUN ejpam-7001 21 35 of of ADP ejpam-7001 21 36 the the DET ejpam-7001 21 37 weibull weibull NOUN ejpam-7001 21 38 distribution distribution NOUN ejpam-7001 21 39 , , PUNCT ejpam-7001 21 40 which which PRON ejpam-7001 21 41 they they PRON ejpam-7001 21 42 dubbed dub VERB ejpam-7001 21 43 the the DET ejpam-7001 21 44 transmuted transmuted ADJ ejpam-7001 21 45 weibull weibull NOUN ejpam-7001 21 46 ( ( PUNCT ejpam-7001 21 47 tw tw NOUN ejpam-7001 21 48 ) ) PUNCT ejpam-7001 21 49 distribution distribution NOUN ejpam-7001 21 50 . . PUNCT ejpam-7001 22 1 the the DET ejpam-7001 22 2 characteristics characteristic NOUN ejpam-7001 22 3 and and CCONJ ejpam-7001 22 4 longevity longevity NOUN ejpam-7001 22 5 of of ADP ejpam-7001 22 6 tw tw NOUN ejpam-7001 22 7 dispersion dispersion NOUN ejpam-7001 22 8 , , PUNCT ejpam-7001 22 9 as as ADV ejpam-7001 22 10 well well ADV ejpam-7001 22 11 as as ADP ejpam-7001 22 12 its its PRON ejpam-7001 22 13 uses use NOUN ejpam-7001 22 14 in in ADP ejpam-7001 22 15 industry industry NOUN ejpam-7001 22 16 and and CCONJ ejpam-7001 22 17 healthcare healthcare PROPN ejpam-7001 22 18 , , PUNCT ejpam-7001 22 19 were be AUX ejpam-7001 22 20 investigated investigate VERB ejpam-7001 22 21 by by ADP ejpam-7001 22 22 [ [ X ejpam-7001 22 23 4 4 NUM ejpam-7001 22 24 ] ] PUNCT ejpam-7001 22 25 . . PUNCT ejpam-7001 23 1 the the DET ejpam-7001 23 2 cubic cubic ADJ ejpam-7001 23 3 rank rank NOUN ejpam-7001 23 4 transmutation transmutation NOUN ejpam-7001 23 5 ( ( PUNCT ejpam-7001 23 6 crt crt ADJ ejpam-7001 23 7 ) ) PUNCT ejpam-7001 23 8 map map NOUN ejpam-7001 23 9 is be AUX ejpam-7001 23 10 an an DET ejpam-7001 23 11 updated update VERB ejpam-7001 23 12 member member NOUN ejpam-7001 23 13 of of ADP ejpam-7001 23 14 the the DET ejpam-7001 23 15 transmutation transmutation NOUN ejpam-7001 23 16 map map NOUN ejpam-7001 23 17 family family NOUN ejpam-7001 23 18 that that PRON ejpam-7001 23 19 was be AUX ejpam-7001 23 20 introduced introduce VERB ejpam-7001 23 21 by by ADP ejpam-7001 23 22 [ [ X ejpam-7001 23 23 5 5 NUM ejpam-7001 23 24 ] ] PUNCT ejpam-7001 23 25 . . PUNCT ejpam-7001 24 1 they they PRON ejpam-7001 24 2 built build VERB ejpam-7001 24 3 the the DET ejpam-7001 24 4 cubic cubic ADJ ejpam-7001 24 5 transmuted transmute VERB ejpam-7001 24 6 log log NOUN ejpam-7001 24 7 - - PUNCT ejpam-7001 24 8 logistic logistic NOUN ejpam-7001 24 9 ( ( PUNCT ejpam-7001 24 10 ctll ctll NOUN ejpam-7001 24 11 ) ) PUNCT ejpam-7001 24 12 and and CCONJ ejpam-7001 24 13 cubic cubic ADJ ejpam-7001 24 14 transmuted transmuted ADJ ejpam-7001 24 15 weibull weibull NOUN ejpam-7001 24 16 ( ( PUNCT ejpam-7001 24 17 ctw ctw NOUN ejpam-7001 24 18 ) ) PUNCT ejpam-7001 24 19 distributions distribution NOUN ejpam-7001 24 20 on on ADP ejpam-7001 24 21 top top NOUN ejpam-7001 24 22 of of ADP ejpam-7001 24 23 this this DET ejpam-7001 24 24 idea idea NOUN ejpam-7001 24 25 . . PUNCT ejpam-7001 25 1 the the DET ejpam-7001 25 2 cubic cubic ADJ ejpam-7001 25 3 transmuted transmute VERB ejpam-7001 25 4 exponential exponential ADJ ejpam-7001 25 5 distribution distribution NOUN ejpam-7001 25 6 was be AUX ejpam-7001 25 7 presented present VERB ejpam-7001 25 8 by by ADP ejpam-7001 25 9 [ [ X ejpam-7001 25 10 6 6 NUM ejpam-7001 25 11 ] ] PUNCT ejpam-7001 25 12 , , PUNCT ejpam-7001 25 13 and and CCONJ ejpam-7001 25 14 its its PRON ejpam-7001 25 15 statistical statistical ADJ ejpam-7001 25 16 features feature NOUN ejpam-7001 25 17 were be AUX ejpam-7001 25 18 investigated investigate VERB ejpam-7001 25 19 through through ADP ejpam-7001 25 20 practical practical ADJ ejpam-7001 25 21 applications application NOUN ejpam-7001 25 22 . . PUNCT ejpam-7001 26 1 the the DET ejpam-7001 26 2 new new ADJ ejpam-7001 26 3 distribution distribution NOUN ejpam-7001 26 4 offers offer VERB ejpam-7001 26 5 a a DET ejpam-7001 26 6 superior superior ADJ ejpam-7001 26 7 fit fit NOUN ejpam-7001 26 8 , , PUNCT ejpam-7001 26 9 according accord VERB ejpam-7001 26 10 to to ADP ejpam-7001 26 11 research research NOUN ejpam-7001 26 12 on on ADP ejpam-7001 26 13 its its PRON ejpam-7001 26 14 statistical statistical ADJ ejpam-7001 26 15 features feature NOUN ejpam-7001 26 16 , , PUNCT ejpam-7001 26 17 which which PRON ejpam-7001 26 18 was be AUX ejpam-7001 26 19 conducted conduct VERB ejpam-7001 26 20 in in ADP ejpam-7001 26 21 relation relation NOUN ejpam-7001 26 22 to to ADP ejpam-7001 26 23 a a DET ejpam-7001 26 24 cubic cubic ADJ ejpam-7001 26 25 transmuted transmute VERB ejpam-7001 26 26 fréchet fréchet NOUN ejpam-7001 26 27 distribution distribution NOUN ejpam-7001 26 28 suggested suggest VERB ejpam-7001 26 29 by by ADP ejpam-7001 26 30 [ [ X ejpam-7001 26 31 7 7 NUM ejpam-7001 26 32 ] ] PUNCT ejpam-7001 26 33 . . PUNCT ejpam-7001 27 1 [ [ X ejpam-7001 27 2 8 8 NUM ejpam-7001 27 3 ] ] PUNCT ejpam-7001 27 4 created create VERB ejpam-7001 27 5 the the DET ejpam-7001 27 6 ctw ctw ADJ ejpam-7001 27 7 distribution distribution NOUN ejpam-7001 27 8 , , PUNCT ejpam-7001 27 9 described describe VERB ejpam-7001 27 10 its its PRON ejpam-7001 27 11 statistical statistical ADJ ejpam-7001 27 12 features feature NOUN ejpam-7001 27 13 in in ADP ejpam-7001 27 14 detail detail NOUN ejpam-7001 27 15 , , PUNCT ejpam-7001 27 16 and and CCONJ ejpam-7001 27 17 offered offer VERB ejpam-7001 27 18 practical practical ADJ ejpam-7001 27 19 examples example NOUN ejpam-7001 27 20 of of ADP ejpam-7001 27 21 its its PRON ejpam-7001 27 22 use use NOUN ejpam-7001 27 23 in in ADP ejpam-7001 27 24 estimation estimation NOUN ejpam-7001 27 25 and and CCONJ ejpam-7001 27 26 real real ADJ ejpam-7001 27 27 - - PUNCT ejpam-7001 27 28 world world NOUN ejpam-7001 27 29 scenarios scenario NOUN ejpam-7001 27 30 . . PUNCT ejpam-7001 28 1 with with ADP ejpam-7001 28 2 the the DET ejpam-7001 28 3 aim aim NOUN ejpam-7001 28 4 of of ADP ejpam-7001 28 5 expanding expand VERB ejpam-7001 28 6 the the DET ejpam-7001 28 7 burr burr NOUN ejpam-7001 28 8 - - PUNCT ejpam-7001 28 9 xii xii NOUN ejpam-7001 28 10 distribution distribution NOUN ejpam-7001 28 11 ’s ’s PART ejpam-7001 28 12 practical practical ADJ ejpam-7001 28 13 utility utility NOUN ejpam-7001 28 14 , , PUNCT ejpam-7001 28 15 particularly particularly ADV ejpam-7001 28 16 in in ADP ejpam-7001 28 17 the the DET ejpam-7001 28 18 fields field NOUN ejpam-7001 28 19 of of ADP ejpam-7001 28 20 household household NOUN ejpam-7001 28 21 income income NOUN ejpam-7001 28 22 , , PUNCT ejpam-7001 28 23 environmental environmental ADJ ejpam-7001 28 24 sciences science NOUN ejpam-7001 28 25 , , PUNCT ejpam-7001 28 26 biology biology NOUN ejpam-7001 28 27 , , PUNCT ejpam-7001 28 28 engineering engineering NOUN ejpam-7001 28 29 , , PUNCT ejpam-7001 28 30 and and CCONJ ejpam-7001 28 31 others other NOUN ejpam-7001 28 32 , , PUNCT ejpam-7001 28 33 [ [ X ejpam-7001 28 34 9 9 NUM ejpam-7001 28 35 ] ] PUNCT ejpam-7001 28 36 presented present VERB ejpam-7001 28 37 the the DET ejpam-7001 28 38 cubic cubic ADJ ejpam-7001 28 39 transmuted transmute VERB ejpam-7001 28 40 burr burr NOUN ejpam-7001 28 41 - - PUNCT ejpam-7001 28 42 xii xii NOUN ejpam-7001 28 43 distribution distribution NOUN ejpam-7001 28 44 . . PUNCT ejpam-7001 29 1 in in ADP ejpam-7001 29 2 their their PRON ejpam-7001 29 3 publication publication NOUN ejpam-7001 29 4 , , PUNCT ejpam-7001 29 5 [ [ X ejpam-7001 29 6 10 10 NUM ejpam-7001 29 7 ] ] PUNCT ejpam-7001 29 8 detailed detail VERB ejpam-7001 29 9 the the DET ejpam-7001 29 10 g g NOUN ejpam-7001 29 11 - - PUNCT ejpam-7001 29 12 transmuted transmute VERB ejpam-7001 29 13 distribution distribution NOUN ejpam-7001 29 14 family family NOUN ejpam-7001 29 15 and and CCONJ ejpam-7001 29 16 delved delve VERB ejpam-7001 29 17 into into ADP ejpam-7001 29 18 the the DET ejpam-7001 29 19 unique unique ADJ ejpam-7001 29 20 instances instance NOUN ejpam-7001 29 21 of of ADP ejpam-7001 29 22 this this DET ejpam-7001 29 23 distribution distribution NOUN ejpam-7001 29 24 . . PUNCT ejpam-7001 30 1 they they PRON ejpam-7001 30 2 continued continue VERB ejpam-7001 30 3 by by ADP ejpam-7001 30 4 applying apply VERB ejpam-7001 30 5 the the DET ejpam-7001 30 6 g g NOUN ejpam-7001 30 7 - - PUNCT ejpam-7001 30 8 transmuted transmute VERB ejpam-7001 30 9 distribution distribution NOUN ejpam-7001 30 10 to to ADP ejpam-7001 30 11 the the DET ejpam-7001 30 12 weibull weibull NOUN ejpam-7001 30 13 distribution distribution NOUN ejpam-7001 30 14 and and CCONJ ejpam-7001 30 15 then then ADV ejpam-7001 30 16 watched watch VERB ejpam-7001 30 17 how how SCONJ ejpam-7001 30 18 the the DET ejpam-7001 30 19 new new ADJ ejpam-7001 30 20 generalised generalise VERB ejpam-7001 30 21 transmuted transmute VERB ejpam-7001 30 22 distribution distribution NOUN ejpam-7001 30 23 behaved behave VERB ejpam-7001 30 24 and and CCONJ ejpam-7001 30 25 how how SCONJ ejpam-7001 30 26 flexible flexible ADJ ejpam-7001 30 27 it it PRON ejpam-7001 30 28 was be AUX ejpam-7001 30 29 . . PUNCT ejpam-7001 31 1 moreover moreover ADV ejpam-7001 31 2 , , PUNCT ejpam-7001 31 3 [ [ X ejpam-7001 31 4 11 11 NUM ejpam-7001 31 5 ] ] PUNCT ejpam-7001 31 6 have have AUX ejpam-7001 31 7 discussed discuss VERB ejpam-7001 31 8 the the DET ejpam-7001 31 9 methodology methodology NOUN ejpam-7001 31 10 of of ADP ejpam-7001 31 11 qrtmp qrtmp NOUN ejpam-7001 31 12 and and CCONJ ejpam-7001 31 13 crt crt ADJ ejpam-7001 31 14 map map NOUN ejpam-7001 31 15 with with ADP ejpam-7001 31 16 some some DET ejpam-7001 31 17 detailed detailed ADJ ejpam-7001 31 18 informations information NOUN ejpam-7001 31 19 on on ADP ejpam-7001 31 20 the the DET ejpam-7001 31 21 developments development NOUN ejpam-7001 31 22 of of ADP ejpam-7001 31 23 both both CCONJ ejpam-7001 31 24 the the DET ejpam-7001 31 25 methods method NOUN ejpam-7001 31 26 that that PRON ejpam-7001 31 27 exists exist VERB ejpam-7001 31 28 in in ADP ejpam-7001 31 29 the the DET ejpam-7001 31 30 literature literature NOUN ejpam-7001 31 31 . . PUNCT ejpam-7001 32 1 the the DET ejpam-7001 32 2 weibull weibull PROPN ejpam-7001 32 3 distribution distribution NOUN ejpam-7001 32 4 [ [ X ejpam-7001 32 5 12 12 NUM ejpam-7001 32 6 ] ] PUNCT ejpam-7001 32 7 is be AUX ejpam-7001 32 8 a a DET ejpam-7001 32 9 prominent prominent ADJ ejpam-7001 32 10 statistical statistical ADJ ejpam-7001 32 11 distribution distribution NOUN ejpam-7001 32 12 extensively extensively ADV ejpam-7001 32 13 utilised utilise VERB ejpam-7001 32 14 for for ADP ejpam-7001 32 15 its its PRON ejpam-7001 32 16 efficacy efficacy NOUN ejpam-7001 32 17 in in ADP ejpam-7001 32 18 modelling model VERB ejpam-7001 32 19 dependable dependable ADJ ejpam-7001 32 20 data datum NOUN ejpam-7001 32 21 . . PUNCT ejpam-7001 33 1 researchers researcher NOUN ejpam-7001 33 2 have have AUX ejpam-7001 33 3 documented document VERB ejpam-7001 33 4 numerous numerous ADJ ejpam-7001 33 5 extensions extension NOUN ejpam-7001 33 6 and and CCONJ ejpam-7001 33 7 altered alter VERB ejpam-7001 33 8 versions version NOUN ejpam-7001 33 9 of of ADP ejpam-7001 33 10 the the DET ejpam-7001 33 11 weibull weibull NOUN ejpam-7001 33 12 distribution distribution NOUN ejpam-7001 33 13 to to PART ejpam-7001 33 14 achieve achieve VERB ejpam-7001 33 15 more more ADV ejpam-7001 33 16 adaptable adaptable ADJ ejpam-7001 33 17 distributions distribution NOUN ejpam-7001 33 18 for for ADP ejpam-7001 33 19 modelling model VERB ejpam-7001 33 20 experimental experimental ADJ ejpam-7001 33 21 data datum NOUN ejpam-7001 33 22 [ [ X ejpam-7001 33 23 13–17 13–17 NUM ejpam-7001 33 24 ] ] PUNCT ejpam-7001 33 25 . . PUNCT ejpam-7001 34 1 they they PRON ejpam-7001 34 2 have have AUX ejpam-7001 34 3 introduced introduce VERB ejpam-7001 34 4 alternative alternative ADJ ejpam-7001 34 5 imliyangba imliyangba PROPN ejpam-7001 34 6 et et PROPN ejpam-7001 34 7 al al PROPN ejpam-7001 34 8 . . PUNCT ejpam-7001 34 9 / / SYM ejpam-7001 34 10 eur eur PROPN ejpam-7001 34 11 . . PUNCT ejpam-7001 35 1 j. j. PROPN ejpam-7001 35 2 pure pure PROPN ejpam-7001 35 3 appl appl PROPN ejpam-7001 35 4 . . PROPN ejpam-7001 35 5 math math PROPN ejpam-7001 35 6 , , PUNCT ejpam-7001 35 7 18 18 NUM ejpam-7001 35 8 ( ( PUNCT ejpam-7001 35 9 4 4 NUM ejpam-7001 35 10 ) ) PUNCT ejpam-7001 35 11 ( ( PUNCT ejpam-7001 35 12 2025 2025 NUM ejpam-7001 35 13 ) ) PUNCT ejpam-7001 35 14 , , PUNCT ejpam-7001 35 15 7001 7001 NUM ejpam-7001 35 16 3 3 NUM ejpam-7001 35 17 of of ADP ejpam-7001 35 18 27 27 NUM ejpam-7001 35 19 forms form NOUN ejpam-7001 35 20 for for ADP ejpam-7001 35 21 generalising generalise VERB ejpam-7001 35 22 the the DET ejpam-7001 35 23 weibull weibull NOUN ejpam-7001 35 24 distribution distribution NOUN ejpam-7001 35 25 , , PUNCT ejpam-7001 35 26 including include VERB ejpam-7001 35 27 the the DET ejpam-7001 35 28 lindley lindley ADJ ejpam-7001 35 29 weibull weibull NOUN ejpam-7001 35 30 distribution distribution NOUN ejpam-7001 35 31 , , PUNCT ejpam-7001 35 32 transmuted transmute VERB ejpam-7001 35 33 g g NOUN ejpam-7001 35 34 - - PUNCT ejpam-7001 35 35 modified modify VERB ejpam-7001 35 36 weibull weibull NOUN ejpam-7001 35 37 distribution distribution NOUN ejpam-7001 35 38 , , PUNCT ejpam-7001 35 39 and and CCONJ ejpam-7001 35 40 gumbel gumbel PROPN ejpam-7001 35 41 weibull weibull NOUN ejpam-7001 35 42 distribution distribution NOUN ejpam-7001 35 43 . . PUNCT ejpam-7001 36 1 additionally additionally ADV ejpam-7001 36 2 , , PUNCT ejpam-7001 36 3 [ [ X ejpam-7001 36 4 18–23 18–23 NUM ejpam-7001 36 5 ] ] PUNCT ejpam-7001 36 6 have have AUX ejpam-7001 36 7 contributed contribute VERB ejpam-7001 36 8 towards towards ADP ejpam-7001 36 9 the the DET ejpam-7001 36 10 extensions extension NOUN ejpam-7001 36 11 of of ADP ejpam-7001 36 12 weibull weibull NOUN ejpam-7001 36 13 distribution distribution NOUN ejpam-7001 36 14 . . PUNCT ejpam-7001 37 1 the the DET ejpam-7001 37 2 fréchet fréchet NOUN ejpam-7001 37 3 distribution distribution NOUN ejpam-7001 37 4 [ [ X ejpam-7001 37 5 24 24 NUM ejpam-7001 37 6 ] ] PUNCT ejpam-7001 37 7 , , PUNCT ejpam-7001 37 8 recognised recognise VERB ejpam-7001 37 9 as as ADP ejpam-7001 37 10 the the DET ejpam-7001 37 11 inverse inverse ADJ ejpam-7001 37 12 weibull weibull NOUN ejpam-7001 37 13 distribution distribution NOUN ejpam-7001 37 14 , , PUNCT ejpam-7001 37 15 is be AUX ejpam-7001 37 16 employed employ VERB ejpam-7001 37 17 to to PART ejpam-7001 37 18 model model VERB ejpam-7001 37 19 extreme extreme ADJ ejpam-7001 37 20 value value NOUN ejpam-7001 37 21 datasets dataset NOUN ejpam-7001 37 22 . . PUNCT ejpam-7001 38 1 [ [ X ejpam-7001 38 2 25 25 NUM ejpam-7001 38 3 ] ] PUNCT ejpam-7001 38 4 presented present VERB ejpam-7001 38 5 a a DET ejpam-7001 38 6 novel novel ADJ ejpam-7001 38 7 lifetime lifetime NOUN ejpam-7001 38 8 model model NOUN ejpam-7001 38 9 known know VERB ejpam-7001 38 10 as as ADP ejpam-7001 38 11 the the DET ejpam-7001 38 12 gamma gamma NOUN ejpam-7001 39 1 extended extend VERB ejpam-7001 39 2 fréchet fréchet NOUN ejpam-7001 39 3 distribution distribution NOUN ejpam-7001 39 4 . . PUNCT ejpam-7001 40 1 [ [ X ejpam-7001 40 2 26 26 NUM ejpam-7001 40 3 ] ] PUNCT ejpam-7001 40 4 presented present VERB ejpam-7001 40 5 the the DET ejpam-7001 40 6 beta beta ADJ ejpam-7001 40 7 fréchet fréchet NOUN ejpam-7001 40 8 ( ( PUNCT ejpam-7001 40 9 bf bf NOUN ejpam-7001 40 10 ) ) PUNCT ejpam-7001 40 11 distribution distribution NOUN ejpam-7001 40 12 , , PUNCT ejpam-7001 40 13 a a DET ejpam-7001 40 14 generalisation generalisation NOUN ejpam-7001 40 15 of of ADP ejpam-7001 40 16 the the DET ejpam-7001 40 17 exponentiated exponentiated ADJ ejpam-7001 40 18 fréchet fréchet NOUN ejpam-7001 40 19 ( ( PUNCT ejpam-7001 40 20 ef ef PROPN ejpam-7001 40 21 ) ) PUNCT ejpam-7001 40 22 and and CCONJ ejpam-7001 40 23 fréchet fréchet NOUN ejpam-7001 40 24 distributions distribution NOUN ejpam-7001 40 25 , , PUNCT ejpam-7001 40 26 whereas whereas SCONJ ejpam-7001 40 27 [ [ X ejpam-7001 40 28 27 27 NUM ejpam-7001 40 29 ] ] PUNCT ejpam-7001 40 30 introduced introduce VERB ejpam-7001 40 31 the the DET ejpam-7001 40 32 transmuted transmuted ADJ ejpam-7001 40 33 fréchet fréchet NOUN ejpam-7001 40 34 distribution distribution NOUN ejpam-7001 40 35 . . PUNCT ejpam-7001 41 1 the the DET ejpam-7001 41 2 exponentiated exponentiated ADJ ejpam-7001 41 3 generalised generalise VERB ejpam-7001 41 4 fréchet fréchet NOUN ejpam-7001 41 5 distribution distribution NOUN ejpam-7001 41 6 was be AUX ejpam-7001 41 7 developed develop VERB ejpam-7001 41 8 by by ADP ejpam-7001 41 9 [ [ X ejpam-7001 41 10 28 28 NUM ejpam-7001 41 11 ] ] PUNCT ejpam-7001 41 12 . . PUNCT ejpam-7001 42 1 additionally additionally ADV ejpam-7001 42 2 , , PUNCT ejpam-7001 42 3 [ [ X ejpam-7001 42 4 29 29 NUM ejpam-7001 42 5 ] ] PUNCT ejpam-7001 42 6 introduced introduce VERB ejpam-7001 42 7 the the DET ejpam-7001 42 8 beta beta NOUN ejpam-7001 42 9 generalised generalise VERB ejpam-7001 42 10 exponentiated exponentiate VERB ejpam-7001 42 11 fréchet fréchet NOUN ejpam-7001 42 12 distribution distribution NOUN ejpam-7001 42 13 along along ADP ejpam-7001 42 14 with with ADP ejpam-7001 42 15 its its PRON ejpam-7001 42 16 applications application NOUN ejpam-7001 42 17 . . PUNCT ejpam-7001 43 1 further far ADV ejpam-7001 44 1 [ [ X ejpam-7001 44 2 30 30 NUM ejpam-7001 44 3 ] ] PUNCT ejpam-7001 44 4 proposed propose VERB ejpam-7001 44 5 a a DET ejpam-7001 44 6 novel novel ADJ ejpam-7001 44 7 extension extension NOUN ejpam-7001 44 8 of of ADP ejpam-7001 44 9 fréchet fréchet NOUN ejpam-7001 44 10 distribution distribution NOUN ejpam-7001 44 11 , , PUNCT ejpam-7001 44 12 called call VERB ejpam-7001 44 13 the the DET ejpam-7001 44 14 novel novel ADJ ejpam-7001 44 15 alpha alpha NOUN ejpam-7001 44 16 power power NOUN ejpam-7001 44 17 fréchet fréchet NOUN ejpam-7001 44 18 distribution distribution NOUN ejpam-7001 44 19 with with ADP ejpam-7001 44 20 real real ADJ ejpam-7001 44 21 life life NOUN ejpam-7001 44 22 applications application NOUN ejpam-7001 44 23 . . PUNCT ejpam-7001 45 1 consequently consequently ADV ejpam-7001 45 2 , , PUNCT ejpam-7001 45 3 multiple multiple ADJ ejpam-7001 45 4 academics academic NOUN ejpam-7001 45 5 have have AUX ejpam-7001 45 6 advanced advance VERB ejpam-7001 45 7 various various ADJ ejpam-7001 45 8 generalisations generalisation NOUN ejpam-7001 45 9 of of ADP ejpam-7001 45 10 the the DET ejpam-7001 45 11 weibull weibull NOUN ejpam-7001 45 12 and and CCONJ ejpam-7001 45 13 fréchet fréchet NOUN ejpam-7001 45 14 distributions distribution NOUN ejpam-7001 45 15 , , PUNCT ejpam-7001 45 16 which which PRON ejpam-7001 45 17 are be AUX ejpam-7001 45 18 capable capable ADJ ejpam-7001 45 19 of of ADP ejpam-7001 45 20 modelling model VERB ejpam-7001 45 21 data datum NOUN ejpam-7001 45 22 across across ADP ejpam-7001 45 23 diverse diverse ADJ ejpam-7001 45 24 domains domain NOUN ejpam-7001 45 25 , , PUNCT ejpam-7001 45 26 including include VERB ejpam-7001 45 27 engineering engineering NOUN ejpam-7001 45 28 , , PUNCT ejpam-7001 45 29 medicine medicine NOUN ejpam-7001 45 30 , , PUNCT ejpam-7001 45 31 and and CCONJ ejpam-7001 45 32 physics physic NOUN ejpam-7001 45 33 , , PUNCT ejpam-7001 45 34 as as ADV ejpam-7001 45 35 well well ADV ejpam-7001 45 36 as as ADP ejpam-7001 45 37 extreme extreme ADJ ejpam-7001 45 38 value value NOUN ejpam-7001 45 39 phenomena phenomenon NOUN ejpam-7001 45 40 such such ADJ ejpam-7001 45 41 as as ADP ejpam-7001 45 42 earthquakes earthquake NOUN ejpam-7001 45 43 and and CCONJ ejpam-7001 45 44 floods flood NOUN ejpam-7001 45 45 . . PUNCT ejpam-7001 46 1 consequently consequently ADV ejpam-7001 46 2 , , PUNCT ejpam-7001 46 3 the the DET ejpam-7001 46 4 relevance relevance NOUN ejpam-7001 46 5 of of ADP ejpam-7001 46 6 extreme extreme ADJ ejpam-7001 46 7 value value NOUN ejpam-7001 46 8 theory theory NOUN ejpam-7001 46 9 and and CCONJ ejpam-7001 46 10 the the DET ejpam-7001 46 11 capacity capacity NOUN ejpam-7001 46 12 to to PART ejpam-7001 46 13 model model VERB ejpam-7001 46 14 data datum NOUN ejpam-7001 46 15 from from ADP ejpam-7001 46 16 diverse diverse ADJ ejpam-7001 46 17 domains domain NOUN ejpam-7001 46 18 using use VERB ejpam-7001 46 19 weibull weibull NOUN ejpam-7001 46 20 and and CCONJ ejpam-7001 46 21 fréchet fréchet NOUN ejpam-7001 46 22 distributions distribution NOUN ejpam-7001 46 23 resulted result VERB ejpam-7001 46 24 in in ADP ejpam-7001 46 25 the the DET ejpam-7001 46 26 formulation formulation NOUN ejpam-7001 46 27 of of ADP ejpam-7001 46 28 the the DET ejpam-7001 46 29 fréchet fréchet NOUN ejpam-7001 46 30 - - PUNCT ejpam-7001 46 31 weibull weibull PROPN ejpam-7001 46 32 ( ( PUNCT ejpam-7001 46 33 fw fw ADJ ejpam-7001 46 34 ) ) PUNCT ejpam-7001 46 35 distribution distribution NOUN ejpam-7001 46 36 by by ADP ejpam-7001 46 37 [ [ X ejpam-7001 46 38 31 31 NUM ejpam-7001 46 39 ] ] PUNCT ejpam-7001 46 40 , , PUNCT ejpam-7001 46 41 which which PRON ejpam-7001 46 42 offers offer VERB ejpam-7001 46 43 enhanced enhance VERB ejpam-7001 46 44 flexibility flexibility NOUN ejpam-7001 46 45 for for ADP ejpam-7001 46 46 engineering engineering NOUN ejpam-7001 46 47 , , PUNCT ejpam-7001 46 48 physics physics NOUN ejpam-7001 46 49 , , PUNCT ejpam-7001 46 50 medicine medicine NOUN ejpam-7001 46 51 , , PUNCT ejpam-7001 46 52 and and CCONJ ejpam-7001 46 53 environmental environmental ADJ ejpam-7001 46 54 datasets dataset NOUN ejpam-7001 46 55 . . PUNCT ejpam-7001 47 1 furthermore furthermore ADV ejpam-7001 47 2 , , PUNCT ejpam-7001 47 3 [ [ X ejpam-7001 47 4 32 32 NUM ejpam-7001 47 5 ] ] PUNCT ejpam-7001 47 6 presented present VERB ejpam-7001 47 7 the the DET ejpam-7001 47 8 fw fw ADJ ejpam-7001 47 9 distribution distribution NOUN ejpam-7001 47 10 and and CCONJ ejpam-7001 47 11 utilised utilise VERB ejpam-7001 47 12 it it PRON ejpam-7001 47 13 on on ADP ejpam-7001 47 14 two two NUM ejpam-7001 47 15 datasets dataset NOUN ejpam-7001 47 16 from from ADP ejpam-7001 47 17 mechanical mechanical ADJ ejpam-7001 47 18 engineering engineering NOUN ejpam-7001 47 19 , , PUNCT ejpam-7001 47 20 demonstrating demonstrate VERB ejpam-7001 47 21 its its PRON ejpam-7001 47 22 superiority superiority NOUN ejpam-7001 47 23 compared compare VERB ejpam-7001 47 24 to to ADP ejpam-7001 47 25 other other ADJ ejpam-7001 47 26 relevant relevant ADJ ejpam-7001 47 27 distributions distribution NOUN ejpam-7001 47 28 considered consider VERB ejpam-7001 47 29 . . PUNCT ejpam-7001 48 1 recently recently ADV ejpam-7001 48 2 , , PUNCT ejpam-7001 48 3 [ [ X ejpam-7001 48 4 33 33 NUM ejpam-7001 48 5 ] ] PUNCT ejpam-7001 48 6 extended extend VERB ejpam-7001 48 7 the the DET ejpam-7001 48 8 fw fw ADJ ejpam-7001 48 9 distribution distribution NOUN ejpam-7001 48 10 by by ADP ejpam-7001 48 11 combing comb VERB ejpam-7001 48 12 the the DET ejpam-7001 48 13 transformed transform VERB ejpam-7001 48 14 transformer transformer NOUN ejpam-7001 48 15 method method NOUN ejpam-7001 48 16 and and CCONJ ejpam-7001 48 17 the the DET ejpam-7001 48 18 new new ADJ ejpam-7001 48 19 generalized generalized ADJ ejpam-7001 48 20 exponentiated exponentiate VERB ejpam-7001 48 21 method method NOUN ejpam-7001 48 22 , , PUNCT ejpam-7001 48 23 proposing propose VERB ejpam-7001 48 24 a a DET ejpam-7001 48 25 new new ADJ ejpam-7001 48 26 generalized generalize VERB ejpam-7001 48 27 exponentiated exponentiate VERB ejpam-7001 48 28 fréchet fréchet VERB ejpam-7001 48 29 weibull weibull NOUN ejpam-7001 48 30 distribution distribution NOUN ejpam-7001 48 31 . . PUNCT ejpam-7001 49 1 [ [ X ejpam-7001 49 2 34 34 NUM ejpam-7001 49 3 ] ] PUNCT ejpam-7001 49 4 proposed propose VERB ejpam-7001 49 5 a a DET ejpam-7001 49 6 new new ADJ ejpam-7001 49 7 distribution distribution NOUN ejpam-7001 49 8 called call VERB ejpam-7001 49 9 the the DET ejpam-7001 49 10 cubic cubic ADJ ejpam-7001 49 11 ranked rank VERB ejpam-7001 49 12 record record NOUN ejpam-7001 49 13 - - PUNCT ejpam-7001 49 14 based base VERB ejpam-7001 49 15 transmuted transmuted ADJ ejpam-7001 49 16 weibull weibull NOUN ejpam-7001 49 17 as as ADP ejpam-7001 49 18 an an DET ejpam-7001 49 19 alternative alternative NOUN ejpam-7001 49 20 to to ADP ejpam-7001 49 21 the the DET ejpam-7001 49 22 weibull weibull NOUN ejpam-7001 49 23 distribution distribution NOUN ejpam-7001 49 24 and and CCONJ ejpam-7001 49 25 related related ADJ ejpam-7001 49 26 ones one NOUN ejpam-7001 49 27 . . PUNCT ejpam-7001 50 1 this this DET ejpam-7001 50 2 study study NOUN ejpam-7001 50 3 focuses focus VERB ejpam-7001 50 4 on on ADP ejpam-7001 50 5 the the DET ejpam-7001 50 6 fw fw ADJ ejpam-7001 50 7 distribution distribution NOUN ejpam-7001 50 8 and and CCONJ ejpam-7001 50 9 proposes propose VERB ejpam-7001 50 10 an an DET ejpam-7001 50 11 extension extension NOUN ejpam-7001 50 12 using use VERB ejpam-7001 50 13 the the DET ejpam-7001 50 14 transmutation transmutation NOUN ejpam-7001 50 15 technique technique NOUN ejpam-7001 50 16 . . PUNCT ejpam-7001 51 1 the the DET ejpam-7001 51 2 resulting result VERB ejpam-7001 51 3 generalized generalized ADJ ejpam-7001 51 4 version version NOUN ejpam-7001 51 5 is be AUX ejpam-7001 51 6 termed term VERB ejpam-7001 51 7 the the DET ejpam-7001 51 8 cubic cubic ADJ ejpam-7001 51 9 rank rank NOUN ejpam-7001 51 10 transmuted transmute VERB ejpam-7001 51 11 fréchet fréchet NOUN ejpam-7001 51 12 - - PUNCT ejpam-7001 51 13 weibull weibull NOUN ejpam-7001 51 14 ( ( PUNCT ejpam-7001 51 15 crtfw crtfw NOUN ejpam-7001 51 16 ) ) PUNCT ejpam-7001 51 17 distribution distribution NOUN ejpam-7001 51 18 . . PUNCT ejpam-7001 52 1 the the DET ejpam-7001 52 2 motivation motivation NOUN ejpam-7001 52 3 for for ADP ejpam-7001 52 4 investigating investigate VERB ejpam-7001 52 5 the the DET ejpam-7001 52 6 crtfw crtfw NOUN ejpam-7001 52 7 distribution distribution NOUN ejpam-7001 52 8 is be AUX ejpam-7001 52 9 multifaceted multifacete VERB ejpam-7001 52 10 and and CCONJ ejpam-7001 52 11 can can AUX ejpam-7001 52 12 be be AUX ejpam-7001 52 13 summarized summarize VERB ejpam-7001 52 14 as as SCONJ ejpam-7001 52 15 follows follow VERB ejpam-7001 52 16 : : PUNCT ejpam-7001 52 17 • • SCONJ ejpam-7001 52 18 the the DET ejpam-7001 52 19 weibull weibull NOUN ejpam-7001 52 20 distribution distribution NOUN ejpam-7001 52 21 is be AUX ejpam-7001 52 22 predominantly predominantly ADV ejpam-7001 52 23 used use VERB ejpam-7001 52 24 for for ADP ejpam-7001 52 25 modeling modeling NOUN ejpam-7001 52 26 monotonically monotonically ADV ejpam-7001 52 27 increasing increase VERB ejpam-7001 52 28 or or CCONJ ejpam-7001 52 29 decreasing decrease VERB ejpam-7001 52 30 failure failure NOUN ejpam-7001 52 31 rate rate NOUN ejpam-7001 52 32 functions function NOUN ejpam-7001 52 33 , , PUNCT ejpam-7001 52 34 whereas whereas SCONJ ejpam-7001 52 35 the the DET ejpam-7001 52 36 fréchet fréchet NOUN ejpam-7001 52 37 distribution distribution NOUN ejpam-7001 52 38 is be AUX ejpam-7001 52 39 widely widely ADV ejpam-7001 52 40 applied apply VERB ejpam-7001 52 41 for for ADP ejpam-7001 52 42 modeling model VERB ejpam-7001 52 43 extreme extreme ADJ ejpam-7001 52 44 value value NOUN ejpam-7001 52 45 phenomena phenomenon NOUN ejpam-7001 52 46 and and CCONJ ejpam-7001 52 47 rare rare ADJ ejpam-7001 52 48 events event NOUN ejpam-7001 52 49 . . PUNCT ejpam-7001 53 1 • • NUM ejpam-7001 53 2 the the DET ejpam-7001 53 3 crt crt ADJ ejpam-7001 53 4 approach approach NOUN ejpam-7001 53 5 allows allow VERB ejpam-7001 53 6 for for ADP ejpam-7001 53 7 greater great ADJ ejpam-7001 53 8 flexibility flexibility NOUN ejpam-7001 53 9 in in ADP ejpam-7001 53 10 simulating simulate VERB ejpam-7001 53 11 hazard hazard NOUN ejpam-7001 53 12 rate rate NOUN ejpam-7001 53 13 functions function NOUN ejpam-7001 53 14 , , PUNCT ejpam-7001 53 15 enabling enable VERB ejpam-7001 53 16 them they PRON ejpam-7001 53 17 to to PART ejpam-7001 53 18 exhibit exhibit VERB ejpam-7001 53 19 various various ADJ ejpam-7001 53 20 shapes shape NOUN ejpam-7001 53 21 such such ADJ ejpam-7001 53 22 as as ADP ejpam-7001 53 23 increasing increase VERB ejpam-7001 53 24 , , PUNCT ejpam-7001 53 25 decreasing decrease VERB ejpam-7001 53 26 , , PUNCT ejpam-7001 53 27 constant constant ADJ ejpam-7001 53 28 , , PUNCT ejpam-7001 53 29 bathtub bathtub NOUN ejpam-7001 53 30 - - PUNCT ejpam-7001 53 31 shaped shape VERB ejpam-7001 53 32 , , PUNCT ejpam-7001 53 33 or or CCONJ ejpam-7001 53 34 upside upside ADV ejpam-7001 53 35 - - PUNCT ejpam-7001 53 36 down down ADP ejpam-7001 53 37 bathtub bathtub NOUN ejpam-7001 53 38 - - PUNCT ejpam-7001 53 39 shaped shape VERB ejpam-7001 53 40 patterns pattern NOUN ejpam-7001 53 41 . . PUNCT ejpam-7001 54 1 • • NUM ejpam-7001 54 2 motivated motivate VERB ejpam-7001 54 3 by by ADP ejpam-7001 54 4 this this DET ejpam-7001 54 5 flexibility flexibility NOUN ejpam-7001 54 6 , , PUNCT ejpam-7001 54 7 we we PRON ejpam-7001 54 8 introduce introduce VERB ejpam-7001 54 9 the the DET ejpam-7001 54 10 crtfw crtfw NOUN ejpam-7001 54 11 distribution distribution NOUN ejpam-7001 54 12 as as ADP ejpam-7001 54 13 a a DET ejpam-7001 54 14 novel novel ADJ ejpam-7001 54 15 generalization generalization NOUN ejpam-7001 54 16 of of ADP ejpam-7001 54 17 the the DET ejpam-7001 54 18 fw fw ADJ ejpam-7001 54 19 distribution distribution NOUN ejpam-7001 54 20 , , PUNCT ejpam-7001 54 21 thereby thereby ADV ejpam-7001 54 22 enhancing enhance VERB ejpam-7001 54 23 the the DET ejpam-7001 54 24 baseline baseline ADJ ejpam-7001 54 25 distribution distribution NOUN ejpam-7001 54 26 ’s ’s PART ejpam-7001 54 27 adaptability adaptability NOUN ejpam-7001 54 28 and and CCONJ ejpam-7001 54 29 reliability reliability NOUN ejpam-7001 54 30 in in ADP ejpam-7001 54 31 practical practical ADJ ejpam-7001 54 32 applications application NOUN ejpam-7001 54 33 . . PUNCT ejpam-7001 55 1 • • NUM ejpam-7001 55 2 additionally additionally ADV ejpam-7001 55 3 , , PUNCT ejpam-7001 55 4 a a DET ejpam-7001 55 5 comparative comparative ADJ ejpam-7001 55 6 analysis analysis NOUN ejpam-7001 55 7 among among ADP ejpam-7001 55 8 the the DET ejpam-7001 55 9 fw fw ADJ ejpam-7001 55 10 , , PUNCT ejpam-7001 55 11 qrtfw qrtfw NOUN ejpam-7001 55 12 , , PUNCT ejpam-7001 55 13 and and CCONJ ejpam-7001 55 14 the the DET ejpam-7001 55 15 proposed propose VERB ejpam-7001 55 16 crtfw crtfw NOUN ejpam-7001 55 17 distributions distribution NOUN ejpam-7001 55 18 is be AUX ejpam-7001 55 19 conducted conduct VERB ejpam-7001 55 20 to to PART ejpam-7001 55 21 demonstrate demonstrate VERB ejpam-7001 55 22 the the DET ejpam-7001 55 23 advantages advantage NOUN ejpam-7001 55 24 and and CCONJ ejpam-7001 55 25 improved improve VERB ejpam-7001 55 26 modeling modeling NOUN ejpam-7001 55 27 capabilities capability NOUN ejpam-7001 55 28 of of ADP ejpam-7001 55 29 the the DET ejpam-7001 55 30 crtfw crtfw NOUN ejpam-7001 55 31 distribution distribution NOUN ejpam-7001 55 32 . . PUNCT ejpam-7001 56 1 imliyangba imliyangba PROPN ejpam-7001 56 2 et et PROPN ejpam-7001 56 3 al al PROPN ejpam-7001 56 4 . . PUNCT ejpam-7001 56 5 / / SYM ejpam-7001 56 6 eur eur PROPN ejpam-7001 56 7 . . PUNCT ejpam-7001 57 1 j. j. PROPN ejpam-7001 57 2 pure pure PROPN ejpam-7001 57 3 appl appl PROPN ejpam-7001 57 4 . . PROPN ejpam-7001 57 5 math math PROPN ejpam-7001 57 6 , , PUNCT ejpam-7001 57 7 18 18 NUM ejpam-7001 57 8 ( ( PUNCT ejpam-7001 57 9 4 4 NUM ejpam-7001 57 10 ) ) PUNCT ejpam-7001 57 11 ( ( PUNCT ejpam-7001 57 12 2025 2025 NUM ejpam-7001 57 13 ) ) PUNCT ejpam-7001 57 14 , , PUNCT ejpam-7001 57 15 7001 7001 NUM ejpam-7001 57 16 4 4 NUM ejpam-7001 57 17 of of ADP ejpam-7001 57 18 27 27 NUM ejpam-7001 57 19 the the DET ejpam-7001 57 20 rest rest NOUN ejpam-7001 57 21 of of ADP ejpam-7001 57 22 the the DET ejpam-7001 57 23 article article NOUN ejpam-7001 57 24 is be AUX ejpam-7001 57 25 organized organize VERB ejpam-7001 57 26 like like ADP ejpam-7001 57 27 this this PRON ejpam-7001 57 28 : : PUNCT ejpam-7001 57 29 sections section NOUN ejpam-7001 57 30 2 2 NUM ejpam-7001 57 31 and and CCONJ ejpam-7001 57 32 3 3 NUM ejpam-7001 57 33 present present ADJ ejpam-7001 57 34 qrtfw qrtfw NOUN ejpam-7001 57 35 and and CCONJ ejpam-7001 57 36 crtfw crtfw NOUN ejpam-7001 57 37 distributions distribution NOUN ejpam-7001 57 38 . . PUNCT ejpam-7001 58 1 in in ADP ejpam-7001 58 2 section section NOUN ejpam-7001 58 3 4 4 NUM ejpam-7001 58 4 , , PUNCT ejpam-7001 58 5 we we PRON ejpam-7001 58 6 have have AUX ejpam-7001 58 7 taken take VERB ejpam-7001 58 8 a a DET ejpam-7001 58 9 look look NOUN ejpam-7001 58 10 at at ADP ejpam-7001 58 11 the the DET ejpam-7001 58 12 moment moment NOUN ejpam-7001 58 13 , , PUNCT ejpam-7001 58 14 quantiles quantile NOUN ejpam-7001 58 15 , , PUNCT ejpam-7001 58 16 mode mode NOUN ejpam-7001 58 17 , , PUNCT ejpam-7001 58 18 moment moment NOUN ejpam-7001 58 19 generating generate VERB ejpam-7001 58 20 function function NOUN ejpam-7001 58 21 , , PUNCT ejpam-7001 58 22 and and CCONJ ejpam-7001 58 23 random random ADJ ejpam-7001 58 24 number number NOUN ejpam-7001 58 25 generation generation NOUN ejpam-7001 58 26 as as ADP ejpam-7001 58 27 part part NOUN ejpam-7001 58 28 of of ADP ejpam-7001 58 29 the the DET ejpam-7001 58 30 newly newly ADV ejpam-7001 58 31 suggested suggest VERB ejpam-7001 58 32 crtfw crtfw NOUN ejpam-7001 58 33 distribution distribution NOUN ejpam-7001 58 34 ’s ’s PART ejpam-7001 58 35 statistical statistical ADJ ejpam-7001 58 36 features feature NOUN ejpam-7001 58 37 . . PUNCT ejpam-7001 59 1 in in ADP ejpam-7001 59 2 section section NOUN ejpam-7001 59 3 5 5 NUM ejpam-7001 59 4 , , PUNCT ejpam-7001 59 5 we we PRON ejpam-7001 59 6 discuss discuss VERB ejpam-7001 59 7 the the DET ejpam-7001 59 8 order order NOUN ejpam-7001 59 9 statistics statistic NOUN ejpam-7001 59 10 distribution distribution NOUN ejpam-7001 59 11 , , PUNCT ejpam-7001 59 12 crtfw crtfw NOUN ejpam-7001 59 13 entropy entropy NOUN ejpam-7001 59 14 and and CCONJ ejpam-7001 59 15 reliability reliability NOUN ejpam-7001 59 16 analysis analysis NOUN ejpam-7001 59 17 . . PUNCT ejpam-7001 60 1 section section NOUN ejpam-7001 60 2 6 6 NUM ejpam-7001 60 3 explains explain VERB ejpam-7001 60 4 how how SCONJ ejpam-7001 60 5 the the DET ejpam-7001 60 6 maximal maximal ADJ ejpam-7001 60 7 likelihood likelihood NOUN ejpam-7001 60 8 estimation estimation NOUN ejpam-7001 60 9 approach approach NOUN ejpam-7001 60 10 was be AUX ejpam-7001 60 11 used use VERB ejpam-7001 60 12 to to PART ejpam-7001 60 13 estimate estimate VERB ejpam-7001 60 14 the the DET ejpam-7001 60 15 parameters parameter NOUN ejpam-7001 60 16 of of ADP ejpam-7001 60 17 the the DET ejpam-7001 60 18 proposed propose VERB ejpam-7001 60 19 distribution distribution NOUN ejpam-7001 60 20 . . PUNCT ejpam-7001 61 1 a a DET ejpam-7001 61 2 simulation simulation NOUN ejpam-7001 61 3 study study NOUN ejpam-7001 61 4 is be AUX ejpam-7001 61 5 presented present VERB ejpam-7001 61 6 in in ADP ejpam-7001 61 7 section section NOUN ejpam-7001 61 8 7 7 NUM ejpam-7001 61 9 to to PART ejpam-7001 61 10 examine examine VERB ejpam-7001 61 11 and and CCONJ ejpam-7001 61 12 assess assess VERB ejpam-7001 61 13 the the DET ejpam-7001 61 14 performance performance NOUN ejpam-7001 61 15 of of ADP ejpam-7001 61 16 the the DET ejpam-7001 61 17 model model NOUN ejpam-7001 61 18 estimator estimator NOUN ejpam-7001 61 19 for for ADP ejpam-7001 61 20 different different ADJ ejpam-7001 61 21 sample sample NOUN ejpam-7001 61 22 sizes size NOUN ejpam-7001 61 23 . . PUNCT ejpam-7001 62 1 section section NOUN ejpam-7001 62 2 8 8 NUM ejpam-7001 62 3 examines examine VERB ejpam-7001 62 4 the the DET ejpam-7001 62 5 flexibility flexibility NOUN ejpam-7001 62 6 of of ADP ejpam-7001 62 7 the the DET ejpam-7001 62 8 crtfw crtfw NOUN ejpam-7001 62 9 model model NOUN ejpam-7001 62 10 by by ADP ejpam-7001 62 11 analyzing analyze VERB ejpam-7001 62 12 two two NUM ejpam-7001 62 13 real real ADJ ejpam-7001 62 14 - - PUNCT ejpam-7001 62 15 world world NOUN ejpam-7001 62 16 sustainability sustainability NOUN ejpam-7001 62 17 datasets dataset NOUN ejpam-7001 62 18 . . PUNCT ejpam-7001 63 1 section section NOUN ejpam-7001 63 2 9 9 NUM ejpam-7001 63 3 concludes conclude VERB ejpam-7001 63 4 with with ADP ejpam-7001 63 5 the the DET ejpam-7001 63 6 reporting reporting NOUN ejpam-7001 63 7 of of ADP ejpam-7001 63 8 results result NOUN ejpam-7001 63 9 . . PUNCT ejpam-7001 64 1 2 2 X ejpam-7001 64 2 . . X ejpam-7001 64 3 mathematical mathematical ADJ ejpam-7001 64 4 structure structure NOUN ejpam-7001 64 5 and and CCONJ ejpam-7001 64 6 visualization visualization NOUN ejpam-7001 64 7 of of ADP ejpam-7001 64 8 the the DET ejpam-7001 64 9 quadratic quadratic ADJ ejpam-7001 64 10 rank rank NOUN ejpam-7001 64 11 transmuted transmute VERB ejpam-7001 64 12 fréchet fréchet NOUN ejpam-7001 64 13 - - PUNCT ejpam-7001 64 14 weibull weibull NOUN ejpam-7001 64 15 distribution distribution NOUN ejpam-7001 64 16 the the DET ejpam-7001 64 17 cumulative cumulative ADJ ejpam-7001 64 18 distribution distribution NOUN ejpam-7001 64 19 function function NOUN ejpam-7001 64 20 ( ( PUNCT ejpam-7001 64 21 cdf cdf PROPN ejpam-7001 64 22 ) ) PUNCT ejpam-7001 64 23 of of ADP ejpam-7001 64 24 the the DET ejpam-7001 64 25 quadratic quadratic ADJ ejpam-7001 64 26 rank rank NOUN ejpam-7001 64 27 transmuted transmute VERB ejpam-7001 64 28 model model NOUN ejpam-7001 64 29 ( ( PUNCT ejpam-7001 64 30 qrtm qrtm PROPN ejpam-7001 64 31 ) ) PUNCT ejpam-7001 64 32 , , PUNCT ejpam-7001 64 33 based base VERB ejpam-7001 64 34 on on ADP ejpam-7001 64 35 the the DET ejpam-7001 64 36 approach approach NOUN ejpam-7001 64 37 of of ADP ejpam-7001 64 38 [ [ X ejpam-7001 64 39 5 5 NUM ejpam-7001 64 40 ] ] PUNCT ejpam-7001 64 41 , , PUNCT ejpam-7001 64 42 is be AUX ejpam-7001 64 43 defined define VERB ejpam-7001 64 44 as as ADP ejpam-7001 64 45 f f PROPN ejpam-7001 64 46 ( ( PUNCT ejpam-7001 64 47 x x NOUN ejpam-7001 64 48 ) ) PUNCT ejpam-7001 64 49 = = NOUN ejpam-7001 65 1 λg(x λg(x X ejpam-7001 65 2 ) ) PUNCT ejpam-7001 66 1 + + CCONJ ejpam-7001 66 2 ( ( PUNCT ejpam-7001 66 3 1− 1− NUM ejpam-7001 66 4 λ λ NOUN ejpam-7001 66 5 ) ) PUNCT ejpam-7001 67 1 [ [ X ejpam-7001 67 2 g(x)]2 g(x)]2 NOUN ejpam-7001 67 3 , , PUNCT ejpam-7001 67 4 0 0 NUM ejpam-7001 67 5 ≤ ≤ NUM ejpam-7001 67 6 λ λ X ejpam-7001 67 7 ≤ ≤ NOUN ejpam-7001 67 8 1 1 NUM ejpam-7001 67 9 , , PUNCT ejpam-7001 67 10 ( ( PUNCT ejpam-7001 67 11 1 1 X ejpam-7001 67 12 ) ) PUNCT ejpam-7001 67 13 where where SCONJ ejpam-7001 67 14 g(x g(x NOUN ejpam-7001 67 15 ) ) PUNCT ejpam-7001 67 16 is be AUX ejpam-7001 67 17 the the DET ejpam-7001 67 18 cdf cdf PROPN ejpam-7001 67 19 of of ADP ejpam-7001 67 20 the the DET ejpam-7001 67 21 baseline baseline ADJ ejpam-7001 67 22 distribution distribution NOUN ejpam-7001 67 23 . . PUNCT ejpam-7001 68 1 correspondingly correspondingly ADV ejpam-7001 68 2 , , PUNCT ejpam-7001 68 3 the the DET ejpam-7001 68 4 probability probability NOUN ejpam-7001 68 5 density density NOUN ejpam-7001 68 6 function function NOUN ejpam-7001 68 7 ( ( PUNCT ejpam-7001 68 8 pdf pdf NOUN ejpam-7001 68 9 ) ) PUNCT ejpam-7001 68 10 of of ADP ejpam-7001 68 11 the the DET ejpam-7001 68 12 qrtm qrtm NOUN ejpam-7001 68 13 is be AUX ejpam-7001 68 14 given give VERB ejpam-7001 68 15 by by ADP ejpam-7001 68 16 f(x f(x PROPN ejpam-7001 68 17 ) ) PUNCT ejpam-7001 68 18 = = PUNCT ejpam-7001 69 1 [ [ X ejpam-7001 69 2 λ+ λ+ X ejpam-7001 69 3 2(1− 2(1− NUM ejpam-7001 69 4 λ)g(x λ)g(x X ejpam-7001 69 5 ) ) PUNCT ejpam-7001 69 6 ] ] PUNCT ejpam-7001 70 1 g(x g(x NOUN ejpam-7001 70 2 ) ) PUNCT ejpam-7001 70 3 , , PUNCT ejpam-7001 70 4 ( ( PUNCT ejpam-7001 70 5 2 2 X ejpam-7001 70 6 ) ) PUNCT ejpam-7001 70 7 where where SCONJ ejpam-7001 70 8 g(x g(x NOUN ejpam-7001 70 9 ) ) PUNCT ejpam-7001 70 10 denotes denote VERB ejpam-7001 70 11 the the DET ejpam-7001 70 12 pdf pdf NOUN ejpam-7001 70 13 of of ADP ejpam-7001 70 14 the the DET ejpam-7001 70 15 baseline baseline ADJ ejpam-7001 70 16 distribution distribution NOUN ejpam-7001 70 17 . . PUNCT ejpam-7001 71 1 for for ADP ejpam-7001 71 2 the the DET ejpam-7001 71 3 fw fw ADJ ejpam-7001 71 4 distribution distribution NOUN ejpam-7001 71 5 , , PUNCT ejpam-7001 71 6 as as SCONJ ejpam-7001 71 7 presented present VERB ejpam-7001 71 8 in in ADP ejpam-7001 71 9 [ [ X ejpam-7001 71 10 31 31 NUM ejpam-7001 71 11 ] ] PUNCT ejpam-7001 71 12 , , PUNCT ejpam-7001 71 13 the the DET ejpam-7001 71 14 cdf cdf PROPN ejpam-7001 71 15 and and CCONJ ejpam-7001 71 16 pdf pdf NOUN ejpam-7001 71 17 are be AUX ejpam-7001 71 18 given give VERB ejpam-7001 71 19 by by ADP ejpam-7001 71 20 g(x g(x NOUN ejpam-7001 71 21 ) ) PUNCT ejpam-7001 71 22 = = SYM ejpam-7001 71 23 exp exp NOUN ejpam-7001 71 24 { { PUNCT ejpam-7001 71 25 −βα −βα PROPN ejpam-7001 71 26 ( ( PUNCT ejpam-7001 71 27 m m NOUN ejpam-7001 71 28 x x X ejpam-7001 71 29 ) ) PUNCT ejpam-7001 71 30 αk αk ADP ejpam-7001 71 31 } } PUNCT ejpam-7001 71 32 , , PUNCT ejpam-7001 71 33 x x X ejpam-7001 71 34 > > X ejpam-7001 71 35 0 0 NUM ejpam-7001 71 36 ; ; PUNCT ejpam-7001 71 37 α α NUM ejpam-7001 71 38 , , PUNCT ejpam-7001 71 39 β β X ejpam-7001 71 40 , , PUNCT ejpam-7001 71 41 m m PROPN ejpam-7001 71 42 , , PUNCT ejpam-7001 71 43 k k PROPN ejpam-7001 71 44 > > X ejpam-7001 71 45 0 0 NUM ejpam-7001 71 46 , , PUNCT ejpam-7001 71 47 ( ( PUNCT ejpam-7001 71 48 3 3 NUM ejpam-7001 71 49 ) ) PUNCT ejpam-7001 71 50 and and CCONJ ejpam-7001 71 51 g(x g(x NOUN ejpam-7001 71 52 ) ) PUNCT ejpam-7001 72 1 = = SYM ejpam-7001 72 2 αkβαmαkx−1−αk αkβαmαkx−1−αk NOUN ejpam-7001 72 3 exp exp NOUN ejpam-7001 72 4 { { PUNCT ejpam-7001 72 5 −βα −βα PROPN ejpam-7001 72 6 ( ( PUNCT ejpam-7001 72 7 m m NOUN ejpam-7001 72 8 x x X ejpam-7001 72 9 ) ) PUNCT ejpam-7001 72 10 αk αk ADP ejpam-7001 72 11 } } PUNCT ejpam-7001 72 12 , , PUNCT ejpam-7001 72 13 ( ( PUNCT ejpam-7001 72 14 4 4 X ejpam-7001 72 15 ) ) PUNCT ejpam-7001 72 16 where where SCONJ ejpam-7001 72 17 α α NOUN ejpam-7001 72 18 and and CCONJ ejpam-7001 72 19 k k PROPN ejpam-7001 72 20 are be AUX ejpam-7001 72 21 shape shape NOUN ejpam-7001 72 22 parameters parameter NOUN ejpam-7001 72 23 , , PUNCT ejpam-7001 72 24 and and CCONJ ejpam-7001 72 25 m m PROPN ejpam-7001 72 26 and and CCONJ ejpam-7001 72 27 β β X ejpam-7001 72 28 are be AUX ejpam-7001 72 29 scale scale NOUN ejpam-7001 72 30 parameters parameter NOUN ejpam-7001 72 31 . . PUNCT ejpam-7001 73 1 substituting substitute VERB ejpam-7001 73 2 equation equation NOUN ejpam-7001 73 3 ( ( PUNCT ejpam-7001 73 4 3 3 NUM ejpam-7001 73 5 ) ) PUNCT ejpam-7001 73 6 into into ADP ejpam-7001 73 7 equation equation NOUN ejpam-7001 73 8 ( ( PUNCT ejpam-7001 73 9 1 1 NUM ejpam-7001 73 10 ) ) PUNCT ejpam-7001 73 11 , , PUNCT ejpam-7001 73 12 the the DET ejpam-7001 73 13 cdf cdf PROPN ejpam-7001 73 14 of of ADP ejpam-7001 73 15 the the DET ejpam-7001 73 16 qrtfw qrtfw ADJ ejpam-7001 73 17 distribution distribution NOUN ejpam-7001 73 18 becomes become VERB ejpam-7001 73 19 f f PROPN ejpam-7001 73 20 ( ( PUNCT ejpam-7001 73 21 x x NOUN ejpam-7001 73 22 ) ) PUNCT ejpam-7001 73 23 = = SYM ejpam-7001 73 24 λ λ NOUN ejpam-7001 73 25 exp exp X ejpam-7001 73 26 { { PUNCT ejpam-7001 73 27 −βα −βα PROPN ejpam-7001 73 28 ( ( PUNCT ejpam-7001 73 29 m m NOUN ejpam-7001 73 30 x x X ejpam-7001 73 31 ) ) PUNCT ejpam-7001 73 32 αk αk ADP ejpam-7001 73 33 } } PUNCT ejpam-7001 73 34 + + CCONJ ejpam-7001 73 35 ( ( PUNCT ejpam-7001 73 36 1− 1− NUM ejpam-7001 73 37 λ λ NOUN ejpam-7001 73 38 ) ) PUNCT ejpam-7001 73 39 [ [ PUNCT ejpam-7001 73 40 exp exp X ejpam-7001 73 41 { { PUNCT ejpam-7001 73 42 −βα −βα PROPN ejpam-7001 73 43 ( ( PUNCT ejpam-7001 73 44 m m NOUN ejpam-7001 73 45 x x X ejpam-7001 73 46 ) ) PUNCT ejpam-7001 73 47 αk}]2 αk}]2 NUM ejpam-7001 73 48 , , PUNCT ejpam-7001 73 49 ( ( PUNCT ejpam-7001 73 50 5 5 NUM ejpam-7001 73 51 ) ) PUNCT ejpam-7001 73 52 with with ADP ejpam-7001 73 53 x x PROPN ejpam-7001 73 54 > > X ejpam-7001 73 55 0 0 NUM ejpam-7001 73 56 , , PUNCT ejpam-7001 73 57 α α X ejpam-7001 73 58 , , PUNCT ejpam-7001 73 59 β β X ejpam-7001 73 60 , , PUNCT ejpam-7001 73 61 m m PROPN ejpam-7001 73 62 , , PUNCT ejpam-7001 73 63 k k PROPN ejpam-7001 73 64 > > X ejpam-7001 73 65 0 0 NUM ejpam-7001 73 66 , , PUNCT ejpam-7001 73 67 and and CCONJ ejpam-7001 73 68 λ λ X ejpam-7001 73 69 ∈ ∈ PROPN ejpam-7001 74 1 [ [ X ejpam-7001 74 2 0 0 NUM ejpam-7001 74 3 , , PUNCT ejpam-7001 74 4 1 1 NUM ejpam-7001 74 5 ] ] PUNCT ejpam-7001 74 6 . . PUNCT ejpam-7001 75 1 the the DET ejpam-7001 75 2 corresponding correspond VERB ejpam-7001 75 3 pdf pdf NOUN ejpam-7001 75 4 is be AUX ejpam-7001 75 5 obtained obtain VERB ejpam-7001 75 6 by by ADP ejpam-7001 75 7 differentiating differentiate VERB ejpam-7001 75 8 equation equation NOUN ejpam-7001 75 9 ( ( PUNCT ejpam-7001 75 10 5 5 NUM ejpam-7001 75 11 ) ) PUNCT ejpam-7001 75 12 with with ADP ejpam-7001 75 13 respect respect NOUN ejpam-7001 75 14 to to ADP ejpam-7001 75 15 x x PRON ejpam-7001 75 16 , , PUNCT ejpam-7001 75 17 yielding yield VERB ejpam-7001 75 18 f(x f(x PROPN ejpam-7001 75 19 ) ) PUNCT ejpam-7001 76 1 = = PUNCT ejpam-7001 76 2 [ [ PUNCT ejpam-7001 76 3 λ+ λ+ NUM ejpam-7001 76 4 2(1− 2(1− NUM ejpam-7001 76 5 λ λ NOUN ejpam-7001 76 6 ) ) PUNCT ejpam-7001 76 7 exp exp NOUN ejpam-7001 76 8 { { PUNCT ejpam-7001 76 9 −βα −βα PROPN ejpam-7001 76 10 ( ( PUNCT ejpam-7001 76 11 m m NOUN ejpam-7001 76 12 x x X ejpam-7001 76 13 ) ) PUNCT ejpam-7001 76 14 αk αk ADP ejpam-7001 76 15 } } PUNCT ejpam-7001 76 16 ] ] PUNCT ejpam-7001 76 17 αkβαmαkx−1−αk αkβαmαkx−1−αk NOUN ejpam-7001 76 18 exp exp X ejpam-7001 76 19 { { PUNCT ejpam-7001 76 20 −βα −βα PROPN ejpam-7001 76 21 ( ( PUNCT ejpam-7001 76 22 m m NOUN ejpam-7001 76 23 x x X ejpam-7001 76 24 ) ) PUNCT ejpam-7001 76 25 αk αk ADP ejpam-7001 76 26 } } PUNCT ejpam-7001 76 27 . . PUNCT ejpam-7001 77 1 ( ( PUNCT ejpam-7001 77 2 6 6 X ejpam-7001 77 3 ) ) PUNCT ejpam-7001 77 4 imliyangba imliyangba PROPN ejpam-7001 77 5 et et PROPN ejpam-7001 77 6 al al PROPN ejpam-7001 77 7 . . PUNCT ejpam-7001 77 8 / / SYM ejpam-7001 77 9 eur eur PROPN ejpam-7001 77 10 . . PUNCT ejpam-7001 78 1 j. j. PROPN ejpam-7001 78 2 pure pure PROPN ejpam-7001 78 3 appl appl PROPN ejpam-7001 78 4 . . PROPN ejpam-7001 78 5 math math PROPN ejpam-7001 78 6 , , PUNCT ejpam-7001 78 7 18 18 NUM ejpam-7001 78 8 ( ( PUNCT ejpam-7001 78 9 4 4 NUM ejpam-7001 78 10 ) ) PUNCT ejpam-7001 78 11 ( ( PUNCT ejpam-7001 78 12 2025 2025 NUM ejpam-7001 78 13 ) ) PUNCT ejpam-7001 78 14 , , PUNCT ejpam-7001 78 15 7001 7001 NUM ejpam-7001 78 16 5 5 NUM ejpam-7001 78 17 of of ADP ejpam-7001 78 18 27 27 NUM ejpam-7001 78 19 figure figure NOUN ejpam-7001 78 20 1 1 NUM ejpam-7001 78 21 : : PUNCT ejpam-7001 78 22 density density NOUN ejpam-7001 78 23 function function NOUN ejpam-7001 78 24 of of ADP ejpam-7001 78 25 qrtfw qrtfw ADJ ejpam-7001 78 26 distribution distribution NOUN ejpam-7001 78 27 . . PUNCT ejpam-7001 79 1 some some DET ejpam-7001 79 2 possible possible ADJ ejpam-7001 79 3 shapes shape NOUN ejpam-7001 79 4 of of ADP ejpam-7001 79 5 the the DET ejpam-7001 79 6 pdf pdf NOUN ejpam-7001 79 7 of of ADP ejpam-7001 79 8 the the DET ejpam-7001 79 9 qrtfw qrtfw ADJ ejpam-7001 79 10 distribution distribution NOUN ejpam-7001 79 11 for for ADP ejpam-7001 79 12 selected select VERB ejpam-7001 79 13 values value NOUN ejpam-7001 79 14 of of ADP ejpam-7001 79 15 λ λ PROPN ejpam-7001 79 16 and and CCONJ ejpam-7001 79 17 m m PROPN ejpam-7001 79 18 , , PUNCT ejpam-7001 79 19 with with ADP ejpam-7001 79 20 α α NOUN ejpam-7001 79 21 = = SYM ejpam-7001 79 22 0.5 0.5 NUM ejpam-7001 79 23 , , PUNCT ejpam-7001 79 24 β β X ejpam-7001 79 25 = = SYM ejpam-7001 79 26 0.5 0.5 NUM ejpam-7001 79 27 , , PUNCT ejpam-7001 79 28 and and CCONJ ejpam-7001 79 29 k k PROPN ejpam-7001 79 30 = = SYM ejpam-7001 79 31 5 5 NUM ejpam-7001 79 32 , , PUNCT ejpam-7001 79 33 are be AUX ejpam-7001 79 34 illustrated illustrate VERB ejpam-7001 79 35 in in ADP ejpam-7001 79 36 figure figure NOUN ejpam-7001 79 37 1(left 1(left NUM ejpam-7001 79 38 ) ) PUNCT ejpam-7001 79 39 . . PUNCT ejpam-7001 80 1 figure figure NOUN ejpam-7001 80 2 1(right 1(right NUM ejpam-7001 80 3 ) ) PUNCT ejpam-7001 80 4 shows show VERB ejpam-7001 80 5 the the DET ejpam-7001 80 6 pdf pdf NOUN ejpam-7001 80 7 for for ADP ejpam-7001 80 8 selected select VERB ejpam-7001 80 9 values value NOUN ejpam-7001 80 10 of of ADP ejpam-7001 80 11 α α NOUN ejpam-7001 80 12 , , PUNCT ejpam-7001 80 13 setting set VERB ejpam-7001 80 14 β β X ejpam-7001 80 15 = = SYM ejpam-7001 80 16 0.5 0.5 NUM ejpam-7001 80 17 , , PUNCT ejpam-7001 80 18 λ λ X ejpam-7001 80 19 = = NOUN ejpam-7001 80 20 0.05 0.05 NUM ejpam-7001 80 21 , , PUNCT ejpam-7001 80 22 m m NOUN ejpam-7001 80 23 = = NOUN ejpam-7001 80 24 0.5 0.5 NUM ejpam-7001 80 25 , , PUNCT ejpam-7001 80 26 and and CCONJ ejpam-7001 81 1 k k X ejpam-7001 81 2 = = NOUN ejpam-7001 81 3 1 1 X ejpam-7001 81 4 . . PUNCT ejpam-7001 82 1 the the DET ejpam-7001 82 2 qrtfw qrtfw PROPN ejpam-7001 82 3 distribution distribution NOUN ejpam-7001 82 4 ’s ’s PART ejpam-7001 82 5 pdf pdf NOUN ejpam-7001 82 6 is be AUX ejpam-7001 82 7 shown show VERB ejpam-7001 82 8 in in ADP ejpam-7001 82 9 figure figure NOUN ejpam-7001 82 10 1 1 NUM ejpam-7001 82 11 , , PUNCT ejpam-7001 82 12 which which PRON ejpam-7001 82 13 highlights highlight VERB ejpam-7001 82 14 a a DET ejpam-7001 82 15 range range NOUN ejpam-7001 82 16 of of ADP ejpam-7001 82 17 potential potential ADJ ejpam-7001 82 18 morphologies morphology NOUN ejpam-7001 82 19 . . PUNCT ejpam-7001 83 1 in in ADP ejpam-7001 83 2 particular particular ADJ ejpam-7001 83 3 , , PUNCT ejpam-7001 83 4 depending depend VERB ejpam-7001 83 5 on on ADP ejpam-7001 83 6 the the DET ejpam-7001 83 7 parameter parameter NOUN ejpam-7001 83 8 values value NOUN ejpam-7001 83 9 selected select VERB ejpam-7001 83 10 , , PUNCT ejpam-7001 83 11 the the DET ejpam-7001 83 12 figure figure NOUN ejpam-7001 83 13 shows show VERB ejpam-7001 83 14 density density NOUN ejpam-7001 83 15 curves curve NOUN ejpam-7001 83 16 with with ADP ejpam-7001 83 17 symmetric symmetric ADJ ejpam-7001 83 18 forms form NOUN ejpam-7001 83 19 , , PUNCT ejpam-7001 83 20 positively positively ADV ejpam-7001 83 21 skewed skewed ADJ ejpam-7001 83 22 behaviour behaviour NOUN ejpam-7001 83 23 , , PUNCT ejpam-7001 83 24 and and CCONJ ejpam-7001 83 25 increasingdecreasing increasingdecrease VERB ejpam-7001 83 26 patterns pattern NOUN ejpam-7001 83 27 . . PUNCT ejpam-7001 84 1 this this PRON ejpam-7001 84 2 demonstrates demonstrate VERB ejpam-7001 84 3 unequivocally unequivocally ADV ejpam-7001 84 4 the the DET ejpam-7001 84 5 qrtfw qrtfw ADJ ejpam-7001 84 6 distribution distribution NOUN ejpam-7001 84 7 ’s ’s PART ejpam-7001 84 8 adaptability adaptability NOUN ejpam-7001 84 9 to to ADP ejpam-7001 84 10 modelling model VERB ejpam-7001 84 11 a a DET ejpam-7001 84 12 variety variety NOUN ejpam-7001 84 13 of of ADP ejpam-7001 84 14 data datum NOUN ejpam-7001 84 15 types type NOUN ejpam-7001 84 16 . . PUNCT ejpam-7001 85 1 3 3 X ejpam-7001 85 2 . . NOUN ejpam-7001 85 3 mathematical mathematical ADJ ejpam-7001 85 4 formulation formulation NOUN ejpam-7001 85 5 and and CCONJ ejpam-7001 85 6 graphical graphical ADJ ejpam-7001 85 7 representation representation NOUN ejpam-7001 85 8 of of ADP ejpam-7001 85 9 the the DET ejpam-7001 85 10 cubic cubic ADJ ejpam-7001 85 11 rank rank NOUN ejpam-7001 85 12 transmuted transmute VERB ejpam-7001 85 13 fréchet fréchet NOUN ejpam-7001 85 14 - - PUNCT ejpam-7001 85 15 weibull weibull NOUN ejpam-7001 85 16 distribution distribution NOUN ejpam-7001 85 17 according accord VERB ejpam-7001 85 18 to to ADP ejpam-7001 85 19 [ [ X ejpam-7001 85 20 5 5 NUM ejpam-7001 85 21 ] ] PUNCT ejpam-7001 85 22 , , PUNCT ejpam-7001 85 23 the the DET ejpam-7001 85 24 cdf cdf PROPN ejpam-7001 85 25 of of ADP ejpam-7001 85 26 the the DET ejpam-7001 85 27 cubic cubic ADJ ejpam-7001 85 28 rank rank NOUN ejpam-7001 85 29 transmuted transmute VERB ejpam-7001 85 30 model model NOUN ejpam-7001 85 31 ( ( PUNCT ejpam-7001 85 32 crtm crtm NOUN ejpam-7001 85 33 ) ) PUNCT ejpam-7001 85 34 is be AUX ejpam-7001 85 35 defined define VERB ejpam-7001 85 36 as as ADP ejpam-7001 85 37 : : PUNCT ejpam-7001 85 38 f f PROPN ejpam-7001 85 39 ( ( PUNCT ejpam-7001 85 40 x x X ejpam-7001 85 41 ) ) PUNCT ejpam-7001 85 42 = = SYM ejpam-7001 85 43 λ1g(x λ1g(x X ejpam-7001 85 44 ) ) PUNCT ejpam-7001 86 1 + + CCONJ ejpam-7001 86 2 ( ( PUNCT ejpam-7001 86 3 λ2 λ2 NOUN ejpam-7001 86 4 − − PROPN ejpam-7001 86 5 λ1 λ1 PROPN ejpam-7001 86 6 ) ) PUNCT ejpam-7001 87 1 [ [ X ejpam-7001 87 2 g(x)]2 g(x)]2 NOUN ejpam-7001 87 3 + + CCONJ ejpam-7001 87 4 ( ( PUNCT ejpam-7001 87 5 1− 1− NUM ejpam-7001 87 6 λ1 λ1 ADJ ejpam-7001 87 7 ) ) PUNCT ejpam-7001 88 1 [ [ X ejpam-7001 88 2 g(x)]3 g(x)]3 ADJ ejpam-7001 88 3 , , PUNCT ejpam-7001 88 4 ( ( PUNCT ejpam-7001 88 5 7 7 NUM ejpam-7001 88 6 ) ) PUNCT ejpam-7001 88 7 and and CCONJ ejpam-7001 88 8 the the DET ejpam-7001 88 9 corresponding correspond VERB ejpam-7001 88 10 pdf pdf NOUN ejpam-7001 88 11 is be AUX ejpam-7001 88 12 f(x f(x PROPN ejpam-7001 88 13 ) ) PUNCT ejpam-7001 89 1 = = PRON ejpam-7001 89 2 { { PUNCT ejpam-7001 89 3 λ1 λ1 PROPN ejpam-7001 89 4 + + NUM ejpam-7001 89 5 2(λ2 2(λ2 NUM ejpam-7001 89 6 − − NOUN ejpam-7001 89 7 λ1)g(x λ1)g(x NUM ejpam-7001 89 8 ) ) PUNCT ejpam-7001 90 1 + + CCONJ ejpam-7001 91 1 3(1− 3(1− NUM ejpam-7001 91 2 λ1 λ1 NUM ejpam-7001 91 3 ) ) PUNCT ejpam-7001 92 1 [ [ X ejpam-7001 92 2 g(x)]2 g(x)]2 NOUN ejpam-7001 92 3 } } PUNCT ejpam-7001 92 4 g(x g(x PROPN ejpam-7001 92 5 ) ) PUNCT ejpam-7001 92 6 , , PUNCT ejpam-7001 92 7 0 0 NUM ejpam-7001 92 8 ≤ ≤ NUM ejpam-7001 92 9 λ1 λ1 ADJ ejpam-7001 92 10 ≤ ≤ NOUN ejpam-7001 92 11 1 1 NUM ejpam-7001 92 12 , , PUNCT ejpam-7001 92 13 −1 −1 NOUN ejpam-7001 92 14 ≤ ≤ NUM ejpam-7001 92 15 λ2 λ2 NOUN ejpam-7001 92 16 ≤ ≤ NUM ejpam-7001 92 17 1 1 NUM ejpam-7001 92 18 , , PUNCT ejpam-7001 92 19 where where SCONJ ejpam-7001 92 20 g(x g(x NOUN ejpam-7001 92 21 ) ) PUNCT ejpam-7001 92 22 and and CCONJ ejpam-7001 92 23 g(x g(x NOUN ejpam-7001 92 24 ) ) PUNCT ejpam-7001 92 25 are be AUX ejpam-7001 92 26 the the DET ejpam-7001 92 27 cdf cdf PROPN ejpam-7001 92 28 and and CCONJ ejpam-7001 92 29 pdf pdf NOUN ejpam-7001 92 30 of of ADP ejpam-7001 92 31 the the DET ejpam-7001 92 32 baseline baseline NOUN ejpam-7001 92 33 distribution distribution NOUN ejpam-7001 92 34 , , PUNCT ejpam-7001 92 35 respectively respectively ADV ejpam-7001 92 36 . . PUNCT ejpam-7001 93 1 substituting substitute VERB ejpam-7001 93 2 g(x g(x NOUN ejpam-7001 93 3 ) ) PUNCT ejpam-7001 93 4 from from ADP ejpam-7001 93 5 equation equation NOUN ejpam-7001 93 6 ( ( PUNCT ejpam-7001 93 7 3 3 NUM ejpam-7001 93 8 ) ) PUNCT ejpam-7001 93 9 into into ADP ejpam-7001 93 10 equation equation NOUN ejpam-7001 93 11 ( ( PUNCT ejpam-7001 93 12 7 7 NUM ejpam-7001 93 13 ) ) PUNCT ejpam-7001 93 14 , , PUNCT ejpam-7001 93 15 the the DET ejpam-7001 93 16 cdf cdf PROPN ejpam-7001 93 17 of of ADP ejpam-7001 93 18 the the DET ejpam-7001 93 19 crtfw crtfw NOUN ejpam-7001 93 20 distribution distribution NOUN ejpam-7001 93 21 is be AUX ejpam-7001 93 22 obtained obtain VERB ejpam-7001 93 23 as as ADP ejpam-7001 93 24 f f PROPN ejpam-7001 93 25 ( ( PUNCT ejpam-7001 93 26 x x NOUN ejpam-7001 93 27 ) ) PUNCT ejpam-7001 93 28 = = SYM ejpam-7001 93 29 λ1 λ1 ADJ ejpam-7001 93 30 exp exp NOUN ejpam-7001 93 31 { { PUNCT ejpam-7001 93 32 −βα −βα PROPN ejpam-7001 93 33 ( ( PUNCT ejpam-7001 93 34 m m NOUN ejpam-7001 93 35 x x X ejpam-7001 93 36 ) ) PUNCT ejpam-7001 93 37 αk αk ADP ejpam-7001 93 38 } } PUNCT ejpam-7001 93 39 + + ADJ ejpam-7001 93 40 ( ( PUNCT ejpam-7001 93 41 λ2−λ1 λ2−λ1 ADJ ejpam-7001 93 42 ) ) PUNCT ejpam-7001 94 1 [ [ X ejpam-7001 94 2 g(x)]2+(1−λ1 g(x)]2+(1−λ1 X ejpam-7001 94 3 ) ) PUNCT ejpam-7001 94 4 [ [ PUNCT ejpam-7001 94 5 exp exp X ejpam-7001 94 6 { { PUNCT ejpam-7001 94 7 −βα −βα PROPN ejpam-7001 94 8 ( ( PUNCT ejpam-7001 94 9 m m NOUN ejpam-7001 94 10 x x SYM ejpam-7001 94 11 ) ) PUNCT ejpam-7001 94 12 αk}]3 αk}]3 NOUN ejpam-7001 94 13 , , PUNCT ejpam-7001 94 14 ( ( PUNCT ejpam-7001 94 15 8) 8) NUM ejpam-7001 94 16 where where SCONJ ejpam-7001 94 17 x x DET ejpam-7001 94 18 > > X ejpam-7001 94 19 0 0 NUM ejpam-7001 94 20 , , PUNCT ejpam-7001 94 21 α α X ejpam-7001 94 22 , , PUNCT ejpam-7001 94 23 β β X ejpam-7001 94 24 , , PUNCT ejpam-7001 94 25 m m PROPN ejpam-7001 94 26 , , PUNCT ejpam-7001 94 27 k k PROPN ejpam-7001 94 28 > > X ejpam-7001 94 29 0 0 PROPN ejpam-7001 94 30 , , PUNCT ejpam-7001 94 31 λ1 λ1 PROPN ejpam-7001 94 32 ∈ ∈ PROPN ejpam-7001 94 33 [ [ X ejpam-7001 94 34 0 0 NUM ejpam-7001 94 35 , , PUNCT ejpam-7001 94 36 1 1 NUM ejpam-7001 94 37 ] ] PUNCT ejpam-7001 94 38 , , PUNCT ejpam-7001 94 39 and and CCONJ ejpam-7001 94 40 λ2 λ2 NOUN ejpam-7001 94 41 ∈ ∈ PROPN ejpam-7001 95 1 [ [ X ejpam-7001 95 2 −1 −1 NOUN ejpam-7001 95 3 , , PUNCT ejpam-7001 95 4 1 1 NUM ejpam-7001 95 5 ] ] PUNCT ejpam-7001 95 6 . . PUNCT ejpam-7001 96 1 differentiating differentiate VERB ejpam-7001 96 2 equation equation NOUN ejpam-7001 96 3 ( ( PUNCT ejpam-7001 96 4 8) 8) NUM ejpam-7001 96 5 with with ADP ejpam-7001 96 6 respect respect NOUN ejpam-7001 96 7 to to ADP ejpam-7001 96 8 x x X ejpam-7001 96 9 gives give VERB ejpam-7001 96 10 the the DET ejpam-7001 96 11 corresponding correspond VERB ejpam-7001 96 12 pdf pdf NOUN ejpam-7001 96 13 as as ADP ejpam-7001 96 14 f(x f(x PROPN ejpam-7001 96 15 ) ) PUNCT ejpam-7001 97 1 = = PRON ejpam-7001 97 2 { { PUNCT ejpam-7001 97 3 λ1 λ1 PROPN ejpam-7001 97 4 + + NUM ejpam-7001 97 5 2(λ2 2(λ2 NUM ejpam-7001 97 6 − − NOUN ejpam-7001 97 7 λ1 λ1 PROPN ejpam-7001 97 8 ) ) PUNCT ejpam-7001 97 9 exp exp NOUN ejpam-7001 97 10 { { PUNCT ejpam-7001 97 11 −βα −βα PROPN ejpam-7001 97 12 ( ( PUNCT ejpam-7001 97 13 m m NOUN ejpam-7001 97 14 x x X ejpam-7001 97 15 ) ) PUNCT ejpam-7001 97 16 αk αk ADP ejpam-7001 97 17 } } PUNCT ejpam-7001 97 18 + + CCONJ ejpam-7001 97 19 3(1− 3(1− NUM ejpam-7001 97 20 λ1 λ1 NUM ejpam-7001 97 21 ) ) PUNCT ejpam-7001 97 22 [ [ PUNCT ejpam-7001 97 23 exp exp X ejpam-7001 97 24 { { PUNCT ejpam-7001 97 25 −βα −βα PROPN ejpam-7001 97 26 ( ( PUNCT ejpam-7001 97 27 m m NOUN ejpam-7001 97 28 x x SYM ejpam-7001 97 29 ) ) PUNCT ejpam-7001 97 30 αk}]2 αk}]2 NUM ejpam-7001 97 31 } } PUNCT ejpam-7001 97 32 imliyangba imliyangba PROPN ejpam-7001 97 33 et et PROPN ejpam-7001 97 34 al al PROPN ejpam-7001 97 35 . . PUNCT ejpam-7001 97 36 / / SYM ejpam-7001 97 37 eur eur PROPN ejpam-7001 97 38 . . PUNCT ejpam-7001 98 1 j. j. PROPN ejpam-7001 98 2 pure pure PROPN ejpam-7001 98 3 appl appl PROPN ejpam-7001 98 4 . . PROPN ejpam-7001 98 5 math math PROPN ejpam-7001 98 6 , , PUNCT ejpam-7001 98 7 18 18 NUM ejpam-7001 98 8 ( ( PUNCT ejpam-7001 98 9 4 4 NUM ejpam-7001 98 10 ) ) PUNCT ejpam-7001 98 11 ( ( PUNCT ejpam-7001 98 12 2025 2025 NUM ejpam-7001 98 13 ) ) PUNCT ejpam-7001 98 14 , , PUNCT ejpam-7001 98 15 7001 7001 NUM ejpam-7001 98 16 6 6 NUM ejpam-7001 98 17 of of ADP ejpam-7001 98 18 27 27 NUM ejpam-7001 98 19 ×αkβαmαkx−1−αk ×αkβαmαkx−1−αk NOUN ejpam-7001 98 20 exp exp X ejpam-7001 98 21 { { PUNCT ejpam-7001 98 22 −βα −βα PROPN ejpam-7001 98 23 ( ( PUNCT ejpam-7001 98 24 m m NOUN ejpam-7001 98 25 x x X ejpam-7001 98 26 ) ) PUNCT ejpam-7001 98 27 αk αk ADP ejpam-7001 98 28 } } PUNCT ejpam-7001 98 29 , , PUNCT ejpam-7001 98 30 ( ( PUNCT ejpam-7001 98 31 9 9 X ejpam-7001 98 32 ) ) PUNCT ejpam-7001 98 33 where where SCONJ ejpam-7001 98 34 α α NOUN ejpam-7001 98 35 and and CCONJ ejpam-7001 98 36 k k PROPN ejpam-7001 98 37 are be AUX ejpam-7001 98 38 shape shape NOUN ejpam-7001 98 39 parameters parameter NOUN ejpam-7001 98 40 and and CCONJ ejpam-7001 98 41 m m PROPN ejpam-7001 98 42 and and CCONJ ejpam-7001 98 43 β β X ejpam-7001 98 44 are be AUX ejpam-7001 98 45 scale scale NOUN ejpam-7001 98 46 parameters parameter NOUN ejpam-7001 98 47 . . PUNCT ejpam-7001 99 1 some some DET ejpam-7001 99 2 sub sub NOUN ejpam-7001 99 3 - - NOUN ejpam-7001 99 4 models model NOUN ejpam-7001 99 5 and and CCONJ ejpam-7001 99 6 extensions extension NOUN ejpam-7001 99 7 of of ADP ejpam-7001 99 8 the the DET ejpam-7001 99 9 crtfw crtfw NOUN ejpam-7001 99 10 distribution distribution NOUN ejpam-7001 99 11 include include VERB ejpam-7001 99 12 : : PUNCT ejpam-7001 99 13 • • NUM ejpam-7001 99 14 setting set VERB ejpam-7001 99 15 λ1 λ1 ADJ ejpam-7001 99 16 = = SYM ejpam-7001 99 17 λ2 λ2 NOUN ejpam-7001 99 18 = = SYM ejpam-7001 99 19 1 1 NUM ejpam-7001 99 20 in in ADP ejpam-7001 99 21 equation equation NOUN ejpam-7001 99 22 ( ( PUNCT ejpam-7001 99 23 8) 8) NUM ejpam-7001 99 24 reduces reduce VERB ejpam-7001 99 25 it it PRON ejpam-7001 99 26 to to ADP ejpam-7001 99 27 the the DET ejpam-7001 99 28 fw fw ADJ ejpam-7001 99 29 distribution distribution NOUN ejpam-7001 99 30 [ [ X ejpam-7001 99 31 31 31 NUM ejpam-7001 99 32 ] ] PUNCT ejpam-7001 99 33 as as ADP ejpam-7001 99 34 in in ADP ejpam-7001 99 35 equation equation NOUN ejpam-7001 99 36 ( ( PUNCT ejpam-7001 99 37 3 3 NUM ejpam-7001 99 38 ) ) PUNCT ejpam-7001 99 39 . . PUNCT ejpam-7001 100 1 • • NUM ejpam-7001 100 2 setting set VERB ejpam-7001 100 3 λ1 λ1 ADJ ejpam-7001 100 4 = = SYM ejpam-7001 100 5 λ2 λ2 NOUN ejpam-7001 100 6 = = NOUN ejpam-7001 100 7 m m NOUN ejpam-7001 100 8 = = SYM ejpam-7001 100 9 k k NOUN ejpam-7001 100 10 = = SYM ejpam-7001 100 11 1 1 NUM ejpam-7001 100 12 in in ADP ejpam-7001 100 13 equation equation NOUN ejpam-7001 100 14 ( ( PUNCT ejpam-7001 100 15 8) 8) NUM ejpam-7001 100 16 gives give VERB ejpam-7001 100 17 the the DET ejpam-7001 100 18 fréchet fréchet NOUN ejpam-7001 100 19 distribution distribution NOUN ejpam-7001 100 20 [ [ X ejpam-7001 100 21 24 24 NUM ejpam-7001 100 22 ] ] PUNCT ejpam-7001 100 23 with with ADP ejpam-7001 100 24 parameters parameter NOUN ejpam-7001 100 25 α α NOUN ejpam-7001 100 26 and and CCONJ ejpam-7001 100 27 β β NOUN ejpam-7001 100 28 . . NOUN ejpam-7001 100 29 • • NOUN ejpam-7001 100 30 setting set VERB ejpam-7001 100 31 β β NOUN ejpam-7001 100 32 = = SYM ejpam-7001 100 33 1 1 NUM ejpam-7001 100 34 in in ADP ejpam-7001 100 35 equation equation NOUN ejpam-7001 100 36 ( ( PUNCT ejpam-7001 100 37 3 3 X ejpam-7001 100 38 ) ) PUNCT ejpam-7001 100 39 results result NOUN ejpam-7001 100 40 in in ADP ejpam-7001 100 41 the the DET ejpam-7001 100 42 cubic cubic ADJ ejpam-7001 100 43 rank rank NOUN ejpam-7001 100 44 transmuted transmute VERB ejpam-7001 100 45 fréchet fréchet NOUN ejpam-7001 100 46 distribution distribution NOUN ejpam-7001 100 47 [ [ X ejpam-7001 100 48 7 7 NUM ejpam-7001 100 49 ] ] PUNCT ejpam-7001 100 50 . . PUNCT ejpam-7001 101 1 • • NUM ejpam-7001 101 2 setting set VERB ejpam-7001 101 3 λ2 λ2 NOUN ejpam-7001 101 4 = = SYM ejpam-7001 101 5 2 2 NUM ejpam-7001 101 6 in in ADP ejpam-7001 101 7 equation equation NOUN ejpam-7001 101 8 ( ( PUNCT ejpam-7001 101 9 3 3 X ejpam-7001 101 10 ) ) PUNCT ejpam-7001 101 11 defines define VERB ejpam-7001 101 12 a a DET ejpam-7001 101 13 new new ADJ ejpam-7001 101 14 quadratic quadratic ADJ ejpam-7001 101 15 rank rank NOUN ejpam-7001 101 16 transmuted transmute VERB ejpam-7001 101 17 fréchetweibull fréchetweibull NOUN ejpam-7001 101 18 distribution distribution NOUN ejpam-7001 101 19 , , PUNCT ejpam-7001 101 20 introduced introduce VERB ejpam-7001 101 21 in in ADP ejpam-7001 101 22 section section NOUN ejpam-7001 101 23 2 2 NUM ejpam-7001 101 24 . . PUNCT ejpam-7001 101 25 figure figure NOUN ejpam-7001 101 26 2(left 2(left NOUN ejpam-7001 101 27 ) ) PUNCT ejpam-7001 101 28 illustrates illustrate VERB ejpam-7001 101 29 possible possible ADJ ejpam-7001 101 30 shapes shape NOUN ejpam-7001 101 31 of of ADP ejpam-7001 101 32 the the DET ejpam-7001 101 33 pdf pdf NOUN ejpam-7001 101 34 for for ADP ejpam-7001 101 35 selected select VERB ejpam-7001 101 36 k k PROPN ejpam-7001 101 37 values value NOUN ejpam-7001 101 38 with with ADP ejpam-7001 101 39 λ1 λ1 PROPN ejpam-7001 101 40 = = NOUN ejpam-7001 101 41 0.005 0.005 NUM ejpam-7001 101 42 , , PUNCT ejpam-7001 101 43 λ2 λ2 NOUN ejpam-7001 101 44 = = SYM ejpam-7001 101 45 −0.05 −0.05 PROPN ejpam-7001 101 46 , , PUNCT ejpam-7001 101 47 α α NOUN ejpam-7001 101 48 = = SYM ejpam-7001 101 49 0.5 0.5 NUM ejpam-7001 101 50 , , PUNCT ejpam-7001 101 51 β β X ejpam-7001 101 52 = = SYM ejpam-7001 101 53 0.5 0.5 NUM ejpam-7001 101 54 , , PUNCT ejpam-7001 101 55 and and CCONJ ejpam-7001 101 56 m m PROPN ejpam-7001 101 57 = = ADJ ejpam-7001 101 58 1.5 1.5 NUM ejpam-7001 101 59 . . PUNCT ejpam-7001 102 1 figure figure NOUN ejpam-7001 102 2 2(right 2(right NUM ejpam-7001 102 3 ) ) PUNCT ejpam-7001 102 4 shows show VERB ejpam-7001 102 5 the the DET ejpam-7001 102 6 pdf pdf NOUN ejpam-7001 102 7 for for ADP ejpam-7001 102 8 selected select VERB ejpam-7001 102 9 m m PROPN ejpam-7001 102 10 values value NOUN ejpam-7001 102 11 with with ADP ejpam-7001 102 12 λ1 λ1 PROPN ejpam-7001 102 13 = = NOUN ejpam-7001 102 14 0.005 0.005 NUM ejpam-7001 102 15 , , PUNCT ejpam-7001 102 16 λ2 λ2 NOUN ejpam-7001 102 17 = = SYM ejpam-7001 102 18 −0.05 −0.05 PROPN ejpam-7001 102 19 , , PUNCT ejpam-7001 102 20 α α NOUN ejpam-7001 102 21 = = SYM ejpam-7001 102 22 0.5 0.5 NUM ejpam-7001 102 23 , , PUNCT ejpam-7001 102 24 β β X ejpam-7001 102 25 = = SYM ejpam-7001 102 26 0.5 0.5 NUM ejpam-7001 102 27 , , PUNCT ejpam-7001 102 28 and and CCONJ ejpam-7001 102 29 k k PROPN ejpam-7001 102 30 = = SYM ejpam-7001 102 31 3 3 X ejpam-7001 102 32 . . PUNCT ejpam-7001 102 33 similarly similarly ADV ejpam-7001 102 34 , , PUNCT ejpam-7001 102 35 figures figure NOUN ejpam-7001 102 36 4 4 NUM ejpam-7001 102 37 and and CCONJ ejpam-7001 102 38 5 5 NUM ejpam-7001 102 39 show show VERB ejpam-7001 102 40 the the DET ejpam-7001 102 41 pdf pdf NOUN ejpam-7001 102 42 and and CCONJ ejpam-7001 102 43 cdf cdf PROPN ejpam-7001 102 44 of of ADP ejpam-7001 102 45 crtfw crtfw ADJ ejpam-7001 102 46 distribution distribution NOUN ejpam-7001 102 47 for for ADP ejpam-7001 102 48 different different ADJ ejpam-7001 102 49 values value NOUN ejpam-7001 102 50 of of ADP ejpam-7001 102 51 λ1 λ1 PROPN ejpam-7001 102 52 and and CCONJ ejpam-7001 102 53 λ2 λ2 NOUN ejpam-7001 102 54 . . PUNCT ejpam-7001 103 1 clearly clearly ADV ejpam-7001 103 2 , , PUNCT ejpam-7001 103 3 figures figure NOUN ejpam-7001 103 4 2 2 NUM ejpam-7001 103 5 and and CCONJ ejpam-7001 103 6 4 4 NUM ejpam-7001 103 7 demonstrate demonstrate VERB ejpam-7001 103 8 increasing increase VERB ejpam-7001 103 9 - - PUNCT ejpam-7001 103 10 decreasing decrease VERB ejpam-7001 103 11 , , PUNCT ejpam-7001 103 12 positively positively ADV ejpam-7001 103 13 skewed skewed ADJ ejpam-7001 103 14 , , PUNCT ejpam-7001 103 15 and and CCONJ ejpam-7001 103 16 symmetric symmetric ADJ ejpam-7001 103 17 behaviors behavior NOUN ejpam-7001 103 18 of of ADP ejpam-7001 103 19 the the DET ejpam-7001 103 20 density density NOUN ejpam-7001 103 21 function function NOUN ejpam-7001 103 22 , , PUNCT ejpam-7001 103 23 whereas whereas SCONJ ejpam-7001 103 24 figures figure NOUN ejpam-7001 103 25 3 3 NUM ejpam-7001 103 26 and and CCONJ ejpam-7001 103 27 5 5 NUM ejpam-7001 103 28 show show VERB ejpam-7001 103 29 monotonically monotonically ADV ejpam-7001 103 30 increasing increase VERB ejpam-7001 103 31 patterns pattern NOUN ejpam-7001 103 32 of of ADP ejpam-7001 103 33 the the DET ejpam-7001 103 34 distribution distribution NOUN ejpam-7001 103 35 function function NOUN ejpam-7001 103 36 . . PUNCT ejpam-7001 104 1 figure figure VERB ejpam-7001 104 2 2 2 NUM ejpam-7001 104 3 : : PUNCT ejpam-7001 104 4 probability probability NOUN ejpam-7001 104 5 density density NOUN ejpam-7001 104 6 function function NOUN ejpam-7001 104 7 of of ADP ejpam-7001 104 8 crtfw crtfw ADJ ejpam-7001 104 9 distribution distribution NOUN ejpam-7001 104 10 for for ADP ejpam-7001 104 11 selected select VERB ejpam-7001 104 12 values value NOUN ejpam-7001 104 13 of of ADP ejpam-7001 104 14 k k PROPN ejpam-7001 104 15 and and CCONJ ejpam-7001 104 16 m. m. NOUN ejpam-7001 104 17 4 4 NUM ejpam-7001 104 18 . . PUNCT ejpam-7001 104 19 key key ADJ ejpam-7001 104 20 statistical statistical ADJ ejpam-7001 104 21 features feature NOUN ejpam-7001 104 22 of of ADP ejpam-7001 104 23 the the DET ejpam-7001 104 24 cubic cubic ADJ ejpam-7001 104 25 rank rank NOUN ejpam-7001 104 26 transmuted transmute VERB ejpam-7001 104 27 fréchet fréchet NOUN ejpam-7001 104 28 - - PUNCT ejpam-7001 104 29 weibull weibull NOUN ejpam-7001 104 30 distribution distribution NOUN ejpam-7001 104 31 4.1 4.1 NUM ejpam-7001 104 32 . . PUNCT ejpam-7001 105 1 quantile quantile ADJ ejpam-7001 105 2 function function NOUN ejpam-7001 105 3 and and CCONJ ejpam-7001 105 4 mode mode VERB ejpam-7001 105 5 the the DET ejpam-7001 105 6 quantile quantile ADJ ejpam-7001 105 7 function function NOUN ejpam-7001 105 8 , , PUNCT ejpam-7001 105 9 also also ADV ejpam-7001 105 10 known know VERB ejpam-7001 105 11 as as ADP ejpam-7001 105 12 the the DET ejpam-7001 105 13 inverse inverse NOUN ejpam-7001 105 14 cumulative cumulative ADJ ejpam-7001 105 15 distribution distribution NOUN ejpam-7001 105 16 function function NOUN ejpam-7001 105 17 ( ( PUNCT ejpam-7001 105 18 cdf cdf PROPN ejpam-7001 105 19 ) ) PUNCT ejpam-7001 105 20 , , PUNCT ejpam-7001 105 21 provides provide VERB ejpam-7001 105 22 the the DET ejpam-7001 105 23 value value NOUN ejpam-7001 105 24 in in ADP ejpam-7001 105 25 a a DET ejpam-7001 105 26 probability probability NOUN ejpam-7001 105 27 distribution distribution NOUN ejpam-7001 105 28 that that PRON ejpam-7001 105 29 corresponds correspond VERB ejpam-7001 105 30 to to ADP ejpam-7001 105 31 a a DET ejpam-7001 105 32 given give VERB ejpam-7001 105 33 cuimliyangba cuimliyangba PROPN ejpam-7001 105 34 et et PROPN ejpam-7001 105 35 al al PROPN ejpam-7001 105 36 . . PUNCT ejpam-7001 105 37 / / SYM ejpam-7001 105 38 eur eur PROPN ejpam-7001 105 39 . . PUNCT ejpam-7001 106 1 j. j. PROPN ejpam-7001 106 2 pure pure PROPN ejpam-7001 106 3 appl appl PROPN ejpam-7001 106 4 . . PROPN ejpam-7001 106 5 math math PROPN ejpam-7001 106 6 , , PUNCT ejpam-7001 106 7 18 18 NUM ejpam-7001 106 8 ( ( PUNCT ejpam-7001 106 9 4 4 NUM ejpam-7001 106 10 ) ) PUNCT ejpam-7001 106 11 ( ( PUNCT ejpam-7001 106 12 2025 2025 NUM ejpam-7001 106 13 ) ) PUNCT ejpam-7001 106 14 , , PUNCT ejpam-7001 106 15 7001 7001 NUM ejpam-7001 106 16 7 7 NUM ejpam-7001 106 17 of of ADP ejpam-7001 106 18 27 27 NUM ejpam-7001 106 19 figure figure NOUN ejpam-7001 106 20 3 3 NUM ejpam-7001 106 21 : : PUNCT ejpam-7001 106 22 cumulative cumulative ADJ ejpam-7001 106 23 distribution distribution NOUN ejpam-7001 106 24 function function NOUN ejpam-7001 106 25 of of ADP ejpam-7001 106 26 crtfw crtfw ADJ ejpam-7001 106 27 distribution distribution NOUN ejpam-7001 106 28 for for ADP ejpam-7001 106 29 selected select VERB ejpam-7001 106 30 values value NOUN ejpam-7001 106 31 of of ADP ejpam-7001 106 32 α α PROPN ejpam-7001 106 33 and and CCONJ ejpam-7001 106 34 β β X ejpam-7001 106 35 . . PUNCT ejpam-7001 106 36 figure figure VERB ejpam-7001 106 37 4 4 NUM ejpam-7001 106 38 : : PUNCT ejpam-7001 106 39 density density NOUN ejpam-7001 106 40 function function NOUN ejpam-7001 106 41 of of ADP ejpam-7001 106 42 crtfw crtfw ADJ ejpam-7001 106 43 distribution distribution NOUN ejpam-7001 106 44 for for ADP ejpam-7001 106 45 selected select VERB ejpam-7001 106 46 values value NOUN ejpam-7001 106 47 of of ADP ejpam-7001 106 48 λ1 λ1 PROPN ejpam-7001 106 49 and and CCONJ ejpam-7001 106 50 λ2 λ2 PROPN ejpam-7001 106 51 . . PUNCT ejpam-7001 107 1 figure figure NOUN ejpam-7001 107 2 5 5 NUM ejpam-7001 107 3 : : PUNCT ejpam-7001 107 4 distribution distribution NOUN ejpam-7001 107 5 function function NOUN ejpam-7001 107 6 of of ADP ejpam-7001 107 7 crtfw crtfw ADJ ejpam-7001 107 8 distribution distribution NOUN ejpam-7001 107 9 for for ADP ejpam-7001 107 10 selected select VERB ejpam-7001 107 11 values value NOUN ejpam-7001 107 12 of of ADP ejpam-7001 107 13 λ1 λ1 PROPN ejpam-7001 107 14 and and CCONJ ejpam-7001 107 15 λ2 λ2 NOUN ejpam-7001 107 16 . . PUNCT ejpam-7001 108 1 mulative mulative ADJ ejpam-7001 108 2 probability probability NOUN ejpam-7001 108 3 . . PUNCT ejpam-7001 109 1 meanwhile meanwhile ADV ejpam-7001 109 2 , , PUNCT ejpam-7001 109 3 mode mode PROPN ejpam-7001 109 4 is be AUX ejpam-7001 109 5 a a DET ejpam-7001 109 6 measure measure NOUN ejpam-7001 109 7 of of ADP ejpam-7001 109 8 central central ADJ ejpam-7001 109 9 tendency tendency NOUN ejpam-7001 109 10 , , PUNCT ejpam-7001 109 11 highlighting highlight VERB ejpam-7001 109 12 the the DET ejpam-7001 109 13 most most ADV ejpam-7001 109 14 typical typical ADJ ejpam-7001 109 15 item item NOUN ejpam-7001 109 16 by by ADP ejpam-7001 109 17 identifying identify VERB ejpam-7001 109 18 the the DET ejpam-7001 109 19 value value NOUN ejpam-7001 109 20 that that PRON ejpam-7001 109 21 appears appear VERB ejpam-7001 109 22 most most ADV ejpam-7001 109 23 frequently frequently ADV ejpam-7001 109 24 in in ADP ejpam-7001 109 25 a a DET ejpam-7001 109 26 data data NOUN ejpam-7001 109 27 set set VERB ejpam-7001 109 28 . . PUNCT ejpam-7001 110 1 the the DET ejpam-7001 110 2 following follow VERB ejpam-7001 110 3 derivations derivation NOUN ejpam-7001 110 4 represent represent VERB ejpam-7001 110 5 the the DET ejpam-7001 110 6 quantile quantile ADJ ejpam-7001 110 7 function function NOUN ejpam-7001 110 8 and and CCONJ ejpam-7001 110 9 mode mode NOUN ejpam-7001 110 10 of of ADP ejpam-7001 110 11 crtfw crtfw NOUN ejpam-7001 110 12 distribution distribution NOUN ejpam-7001 110 13 , , PUNCT ejpam-7001 110 14 respectively respectively ADV ejpam-7001 110 15 . . PUNCT ejpam-7001 111 1 imliyangba imliyangba PROPN ejpam-7001 111 2 et et PROPN ejpam-7001 111 3 al al PROPN ejpam-7001 111 4 . . PUNCT ejpam-7001 111 5 / / SYM ejpam-7001 111 6 eur eur PROPN ejpam-7001 111 7 . . PUNCT ejpam-7001 112 1 j. j. PROPN ejpam-7001 112 2 pure pure PROPN ejpam-7001 112 3 appl appl PROPN ejpam-7001 112 4 . . PROPN ejpam-7001 112 5 math math PROPN ejpam-7001 112 6 , , PUNCT ejpam-7001 112 7 18 18 NUM ejpam-7001 112 8 ( ( PUNCT ejpam-7001 112 9 4 4 NUM ejpam-7001 112 10 ) ) PUNCT ejpam-7001 112 11 ( ( PUNCT ejpam-7001 112 12 2025 2025 NUM ejpam-7001 112 13 ) ) PUNCT ejpam-7001 112 14 , , PUNCT ejpam-7001 112 15 7001 7001 NUM ejpam-7001 112 16 8 8 NUM ejpam-7001 112 17 of of ADP ejpam-7001 112 18 27 27 NUM ejpam-7001 112 19 the the DET ejpam-7001 112 20 qth qth NOUN ejpam-7001 112 21 quantile quantile NOUN ejpam-7001 112 22 xq xq PROPN ejpam-7001 112 23 of of ADP ejpam-7001 112 24 the the DET ejpam-7001 112 25 crtfw crtfw NOUN ejpam-7001 112 26 distribution distribution NOUN ejpam-7001 112 27 can can AUX ejpam-7001 112 28 be be AUX ejpam-7001 112 29 obtained obtain VERB ejpam-7001 112 30 by by ADP ejpam-7001 112 31 inverting invert VERB ejpam-7001 112 32 its its PRON ejpam-7001 112 33 cdf cdf PROPN ejpam-7001 112 34 ( ( PUNCT ejpam-7001 112 35 equation equation NOUN ejpam-7001 112 36 8) 8) NUM ejpam-7001 112 37 . . PUNCT ejpam-7001 113 1 let let VERB ejpam-7001 113 2 f f PROPN ejpam-7001 113 3 ( ( PUNCT ejpam-7001 113 4 x x X ejpam-7001 113 5 ) ) PUNCT ejpam-7001 113 6 = = SYM ejpam-7001 114 1 q q ADJ ejpam-7001 114 2 , , PUNCT ejpam-7001 114 3 then then ADV ejpam-7001 114 4 λ1g(x λ1g(x X ejpam-7001 114 5 ) ) PUNCT ejpam-7001 114 6 + + CCONJ ejpam-7001 114 7 ( ( PUNCT ejpam-7001 114 8 λ2 λ2 NOUN ejpam-7001 114 9 − − PROPN ejpam-7001 114 10 λ1 λ1 PROPN ejpam-7001 114 11 ) ) PUNCT ejpam-7001 115 1 [ [ X ejpam-7001 115 2 g(x)]2 g(x)]2 NOUN ejpam-7001 115 3 + + CCONJ ejpam-7001 115 4 ( ( PUNCT ejpam-7001 115 5 1− 1− NUM ejpam-7001 115 6 λ1 λ1 ADJ ejpam-7001 115 7 ) ) PUNCT ejpam-7001 116 1 [ [ X ejpam-7001 116 2 g(x)]3 g(x)]3 X ejpam-7001 116 3 = = SYM ejpam-7001 116 4 q q NOUN ejpam-7001 116 5 , , PUNCT ejpam-7001 116 6 which which PRON ejpam-7001 116 7 can can AUX ejpam-7001 116 8 be be AUX ejpam-7001 116 9 rewritten rewrite VERB ejpam-7001 116 10 as as ADP ejpam-7001 116 11 λ1g(x λ1g(x VERB ejpam-7001 116 12 ) ) PUNCT ejpam-7001 116 13 + + CCONJ ejpam-7001 116 14 ( ( PUNCT ejpam-7001 116 15 λ2 λ2 NOUN ejpam-7001 116 16 − − PROPN ejpam-7001 116 17 λ1 λ1 PROPN ejpam-7001 116 18 ) ) PUNCT ejpam-7001 117 1 [ [ X ejpam-7001 117 2 g(x)]2 g(x)]2 NOUN ejpam-7001 117 3 + + CCONJ ejpam-7001 117 4 ( ( PUNCT ejpam-7001 117 5 1− 1− NUM ejpam-7001 117 6 λ1 λ1 ADJ ejpam-7001 117 7 ) ) PUNCT ejpam-7001 118 1 [ [ X ejpam-7001 118 2 g(x)]3 g(x)]3 X ejpam-7001 118 3 − − ADP ejpam-7001 118 4 q q NOUN ejpam-7001 118 5 = = NOUN ejpam-7001 118 6 0 0 NUM ejpam-7001 118 7 , , PUNCT ejpam-7001 118 8 where where SCONJ ejpam-7001 118 9 g(x g(x NOUN ejpam-7001 118 10 ) ) PUNCT ejpam-7001 118 11 = = SYM ejpam-7001 118 12 exp exp NOUN ejpam-7001 118 13 { { PUNCT ejpam-7001 118 14 −βα −βα PROPN ejpam-7001 118 15 ( ( PUNCT ejpam-7001 118 16 m m NOUN ejpam-7001 118 17 x x X ejpam-7001 118 18 ) ) PUNCT ejpam-7001 118 19 αk αk ADP ejpam-7001 118 20 } } PUNCT ejpam-7001 118 21 . . PUNCT ejpam-7001 119 1 solving solve VERB ejpam-7001 119 2 this this DET ejpam-7001 119 3 cubic cubic ADJ ejpam-7001 119 4 equation equation NOUN ejpam-7001 119 5 for for ADP ejpam-7001 119 6 x x PUNCT ejpam-7001 119 7 gives give VERB ejpam-7001 119 8 xq xq X ejpam-7001 119 9 = = VERB ejpam-7001 119 10 m m PROPN ejpam-7001 119 11 { { PUNCT ejpam-7001 119 12 − − PROPN ejpam-7001 119 13 1 1 NUM ejpam-7001 119 14 βα βα NOUN ejpam-7001 119 15 ln ln PROPN ejpam-7001 119 16 y y PROPN ejpam-7001 119 17 } } PUNCT ejpam-7001 119 18 , , PUNCT ejpam-7001 120 1 where where SCONJ ejpam-7001 120 2 y y PROPN ejpam-7001 120 3 = = PUNCT ejpam-7001 120 4 − − PROPN ejpam-7001 120 5 b b PROPN ejpam-7001 120 6 3a 3a NUM ejpam-7001 120 7 − − NUM ejpam-7001 120 8 3 3 NUM ejpam-7001 120 9 √ √ PROPN ejpam-7001 120 10 2ξ1 2ξ1 NUM ejpam-7001 120 11 3a 3a NUM ejpam-7001 120 12 { { PUNCT ejpam-7001 120 13 ξ2 ξ2 NOUN ejpam-7001 120 14 + + CCONJ ejpam-7001 120 15 √ √ VERB ejpam-7001 120 16 4ξ31 4ξ31 NOUN ejpam-7001 120 17 + + CCONJ ejpam-7001 120 18 ξ22 ξ22 NUM ejpam-7001 120 19 } } PUNCT ejpam-7001 120 20 1/3 1/3 NUM ejpam-7001 120 21 + + CCONJ ejpam-7001 120 22 { { PUNCT ejpam-7001 120 23 ξ2 ξ2 NOUN ejpam-7001 120 24 + + CCONJ ejpam-7001 120 25 √ √ VERB ejpam-7001 120 26 4ξ31 4ξ31 NOUN ejpam-7001 120 27 + + CCONJ ejpam-7001 120 28 ξ22 ξ22 NUM ejpam-7001 120 29 } } PUNCT ejpam-7001 120 30 1/3 1/3 NUM ejpam-7001 120 31 3a 3a NUM ejpam-7001 120 32 3 3 NUM ejpam-7001 120 33 √ √ NUM ejpam-7001 120 34 2 2 NUM ejpam-7001 120 35 , , PUNCT ejpam-7001 120 36 ξ1 ξ1 NOUN ejpam-7001 120 37 = = SYM ejpam-7001 120 38 −b2 −b2 PROPN ejpam-7001 120 39 + + CCONJ ejpam-7001 120 40 3ac 3ac ADJ ejpam-7001 120 41 , , PUNCT ejpam-7001 120 42 ξ2 ξ2 NOUN ejpam-7001 120 43 = = SYM ejpam-7001 120 44 −2b3 −2b3 PUNCT ejpam-7001 120 45 + + CCONJ ejpam-7001 120 46 9abc− 9abc− ADJ ejpam-7001 120 47 27a2d 27a2d NOUN ejpam-7001 120 48 , , PUNCT ejpam-7001 120 49 a a DET ejpam-7001 120 50 = = SYM ejpam-7001 120 51 1− 1− NUM ejpam-7001 120 52 λ2 λ2 NOUN ejpam-7001 120 53 , , PUNCT ejpam-7001 120 54 b b NOUN ejpam-7001 120 55 = = SYM ejpam-7001 120 56 λ2 λ2 PROPN ejpam-7001 120 57 − − PROPN ejpam-7001 120 58 λ1 λ1 PROPN ejpam-7001 120 59 , , PUNCT ejpam-7001 120 60 c c NOUN ejpam-7001 120 61 = = SYM ejpam-7001 120 62 λ1 λ1 PROPN ejpam-7001 120 63 , , PUNCT ejpam-7001 120 64 d d NOUN ejpam-7001 120 65 = = SYM ejpam-7001 120 66 −q −q NOUN ejpam-7001 120 67 . . PUNCT ejpam-7001 121 1 ( ( PUNCT ejpam-7001 121 2 10 10 NUM ejpam-7001 121 3 ) ) PUNCT ejpam-7001 121 4 by by ADP ejpam-7001 121 5 setting set VERB ejpam-7001 121 6 q q NOUN ejpam-7001 121 7 = = PUNCT ejpam-7001 121 8 0.25 0.25 NUM ejpam-7001 121 9 , , PUNCT ejpam-7001 121 10 0.50 0.50 NUM ejpam-7001 121 11 , , PUNCT ejpam-7001 121 12 and and CCONJ ejpam-7001 121 13 0.75 0.75 NUM ejpam-7001 121 14 , , PUNCT ejpam-7001 121 15 we we PRON ejpam-7001 121 16 obtain obtain VERB ejpam-7001 121 17 the the DET ejpam-7001 121 18 first first ADJ ejpam-7001 121 19 , , PUNCT ejpam-7001 121 20 second second ADJ ejpam-7001 121 21 ( ( PUNCT ejpam-7001 121 22 median median NOUN ejpam-7001 121 23 ) ) PUNCT ejpam-7001 121 24 , , PUNCT ejpam-7001 121 25 and and CCONJ ejpam-7001 121 26 third third ADJ ejpam-7001 121 27 quartiles quartile NOUN ejpam-7001 121 28 of of ADP ejpam-7001 121 29 the the DET ejpam-7001 121 30 crtfw crtfw NOUN ejpam-7001 121 31 distribution distribution NOUN ejpam-7001 121 32 , , PUNCT ejpam-7001 121 33 respectively respectively ADV ejpam-7001 121 34 . . PUNCT ejpam-7001 122 1 the the DET ejpam-7001 122 2 mode mode NOUN ejpam-7001 122 3 of of ADP ejpam-7001 122 4 the the DET ejpam-7001 122 5 distribution distribution NOUN ejpam-7001 122 6 is be AUX ejpam-7001 122 7 obtained obtain VERB ejpam-7001 122 8 by by ADP ejpam-7001 122 9 differentiating differentiate VERB ejpam-7001 122 10 the the DET ejpam-7001 122 11 logarithm logarithm NOUN ejpam-7001 122 12 of of ADP ejpam-7001 122 13 the the DET ejpam-7001 122 14 pdf pdf NOUN ejpam-7001 122 15 and and CCONJ ejpam-7001 122 16 setting set VERB ejpam-7001 122 17 it it PRON ejpam-7001 122 18 equal equal ADJ ejpam-7001 122 19 to to ADP ejpam-7001 122 20 zero zero NUM ejpam-7001 122 21 : : PUNCT ejpam-7001 122 22 ln ln ADJ ejpam-7001 122 23 f(x f(x PROPN ejpam-7001 122 24 ) ) PUNCT ejpam-7001 123 1 = = SYM ejpam-7001 123 2 ln ln ADJ ejpam-7001 123 3 { { PUNCT ejpam-7001 123 4 λ1 λ1 PROPN ejpam-7001 123 5 + + CCONJ ejpam-7001 123 6 2(λ2 2(λ2 NUM ejpam-7001 123 7 − − NOUN ejpam-7001 123 8 λ1 λ1 PROPN ejpam-7001 123 9 ) ) PUNCT ejpam-7001 123 10 exp{−βα(m exp{−βα(m PROPN ejpam-7001 123 11 / / SYM ejpam-7001 123 12 x)αk}+ x)αk}+ PROPN ejpam-7001 123 13 3(1− 3(1− NUM ejpam-7001 123 14 λ1 λ1 ADJ ejpam-7001 123 15 ) ) PUNCT ejpam-7001 123 16 [ [ PUNCT ejpam-7001 123 17 exp{−βα(m exp{−βα(m PROPN ejpam-7001 123 18 / / SYM ejpam-7001 123 19 x)αk x)αk PROPN ejpam-7001 123 20 } } PUNCT ejpam-7001 123 21 ] ] PUNCT ejpam-7001 123 22 2 2 X ejpam-7001 123 23 } } PUNCT ejpam-7001 123 24 + + CCONJ ejpam-7001 123 25 ln(αk ln(αk PROPN ejpam-7001 123 26 ) ) PUNCT ejpam-7001 123 27 + + CCONJ ejpam-7001 123 28 α α NOUN ejpam-7001 123 29 ln(β ln(β NOUN ejpam-7001 123 30 ) ) PUNCT ejpam-7001 123 31 + + CCONJ ejpam-7001 123 32 ( ( PUNCT ejpam-7001 123 33 αk αk NOUN ejpam-7001 123 34 ) ) PUNCT ejpam-7001 123 35 ln(m)− ln(m)− NOUN ejpam-7001 123 36 ( ( PUNCT ejpam-7001 123 37 1 1 NUM ejpam-7001 123 38 + + CCONJ ejpam-7001 123 39 αk αk NOUN ejpam-7001 123 40 ) ) PUNCT ejpam-7001 123 41 ln(x)− ln(x)− NOUN ejpam-7001 123 42 βα(m βα(m NOUN ejpam-7001 123 43 / / SYM ejpam-7001 123 44 x)αk x)αk PROPN ejpam-7001 123 45 , , PUNCT ejpam-7001 123 46 ∂ ∂ NUM ejpam-7001 123 47 ln ln ADJ ejpam-7001 123 48 f(x f(x PROPN ejpam-7001 123 49 ) ) PUNCT ejpam-7001 123 50 ∂x ∂x PROPN ejpam-7001 123 51 = = SYM ejpam-7001 123 52 0 0 X ejpam-7001 123 53 . . PUNCT ejpam-7001 124 1 explicitly explicitly ADV ejpam-7001 124 2 , , PUNCT ejpam-7001 124 3 the the DET ejpam-7001 124 4 derivative derivative NOUN ejpam-7001 124 5 is be AUX ejpam-7001 124 6 ∂ ∂ NUM ejpam-7001 124 7 ln ln ADJ ejpam-7001 124 8 f(x f(x PROPN ejpam-7001 124 9 ) ) PUNCT ejpam-7001 124 10 ∂x ∂x PROPN ejpam-7001 125 1 = = SYM ejpam-7001 126 1 1 1 NUM ejpam-7001 126 2 x x SYM ejpam-7001 126 3 [ [ PUNCT ejpam-7001 126 4 αkβαmαk αkβαmαk X ejpam-7001 126 5 exp{−βα(m exp{−βα(m SYM ejpam-7001 126 6 / / SYM ejpam-7001 126 7 x)αk x)αk PROPN ejpam-7001 126 8 } } PUNCT ejpam-7001 126 9 { { PUNCT ejpam-7001 126 10 2(λ2 2(λ2 NUM ejpam-7001 126 11 − − NOUN ejpam-7001 126 12 λ1 λ1 PROPN ejpam-7001 126 13 ) ) PUNCT ejpam-7001 127 1 + + CCONJ ejpam-7001 127 2 6(1− 6(1− NUM ejpam-7001 127 3 λ2 λ2 NOUN ejpam-7001 127 4 ) ) PUNCT ejpam-7001 127 5 exp{−βα(m exp{−βα(m PROPN ejpam-7001 127 6 / / SYM ejpam-7001 127 7 x)αk x)αk PROPN ejpam-7001 127 8 } } PUNCT ejpam-7001 127 9 } } PUNCT ejpam-7001 127 10 λ1 λ1 PROPN ejpam-7001 127 11 + + CCONJ ejpam-7001 127 12 2(λ2 2(λ2 NUM ejpam-7001 127 13 − − NOUN ejpam-7001 127 14 λ1 λ1 PROPN ejpam-7001 127 15 ) ) PUNCT ejpam-7001 127 16 exp{−βα(m exp{−βα(m PROPN ejpam-7001 127 17 / / SYM ejpam-7001 127 18 x)αk}+ x)αk}+ PROPN ejpam-7001 128 1 3(1− 3(1− NUM ejpam-7001 128 2 λ1 λ1 ADJ ejpam-7001 128 3 ) ) PUNCT ejpam-7001 128 4 [ [ PUNCT ejpam-7001 128 5 exp{−βα(m exp{−βα(m PROPN ejpam-7001 128 6 / / SYM ejpam-7001 128 7 x)αk x)αk PROPN ejpam-7001 128 8 } } PUNCT ejpam-7001 128 9 ] ] PUNCT ejpam-7001 128 10 2 2 X ejpam-7001 128 11 ] ] PUNCT ejpam-7001 129 1 + + CCONJ ejpam-7001 129 2 αkβαmαk αkβαmαk X ejpam-7001 129 3 x x PUNCT ejpam-7001 129 4 − − PROPN ejpam-7001 129 5 ( ( PUNCT ejpam-7001 129 6 1 1 NUM ejpam-7001 129 7 + + CCONJ ejpam-7001 129 8 αk αk NOUN ejpam-7001 129 9 ) ) PUNCT ejpam-7001 129 10 . . PUNCT ejpam-7001 130 1 by by ADP ejpam-7001 130 2 applying apply VERB ejpam-7001 130 3 the the DET ejpam-7001 130 4 newton newton PROPN ejpam-7001 130 5 - - PUNCT ejpam-7001 130 6 raphson raphson PROPN ejpam-7001 130 7 method method NOUN ejpam-7001 130 8 , , PUNCT ejpam-7001 130 9 the the DET ejpam-7001 130 10 mode mode NOUN ejpam-7001 130 11 of of ADP ejpam-7001 130 12 the the DET ejpam-7001 130 13 crtfw crtfw NOUN ejpam-7001 130 14 distribution distribution NOUN ejpam-7001 130 15 is be AUX ejpam-7001 130 16 found find VERB ejpam-7001 130 17 to to PART ejpam-7001 130 18 be be AUX ejpam-7001 130 19 xmode xmode NOUN ejpam-7001 130 20 = = SYM ejpam-7001 130 21 1.650405 1.650405 NUM ejpam-7001 130 22 . . PUNCT ejpam-7001 131 1 imliyangba imliyangba PROPN ejpam-7001 131 2 et et PROPN ejpam-7001 131 3 al al PROPN ejpam-7001 131 4 . . PUNCT ejpam-7001 131 5 / / SYM ejpam-7001 131 6 eur eur PROPN ejpam-7001 131 7 . . PUNCT ejpam-7001 132 1 j. j. PROPN ejpam-7001 132 2 pure pure PROPN ejpam-7001 132 3 appl appl PROPN ejpam-7001 132 4 . . PROPN ejpam-7001 132 5 math math PROPN ejpam-7001 132 6 , , PUNCT ejpam-7001 132 7 18 18 NUM ejpam-7001 132 8 ( ( PUNCT ejpam-7001 132 9 4 4 NUM ejpam-7001 132 10 ) ) PUNCT ejpam-7001 132 11 ( ( PUNCT ejpam-7001 132 12 2025 2025 NUM ejpam-7001 132 13 ) ) PUNCT ejpam-7001 132 14 , , PUNCT ejpam-7001 132 15 7001 7001 NUM ejpam-7001 132 16 9 9 NUM ejpam-7001 132 17 of of ADP ejpam-7001 132 18 27 27 NUM ejpam-7001 132 19 4.2 4.2 NUM ejpam-7001 132 20 . . PUNCT ejpam-7001 133 1 random random ADJ ejpam-7001 133 2 number number NOUN ejpam-7001 133 3 generation generation NOUN ejpam-7001 133 4 random random ADJ ejpam-7001 133 5 numbers number NOUN ejpam-7001 133 6 from from ADP ejpam-7001 133 7 the the DET ejpam-7001 133 8 cubic cubic ADJ ejpam-7001 133 9 rank rank NOUN ejpam-7001 133 10 transmuted transmute VERB ejpam-7001 133 11 fréchet fréchet NOUN ejpam-7001 133 12 weibull weibull NOUN ejpam-7001 133 13 ( ( PUNCT ejpam-7001 133 14 crtfw crtfw NOUN ejpam-7001 133 15 ) ) PUNCT ejpam-7001 133 16 distribution distribution NOUN ejpam-7001 133 17 can can AUX ejpam-7001 133 18 be be AUX ejpam-7001 133 19 generated generate VERB ejpam-7001 133 20 efficiently efficiently ADV ejpam-7001 133 21 using use VERB ejpam-7001 133 22 the the DET ejpam-7001 133 23 inverse inverse NOUN ejpam-7001 133 24 transform transform NOUN ejpam-7001 133 25 method method NOUN ejpam-7001 133 26 . . PUNCT ejpam-7001 134 1 a a DET ejpam-7001 134 2 random random ADJ ejpam-7001 134 3 observation observation NOUN ejpam-7001 134 4 x x PUNCT ejpam-7001 134 5 from from ADP ejpam-7001 134 6 the the DET ejpam-7001 134 7 distribution distribution NOUN ejpam-7001 134 8 satisfies satisfie NOUN ejpam-7001 134 9 λ1e λ1e X ejpam-7001 134 10 −βα(m −βα(m VERB ejpam-7001 134 11 / / SYM ejpam-7001 134 12 x)αk x)αk PROPN ejpam-7001 134 13 + + CCONJ ejpam-7001 134 14 ( ( PUNCT ejpam-7001 134 15 λ2 λ2 PROPN ejpam-7001 134 16 − − PROPN ejpam-7001 134 17 λ1 λ1 PROPN ejpam-7001 134 18 ) ) PUNCT ejpam-7001 134 19 [ [ PUNCT ejpam-7001 134 20 e−βα(m e−βα(m PROPN ejpam-7001 134 21 / / SYM ejpam-7001 134 22 x)αk x)αk PROPN ejpam-7001 134 23 ] ] PUNCT ejpam-7001 134 24 2 2 NUM ejpam-7001 134 25 + + CCONJ ejpam-7001 134 26 ( ( PUNCT ejpam-7001 134 27 1− 1− NUM ejpam-7001 134 28 λ1 λ1 ADJ ejpam-7001 134 29 ) ) PUNCT ejpam-7001 134 30 [ [ PUNCT ejpam-7001 134 31 e−βα(m e−βα(m PROPN ejpam-7001 134 32 / / SYM ejpam-7001 134 33 x)αk x)αk PROPN ejpam-7001 134 34 ] ] PUNCT ejpam-7001 134 35 3 3 NUM ejpam-7001 134 36 = = SYM ejpam-7001 134 37 u u NOUN ejpam-7001 134 38 , , PUNCT ejpam-7001 134 39 where where SCONJ ejpam-7001 134 40 u u PRON ejpam-7001 134 41 ∼ ∼ VERB ejpam-7001 134 42 u(0 u(0 PROPN ejpam-7001 134 43 , , PUNCT ejpam-7001 134 44 1 1 NUM ejpam-7001 134 45 ) ) PUNCT ejpam-7001 134 46 is be AUX ejpam-7001 134 47 a a DET ejpam-7001 134 48 uniform uniform ADJ ejpam-7001 134 49 random random ADJ ejpam-7001 134 50 variable variable NOUN ejpam-7001 134 51 . . PUNCT ejpam-7001 135 1 simplifying simplify VERB ejpam-7001 135 2 , , PUNCT ejpam-7001 135 3 the the DET ejpam-7001 135 4 random random ADJ ejpam-7001 135 5 variable variable NOUN ejpam-7001 135 6 can can AUX ejpam-7001 135 7 be be AUX ejpam-7001 135 8 expressed express VERB ejpam-7001 135 9 as as ADP ejpam-7001 135 10 xq xq PROPN ejpam-7001 135 11 = = PROPN ejpam-7001 135 12 m m PROPN ejpam-7001 135 13 { { PUNCT ejpam-7001 135 14 − − PROPN ejpam-7001 135 15 1 1 NUM ejpam-7001 135 16 βα βα NOUN ejpam-7001 135 17 ln ln PROPN ejpam-7001 135 18 y y PROPN ejpam-7001 135 19 } } PUNCT ejpam-7001 135 20 −1/(αk −1/(αk PROPN ejpam-7001 135 21 ) ) PUNCT ejpam-7001 135 22 , , PUNCT ejpam-7001 135 23 ( ( PUNCT ejpam-7001 135 24 11 11 NUM ejpam-7001 135 25 ) ) PUNCT ejpam-7001 135 26 where where SCONJ ejpam-7001 135 27 y y PROPN ejpam-7001 135 28 is be AUX ejpam-7001 135 29 computed compute VERB ejpam-7001 135 30 using use VERB ejpam-7001 135 31 equation equation NOUN ejpam-7001 135 32 ( ( PUNCT ejpam-7001 135 33 10 10 NUM ejpam-7001 135 34 ) ) PUNCT ejpam-7001 135 35 with with ADP ejpam-7001 135 36 d d PROPN ejpam-7001 135 37 = = SYM ejpam-7001 135 38 −u −u PROPN ejpam-7001 135 39 . . PUNCT ejpam-7001 136 1 thus thus ADV ejpam-7001 136 2 , , PUNCT ejpam-7001 136 3 given give VERB ejpam-7001 136 4 the the DET ejpam-7001 136 5 parameters parameter NOUN ejpam-7001 136 6 λ1 λ1 ADJ ejpam-7001 136 7 , , PUNCT ejpam-7001 136 8 λ2 λ2 PROPN ejpam-7001 136 9 , , PUNCT ejpam-7001 136 10 α α NOUN ejpam-7001 136 11 , , PUNCT ejpam-7001 136 12 β β X ejpam-7001 136 13 , , PUNCT ejpam-7001 136 14 k k NOUN ejpam-7001 136 15 , , PUNCT ejpam-7001 136 16 and and CCONJ ejpam-7001 136 17 m m PROPN ejpam-7001 136 18 , , PUNCT ejpam-7001 136 19 we we PRON ejpam-7001 136 20 can can AUX ejpam-7001 136 21 generate generate VERB ejpam-7001 136 22 random random ADJ ejpam-7001 136 23 numbers number NOUN ejpam-7001 136 24 from from ADP ejpam-7001 136 25 the the DET ejpam-7001 136 26 crtfw crtfw NOUN ejpam-7001 136 27 distribution distribution NOUN ejpam-7001 136 28 directly directly ADV ejpam-7001 136 29 using use VERB ejpam-7001 136 30 equation equation NOUN ejpam-7001 136 31 ( ( PUNCT ejpam-7001 136 32 11 11 NUM ejpam-7001 136 33 ) ) PUNCT ejpam-7001 136 34 . . PUNCT ejpam-7001 137 1 4.3 4.3 NUM ejpam-7001 137 2 . . PUNCT ejpam-7001 137 3 moments moment NOUN ejpam-7001 137 4 and and CCONJ ejpam-7001 137 5 associated associated ADJ ejpam-7001 137 6 measures measure NOUN ejpam-7001 137 7 moments moment NOUN ejpam-7001 137 8 play play VERB ejpam-7001 137 9 a a DET ejpam-7001 137 10 fundamental fundamental ADJ ejpam-7001 137 11 role role NOUN ejpam-7001 137 12 in in ADP ejpam-7001 137 13 characterising characterise VERB ejpam-7001 137 14 the the DET ejpam-7001 137 15 shape shape NOUN ejpam-7001 137 16 and and CCONJ ejpam-7001 137 17 properties property NOUN ejpam-7001 137 18 of of ADP ejpam-7001 137 19 a a DET ejpam-7001 137 20 probability probability NOUN ejpam-7001 137 21 distribution distribution NOUN ejpam-7001 137 22 . . PUNCT ejpam-7001 138 1 specifically specifically ADV ejpam-7001 138 2 , , PUNCT ejpam-7001 138 3 for for ADP ejpam-7001 138 4 a a DET ejpam-7001 138 5 given give VERB ejpam-7001 138 6 distribution distribution NOUN ejpam-7001 138 7 , , PUNCT ejpam-7001 138 8 the the DET ejpam-7001 138 9 first first ADJ ejpam-7001 138 10 moment moment NOUN ejpam-7001 138 11 represents represent VERB ejpam-7001 138 12 the the DET ejpam-7001 138 13 expected expect VERB ejpam-7001 138 14 value value NOUN ejpam-7001 138 15 , , PUNCT ejpam-7001 138 16 the the DET ejpam-7001 138 17 second second ADJ ejpam-7001 138 18 central central ADJ ejpam-7001 138 19 moment moment NOUN ejpam-7001 138 20 corresponds correspond VERB ejpam-7001 138 21 to to ADP ejpam-7001 138 22 the the DET ejpam-7001 138 23 variance variance NOUN ejpam-7001 138 24 , , PUNCT ejpam-7001 138 25 and and CCONJ ejpam-7001 138 26 the the DET ejpam-7001 138 27 third third ADJ ejpam-7001 138 28 and and CCONJ ejpam-7001 138 29 fourth fourth ADJ ejpam-7001 138 30 standardized standardized ADJ ejpam-7001 138 31 moments moment NOUN ejpam-7001 138 32 describe describe VERB ejpam-7001 138 33 skewness skewness NOUN ejpam-7001 138 34 and and CCONJ ejpam-7001 138 35 kurtosis kurtosis NOUN ejpam-7001 138 36 , , PUNCT ejpam-7001 138 37 respectively respectively ADV ejpam-7001 138 38 . . PUNCT ejpam-7001 139 1 let let VERB ejpam-7001 139 2 x x PRON ejpam-7001 139 3 be be AUX ejpam-7001 139 4 a a DET ejpam-7001 139 5 random random ADJ ejpam-7001 139 6 variable variable NOUN ejpam-7001 139 7 . . PUNCT ejpam-7001 140 1 then then ADV ejpam-7001 140 2 , , PUNCT ejpam-7001 140 3 the the DET ejpam-7001 140 4 rth rth NOUN ejpam-7001 140 5 moment moment NOUN ejpam-7001 140 6 about about ADP ejpam-7001 140 7 the the DET ejpam-7001 140 8 origin origin NOUN ejpam-7001 140 9 is be AUX ejpam-7001 140 10 defined define VERB ejpam-7001 140 11 as as ADP ejpam-7001 140 12 : : PUNCT ejpam-7001 140 13 µ′ µ′ NOUN ejpam-7001 140 14 r r NOUN ejpam-7001 140 15 = = SYM ejpam-7001 140 16 e(xr e(xr X ejpam-7001 140 17 ) ) PUNCT ejpam-7001 140 18 = = SYM ejpam-7001 141 1 ∫ ∫ PROPN ejpam-7001 141 2 ∞ ∞ PROPN ejpam-7001 141 3 0 0 NUM ejpam-7001 142 1 xrf(x xrf(x PROPN ejpam-7001 142 2 ) ) PUNCT ejpam-7001 142 3 dx dx PROPN ejpam-7001 142 4 . . PUNCT ejpam-7001 143 1 using use VERB ejpam-7001 143 2 the the DET ejpam-7001 143 3 pdf pdf NOUN ejpam-7001 143 4 f(x f(x PROPN ejpam-7001 143 5 ) ) PUNCT ejpam-7001 143 6 from from ADP ejpam-7001 143 7 equation equation NOUN ejpam-7001 143 8 ( ( PUNCT ejpam-7001 143 9 9 9 NUM ejpam-7001 143 10 ) ) PUNCT ejpam-7001 143 11 , , PUNCT ejpam-7001 143 12 the the DET ejpam-7001 143 13 rth rth PROPN ejpam-7001 143 14 moment moment NOUN ejpam-7001 143 15 of of ADP ejpam-7001 143 16 the the DET ejpam-7001 143 17 crtfw crtfw NOUN ejpam-7001 143 18 distribution distribution NOUN ejpam-7001 143 19 can can AUX ejpam-7001 143 20 be be AUX ejpam-7001 143 21 expressed express VERB ejpam-7001 143 22 as as ADP ejpam-7001 143 23 µ′ µ′ NOUN ejpam-7001 143 24 r r NOUN ejpam-7001 143 25 = = SYM ejpam-7001 143 26 ∫ ∫ PROPN ejpam-7001 143 27 ∞ ∞ PROPN ejpam-7001 143 28 0 0 NUM ejpam-7001 143 29 xr xr PROPN ejpam-7001 143 30 [ [ PUNCT ejpam-7001 143 31 λ1 λ1 PROPN ejpam-7001 143 32 + + CCONJ ejpam-7001 143 33 2(λ2 2(λ2 NUM ejpam-7001 143 34 − − NOUN ejpam-7001 143 35 λ1 λ1 PROPN ejpam-7001 143 36 ) ) PUNCT ejpam-7001 143 37 exp exp NOUN ejpam-7001 143 38 { { PUNCT ejpam-7001 143 39 − − PROPN ejpam-7001 143 40 βα βα X ejpam-7001 143 41 ( ( PUNCT ejpam-7001 143 42 m m NOUN ejpam-7001 143 43 x x X ejpam-7001 143 44 ) ) PUNCT ejpam-7001 143 45 αk αk ADP ejpam-7001 143 46 } } PUNCT ejpam-7001 144 1 + + CCONJ ejpam-7001 144 2 3(1− 3(1− NUM ejpam-7001 144 3 λ2 λ2 NOUN ejpam-7001 144 4 ) ) PUNCT ejpam-7001 144 5 [ [ PUNCT ejpam-7001 144 6 exp exp NOUN ejpam-7001 144 7 { { PUNCT ejpam-7001 144 8 − − PROPN ejpam-7001 144 9 βα βα X ejpam-7001 144 10 ( ( PUNCT ejpam-7001 144 11 m m NOUN ejpam-7001 144 12 x x X ejpam-7001 144 13 ) ) PUNCT ejpam-7001 144 14 αk αk NOUN ejpam-7001 144 15 } } PUNCT ejpam-7001 144 16 ] ] X ejpam-7001 144 17 2 2 X ejpam-7001 144 18 ] ] PUNCT ejpam-7001 144 19 ×αkβαmαkx−1−αk ×αkβαmαkx−1−αk NOUN ejpam-7001 144 20 exp exp NOUN ejpam-7001 144 21 { { PUNCT ejpam-7001 144 22 − − PROPN ejpam-7001 144 23 βα βα X ejpam-7001 144 24 ( ( PUNCT ejpam-7001 144 25 m m NOUN ejpam-7001 144 26 x x X ejpam-7001 144 27 ) ) PUNCT ejpam-7001 144 28 αk αk ADP ejpam-7001 144 29 } } PUNCT ejpam-7001 144 30 dx dx PROPN ejpam-7001 144 31 . . PUNCT ejpam-7001 145 1 after after ADP ejpam-7001 145 2 simplification simplification NOUN ejpam-7001 145 3 , , PUNCT ejpam-7001 145 4 the the DET ejpam-7001 145 5 rth rth NOUN ejpam-7001 145 6 moment moment NOUN ejpam-7001 145 7 is be AUX ejpam-7001 145 8 given give VERB ejpam-7001 145 9 by by ADP ejpam-7001 145 10 µ′ µ′ NOUN ejpam-7001 145 11 r r NOUN ejpam-7001 145 12 = = SYM ejpam-7001 145 13 mrβr mrβr NOUN ejpam-7001 145 14 / / SYM ejpam-7001 145 15 kγ kγ PROPN ejpam-7001 145 16 ( ( PUNCT ejpam-7001 145 17 1− 1− NUM ejpam-7001 145 18 r r NOUN ejpam-7001 145 19 αk αk NOUN ejpam-7001 145 20 ) ) PUNCT ejpam-7001 145 21 6r/(αk 6r/(αk NUM ejpam-7001 145 22 ) ) PUNCT ejpam-7001 145 23 [ [ PUNCT ejpam-7001 145 24 6r/(αk)λ1 6r/(αk)λ1 NUM ejpam-7001 145 25 + + CCONJ ejpam-7001 145 26 3r/(αk)(λ2 3r/(αk)(λ2 NUM ejpam-7001 145 27 − − NOUN ejpam-7001 145 28 λ1 λ1 PROPN ejpam-7001 145 29 ) ) PUNCT ejpam-7001 145 30 + + NUM ejpam-7001 145 31 2r/(αk)(1− 2r/(αk)(1− NUM ejpam-7001 145 32 λ2 λ2 NOUN ejpam-7001 145 33 ) ) PUNCT ejpam-7001 145 34 ] ] PUNCT ejpam-7001 145 35 . . PUNCT ejpam-7001 146 1 ( ( PUNCT ejpam-7001 146 2 12 12 X ejpam-7001 146 3 ) ) PUNCT ejpam-7001 146 4 substituting substitute VERB ejpam-7001 146 5 r r NOUN ejpam-7001 146 6 = = SYM ejpam-7001 146 7 1 1 NUM ejpam-7001 146 8 in in ADP ejpam-7001 146 9 equation equation NOUN ejpam-7001 146 10 ( ( PUNCT ejpam-7001 146 11 12 12 NUM ejpam-7001 146 12 ) ) PUNCT ejpam-7001 146 13 , , PUNCT ejpam-7001 146 14 the the DET ejpam-7001 146 15 mean mean NOUN ejpam-7001 146 16 of of ADP ejpam-7001 146 17 the the DET ejpam-7001 146 18 crtfw crtfw NOUN ejpam-7001 146 19 distribution distribution NOUN ejpam-7001 146 20 is be AUX ejpam-7001 146 21 µ′ µ′ NOUN ejpam-7001 146 22 1 1 NUM ejpam-7001 146 23 = = SYM ejpam-7001 146 24 mβ1 mβ1 PROPN ejpam-7001 146 25 / / SYM ejpam-7001 146 26 kγ kγ PROPN ejpam-7001 146 27 ( ( PUNCT ejpam-7001 146 28 1− 1− NUM ejpam-7001 146 29 1 1 NUM ejpam-7001 146 30 αk αk NOUN ejpam-7001 146 31 ) ) PUNCT ejpam-7001 146 32 61/(αk 61/(αk NUM ejpam-7001 146 33 ) ) PUNCT ejpam-7001 146 34 [ [ PUNCT ejpam-7001 146 35 61/(αk)λ1 61/(αk)λ1 NUM ejpam-7001 146 36 + + SYM ejpam-7001 146 37 31/(αk)(λ2 31/(αk)(λ2 NUM ejpam-7001 146 38 − − NOUN ejpam-7001 146 39 λ1 λ1 PROPN ejpam-7001 146 40 ) ) PUNCT ejpam-7001 146 41 + + CCONJ ejpam-7001 146 42 21/(αk)(1− 21/(αk)(1− NUM ejpam-7001 146 43 λ2 λ2 NOUN ejpam-7001 146 44 ) ) PUNCT ejpam-7001 146 45 ] ] PUNCT ejpam-7001 146 46 . . PUNCT ejpam-7001 147 1 imliyangba imliyangba PROPN ejpam-7001 147 2 et et PROPN ejpam-7001 147 3 al al PROPN ejpam-7001 147 4 . . PUNCT ejpam-7001 147 5 / / SYM ejpam-7001 147 6 eur eur PROPN ejpam-7001 147 7 . . PUNCT ejpam-7001 148 1 j. j. PROPN ejpam-7001 148 2 pure pure PROPN ejpam-7001 148 3 appl appl PROPN ejpam-7001 148 4 . . PROPN ejpam-7001 148 5 math math PROPN ejpam-7001 148 6 , , PUNCT ejpam-7001 148 7 18 18 NUM ejpam-7001 148 8 ( ( PUNCT ejpam-7001 148 9 4 4 NUM ejpam-7001 148 10 ) ) PUNCT ejpam-7001 148 11 ( ( PUNCT ejpam-7001 148 12 2025 2025 NUM ejpam-7001 148 13 ) ) PUNCT ejpam-7001 148 14 , , PUNCT ejpam-7001 148 15 7001 7001 NUM ejpam-7001 148 16 10 10 NUM ejpam-7001 148 17 of of ADP ejpam-7001 148 18 27 27 NUM ejpam-7001 148 19 the the DET ejpam-7001 148 20 variance variance NOUN ejpam-7001 148 21 can can AUX ejpam-7001 148 22 be be AUX ejpam-7001 148 23 calculated calculate VERB ejpam-7001 148 24 using use VERB ejpam-7001 148 25 var(x var(x PROPN ejpam-7001 148 26 ) ) PUNCT ejpam-7001 149 1 = = SYM ejpam-7001 149 2 µ2 µ2 NOUN ejpam-7001 149 3 = = PUNCT ejpam-7001 149 4 µ′ µ′ NOUN ejpam-7001 149 5 2 2 NUM ejpam-7001 149 6 − − NOUN ejpam-7001 149 7 ( ( PUNCT ejpam-7001 149 8 µ′ µ′ NOUN ejpam-7001 149 9 1 1 NUM ejpam-7001 149 10 ) ) PUNCT ejpam-7001 149 11 2 2 NUM ejpam-7001 149 12 , , PUNCT ejpam-7001 149 13 which which PRON ejpam-7001 149 14 leads lead VERB ejpam-7001 149 15 to to ADP ejpam-7001 149 16 σ2 σ2 PROPN ejpam-7001 149 17 = = SYM ejpam-7001 149 18 m2β2 m2β2 PROPN ejpam-7001 149 19 / / SYM ejpam-7001 149 20 k k NOUN ejpam-7001 149 21 62/(αk 62/(αk NOUN ejpam-7001 149 22 ) ) PUNCT ejpam-7001 149 23 [ [ PUNCT ejpam-7001 149 24 γ γ X ejpam-7001 149 25 ( ( PUNCT ejpam-7001 149 26 1− 1− NUM ejpam-7001 149 27 2 2 NUM ejpam-7001 149 28 αk αk NOUN ejpam-7001 149 29 ) ) PUNCT ejpam-7001 149 30 { { PUNCT ejpam-7001 150 1 62/(αk)λ1 62/(αk)λ1 NUM ejpam-7001 150 2 + + CCONJ ejpam-7001 150 3 32/(αk)(λ2 32/(αk)(λ2 NUM ejpam-7001 150 4 − − NOUN ejpam-7001 150 5 λ1 λ1 NUM ejpam-7001 150 6 ) ) PUNCT ejpam-7001 150 7 + + PROPN ejpam-7001 150 8 62/(αk)(1− 62/(αk)(1− NUM ejpam-7001 150 9 λ2 λ2 NOUN ejpam-7001 150 10 ) ) PUNCT ejpam-7001 150 11 } } PUNCT ejpam-7001 150 12 − − PROPN ejpam-7001 150 13 ( ( PUNCT ejpam-7001 150 14 γ γ X ejpam-7001 150 15 ( ( PUNCT ejpam-7001 150 16 1− 1− NUM ejpam-7001 150 17 1 1 NUM ejpam-7001 150 18 αk αk NOUN ejpam-7001 150 19 ) ) PUNCT ejpam-7001 150 20 { { PUNCT ejpam-7001 150 21 61/(αk)λ1 61/(αk)λ1 NUM ejpam-7001 150 22 + + NUM ejpam-7001 150 23 31/(αk)(λ2 31/(αk)(λ2 NUM ejpam-7001 150 24 − − NOUN ejpam-7001 150 25 λ1 λ1 PROPN ejpam-7001 150 26 ) ) PUNCT ejpam-7001 150 27 + + NUM ejpam-7001 150 28 61/(αk)(1− 61/(αk)(1− NUM ejpam-7001 150 29 λ2 λ2 NOUN ejpam-7001 150 30 ) ) PUNCT ejpam-7001 150 31 } } PUNCT ejpam-7001 150 32 ) ) PUNCT ejpam-7001 150 33 2 2 NUM ejpam-7001 150 34 ] ] PUNCT ejpam-7001 150 35 . . PUNCT ejpam-7001 151 1 higher high ADJ ejpam-7001 151 2 - - PUNCT ejpam-7001 151 3 order order NOUN ejpam-7001 151 4 moments moment NOUN ejpam-7001 151 5 can can AUX ejpam-7001 151 6 be be AUX ejpam-7001 151 7 obtained obtain VERB ejpam-7001 151 8 by by ADP ejpam-7001 151 9 substituting substitute VERB ejpam-7001 151 10 r r NOUN ejpam-7001 151 11 > > X ejpam-7001 151 12 2 2 NUM ejpam-7001 151 13 in in ADP ejpam-7001 151 14 equation equation NOUN ejpam-7001 151 15 ( ( PUNCT ejpam-7001 151 16 12 12 NUM ejpam-7001 151 17 ) ) PUNCT ejpam-7001 151 18 . . PUNCT ejpam-7001 152 1 using use VERB ejpam-7001 152 2 the the DET ejpam-7001 152 3 valyes valye NOUN ejpam-7001 152 4 of of ADP ejpam-7001 152 5 σ2 σ2 NOUN ejpam-7001 152 6 , , PUNCT ejpam-7001 152 7 µ3 µ3 PROPN ejpam-7001 152 8 and and CCONJ ejpam-7001 152 9 µ4 µ4 PROPN ejpam-7001 152 10 ( ( PUNCT ejpam-7001 152 11 see see VERB ejpam-7001 152 12 appendix appendix NOUN ejpam-7001 152 13 ) ) PUNCT ejpam-7001 152 14 , , PUNCT ejpam-7001 152 15 the the DET ejpam-7001 152 16 coefficients coefficient NOUN ejpam-7001 152 17 of of ADP ejpam-7001 152 18 skewness skewness NOUN ejpam-7001 152 19 , , PUNCT ejpam-7001 152 20 kurtosis kurtosis NOUN ejpam-7001 152 21 , , PUNCT ejpam-7001 152 22 and and CCONJ ejpam-7001 152 23 coefficient coefficient NOUN ejpam-7001 152 24 of of ADP ejpam-7001 152 25 variation variation NOUN ejpam-7001 152 26 ( ( PUNCT ejpam-7001 152 27 cv cv NOUN ejpam-7001 152 28 ) ) PUNCT ejpam-7001 152 29 can can AUX ejpam-7001 152 30 be be AUX ejpam-7001 152 31 formulated formulate VERB ejpam-7001 152 32 as as ADP ejpam-7001 152 33 : : PUNCT ejpam-7001 152 34 β1 β1 PROPN ejpam-7001 152 35 = = SYM ejpam-7001 152 36 µ2 µ2 PROPN ejpam-7001 152 37 3 3 NUM ejpam-7001 152 38 µ3 µ3 NOUN ejpam-7001 152 39 2 2 NUM ejpam-7001 152 40 = = SYM ejpam-7001 152 41 ( ( PUNCT ejpam-7001 152 42 c− c− PROPN ejpam-7001 152 43 3ab+ 3ab+ PROPN ejpam-7001 152 44 2a3)2 2a3)2 PROPN ejpam-7001 152 45 ( ( PUNCT ejpam-7001 152 46 b− b− NOUN ejpam-7001 152 47 a2)3 a2)3 NUM ejpam-7001 152 48 , , PUNCT ejpam-7001 152 49 β2 β2 PROPN ejpam-7001 152 50 = = PROPN ejpam-7001 152 51 µ4 µ4 PROPN ejpam-7001 153 1 µ2 µ2 PROPN ejpam-7001 153 2 2 2 NUM ejpam-7001 153 3 = = SYM ejpam-7001 153 4 d− d− PROPN ejpam-7001 153 5 4ac+ 4ac+ NUM ejpam-7001 153 6 6a2b+ 6a2b+ PROPN ejpam-7001 153 7 3a4 3a4 NUM ejpam-7001 153 8 ( ( PUNCT ejpam-7001 153 9 b− b− NOUN ejpam-7001 153 10 a2)2 a2)2 X ejpam-7001 153 11 and and CCONJ ejpam-7001 153 12 cv cv PROPN ejpam-7001 153 13 = = PROPN ejpam-7001 153 14 σ σ PROPN ejpam-7001 153 15 µ µ X ejpam-7001 153 16 = = SYM ejpam-7001 153 17 √ √ PROPN ejpam-7001 153 18 b− b− NOUN ejpam-7001 153 19 a2 a2 PROPN ejpam-7001 153 20 a a DET ejpam-7001 153 21 table table NOUN ejpam-7001 153 22 1 1 NUM ejpam-7001 153 23 : : PUNCT ejpam-7001 153 24 mean mean VERB ejpam-7001 153 25 , , PUNCT ejpam-7001 153 26 variance variance NOUN ejpam-7001 153 27 , , PUNCT ejpam-7001 153 28 skewness skewness NOUN ejpam-7001 153 29 , , PUNCT ejpam-7001 153 30 kurtosis kurtosis NOUN ejpam-7001 153 31 , , PUNCT ejpam-7001 153 32 cv cv NOUN ejpam-7001 153 33 and and CCONJ ejpam-7001 153 34 index index NOUN ejpam-7001 153 35 of of ADP ejpam-7001 153 36 dispersion dispersion NOUN ejpam-7001 153 37 for for ADP ejpam-7001 153 38 the the DET ejpam-7001 153 39 crtfw crtfw NOUN ejpam-7001 153 40 distribution distribution NOUN ejpam-7001 153 41 . . PUNCT ejpam-7001 154 1 mean mean ADJ ejpam-7001 154 2 variance variance NOUN ejpam-7001 154 3 skewness skewness NOUN ejpam-7001 154 4 kurtosis kurtosis VERB ejpam-7001 154 5 cv cv NOUN ejpam-7001 154 6 index index NOUN ejpam-7001 154 7 of of ADP ejpam-7001 154 8 dispersion dispersion NOUN ejpam-7001 154 9 k k NOUN ejpam-7001 154 10 = = SYM ejpam-7001 154 11 0.5 0.5 NUM ejpam-7001 154 12 0.04662 0.04662 NUM ejpam-7001 154 13 0.00071 0.00071 NUM ejpam-7001 154 14 0.17344 0.17344 NUM ejpam-7001 154 15 2.04609 2.04609 NUM ejpam-7001 154 16 0.57111 0.57111 NUM ejpam-7001 154 17 0.01520 0.01520 NUM ejpam-7001 154 18 k k NOUN ejpam-7001 155 1 = = SYM ejpam-7001 155 2 1.5 1.5 NUM ejpam-7001 155 3 0.01512 0.01512 NUM ejpam-7001 155 4 0.00024 0.00024 NUM ejpam-7001 155 5 0.56704 0.56704 NUM ejpam-7001 155 6 1.99222 1.99222 NUM ejpam-7001 155 7 1.02521 1.02521 NUM ejpam-7001 155 8 0.01589 0.01589 NUM ejpam-7001 155 9 k k NOUN ejpam-7001 155 10 = = PUNCT ejpam-7001 155 11 1.8 1.8 NUM ejpam-7001 155 12 0.01159 0.01159 NUM ejpam-7001 155 13 0.00014 0.00014 NUM ejpam-7001 155 14 0.86991 0.86991 NUM ejpam-7001 155 15 2.64790 2.64790 NUM ejpam-7001 155 16 1.02511 1.02511 NUM ejpam-7001 155 17 0.01219 0.01219 NUM ejpam-7001 155 18 k k NOUN ejpam-7001 155 19 = = SYM ejpam-7001 155 20 2.5 2.5 NUM ejpam-7001 155 21 0.00405 0.00405 NUM ejpam-7001 155 22 0.00005 0.00005 NUM ejpam-7001 155 23 1.67504 1.67504 NUM ejpam-7001 155 24 4.71026 4.71026 NUM ejpam-7001 155 25 1.71114 1.71114 NUM ejpam-7001 155 26 0.01185 0.01185 NUM ejpam-7001 155 27 m m NOUN ejpam-7001 155 28 = = NUM ejpam-7001 155 29 0.5 0.5 NUM ejpam-7001 155 30 0.15383 0.15383 NUM ejpam-7001 155 31 0.00804 0.00804 NUM ejpam-7001 155 32 0.00378 0.00378 NUM ejpam-7001 155 33 1.42756 1.42756 NUM ejpam-7001 155 34 0.58290 0.58290 NUM ejpam-7001 155 35 0.05227 0.05227 NUM ejpam-7001 155 36 m m NOUN ejpam-7001 155 37 = = NOUN ejpam-7001 155 38 1.5 1.5 NUM ejpam-7001 155 39 0.01128 0.01128 NUM ejpam-7001 155 40 0.00021 0.00021 NUM ejpam-7001 155 41 0.96897 0.96897 NUM ejpam-7001 156 1 2.53893 2.53893 NUM ejpam-7001 156 2 1.27783 1.27783 NUM ejpam-7001 156 3 0.01842 0.01842 NUM ejpam-7001 156 4 m m NOUN ejpam-7001 156 5 = = VERB ejpam-7001 156 6 2.0 2.0 NUM ejpam-7001 156 7 0.00652 0.00652 NUM ejpam-7001 156 8 0.00007 0.00007 NUM ejpam-7001 156 9 0.75778 0.75778 NUM ejpam-7001 156 10 1.61207 1.61207 NUM ejpam-7001 156 11 1.25843 1.25843 NUM ejpam-7001 156 12 0.01033 0.01033 NUM ejpam-7001 156 13 m m NOUN ejpam-7001 156 14 = = NUM ejpam-7001 156 15 2.5 2.5 NUM ejpam-7001 156 16 0.00460 0.00460 NUM ejpam-7001 156 17 0.00002 0.00002 NUM ejpam-7001 156 18 0.64562 0.64562 NUM ejpam-7001 156 19 1.87735 1.87735 NUM ejpam-7001 156 20 1.02732 1.02732 NUM ejpam-7001 156 21 0.00485 0.00485 NUM ejpam-7001 156 22 the the DET ejpam-7001 156 23 mean mean ADJ ejpam-7001 156 24 , , PUNCT ejpam-7001 156 25 variance variance NOUN ejpam-7001 156 26 , , PUNCT ejpam-7001 156 27 skewness skewness NOUN ejpam-7001 156 28 , , PUNCT ejpam-7001 156 29 kurtosis kurtosis NOUN ejpam-7001 156 30 , , PUNCT ejpam-7001 156 31 cv cv NOUN ejpam-7001 156 32 and and CCONJ ejpam-7001 156 33 index index NOUN ejpam-7001 156 34 of of ADP ejpam-7001 156 35 dispersion dispersion NOUN ejpam-7001 156 36 of of ADP ejpam-7001 156 37 the the DET ejpam-7001 156 38 crtfw crtfw NOUN ejpam-7001 156 39 distribution distribution NOUN ejpam-7001 156 40 for for ADP ejpam-7001 156 41 different different ADJ ejpam-7001 156 42 values value NOUN ejpam-7001 156 43 of of ADP ejpam-7001 156 44 k k PROPN ejpam-7001 156 45 and and CCONJ ejpam-7001 156 46 m m PROPN ejpam-7001 156 47 are be AUX ejpam-7001 156 48 given give VERB ejpam-7001 156 49 in in ADP ejpam-7001 156 50 table table NOUN ejpam-7001 156 51 1 1 NUM ejpam-7001 156 52 . . PUNCT ejpam-7001 157 1 it it PRON ejpam-7001 157 2 can can AUX ejpam-7001 157 3 be be AUX ejpam-7001 157 4 observed observe VERB ejpam-7001 157 5 that that SCONJ ejpam-7001 157 6 the the DET ejpam-7001 157 7 mean mean ADJ ejpam-7001 157 8 , , PUNCT ejpam-7001 157 9 variance variance NOUN ejpam-7001 157 10 and and CCONJ ejpam-7001 157 11 index index NOUN ejpam-7001 157 12 of of ADP ejpam-7001 157 13 diversity diversity NOUN ejpam-7001 157 14 decreases decrease VERB ejpam-7001 157 15 as as ADP ejpam-7001 157 16 the the DET ejpam-7001 157 17 value value NOUN ejpam-7001 157 18 of of ADP ejpam-7001 157 19 k k PROPN ejpam-7001 157 20 and and CCONJ ejpam-7001 157 21 m m PROPN ejpam-7001 157 22 increases increase NOUN ejpam-7001 157 23 for for ADP ejpam-7001 157 24 fixed fix VERB ejpam-7001 157 25 values value NOUN ejpam-7001 157 26 of of ADP ejpam-7001 157 27 α α NOUN ejpam-7001 157 28 = = SYM ejpam-7001 157 29 0.5 0.5 NUM ejpam-7001 157 30 , , PUNCT ejpam-7001 157 31 β β X ejpam-7001 157 32 = = SYM ejpam-7001 157 33 0.5 0.5 NUM ejpam-7001 157 34 , , PUNCT ejpam-7001 157 35 λ1 λ1 ADJ ejpam-7001 157 36 = = NOUN ejpam-7001 157 37 0.005 0.005 NUM ejpam-7001 157 38 , , PUNCT ejpam-7001 157 39 and and CCONJ ejpam-7001 157 40 λ2 λ2 NOUN ejpam-7001 157 41 = = SYM ejpam-7001 158 1 −0.05 −0.05 NOUN ejpam-7001 158 2 . . PUNCT ejpam-7001 159 1 4.4 4.4 NUM ejpam-7001 159 2 . . PUNCT ejpam-7001 160 1 moment moment NOUN ejpam-7001 160 2 generating generate VERB ejpam-7001 160 3 and and CCONJ ejpam-7001 160 4 characteristic characteristic ADJ ejpam-7001 160 5 functions function NOUN ejpam-7001 160 6 the the DET ejpam-7001 160 7 moment moment NOUN ejpam-7001 160 8 generating generate VERB ejpam-7001 160 9 function function NOUN ejpam-7001 160 10 ( ( PUNCT ejpam-7001 160 11 mgf mgf PROPN ejpam-7001 160 12 ) ) PUNCT ejpam-7001 160 13 and and CCONJ ejpam-7001 160 14 the the DET ejpam-7001 160 15 characteristic characteristic ADJ ejpam-7001 160 16 function function NOUN ejpam-7001 160 17 are be AUX ejpam-7001 160 18 important important ADJ ejpam-7001 160 19 tools tool NOUN ejpam-7001 160 20 in in ADP ejpam-7001 160 21 probability probability NOUN ejpam-7001 160 22 theory theory NOUN ejpam-7001 160 23 . . PUNCT ejpam-7001 161 1 they they PRON ejpam-7001 161 2 can can AUX ejpam-7001 161 3 be be AUX ejpam-7001 161 4 used use VERB ejpam-7001 161 5 to to PART ejpam-7001 161 6 generate generate VERB ejpam-7001 161 7 the the DET ejpam-7001 161 8 moments moment NOUN ejpam-7001 161 9 of of ADP ejpam-7001 161 10 a a DET ejpam-7001 161 11 distribution distribution NOUN ejpam-7001 161 12 and and CCONJ ejpam-7001 161 13 are be AUX ejpam-7001 161 14 also also ADV ejpam-7001 161 15 valuable valuable ADJ ejpam-7001 161 16 in in ADP ejpam-7001 161 17 studying study VERB ejpam-7001 161 18 various various ADJ ejpam-7001 161 19 properties property NOUN ejpam-7001 161 20 of of ADP ejpam-7001 161 21 the the DET ejpam-7001 161 22 distribution distribution NOUN ejpam-7001 161 23 . . PUNCT ejpam-7001 162 1 the the DET ejpam-7001 162 2 moment moment NOUN ejpam-7001 162 3 generating generate VERB ejpam-7001 162 4 function function NOUN ejpam-7001 162 5 of of ADP ejpam-7001 162 6 a a DET ejpam-7001 162 7 random random ADJ ejpam-7001 162 8 variable variable NOUN ejpam-7001 162 9 x x PUNCT ejpam-7001 162 10 is be AUX ejpam-7001 162 11 defined define VERB ejpam-7001 162 12 as as ADP ejpam-7001 162 13 : : PUNCT ejpam-7001 162 14 mx(t mx(t NUM ejpam-7001 162 15 ) ) PUNCT ejpam-7001 162 16 = = SYM ejpam-7001 163 1 e(etx e(etx CCONJ ejpam-7001 163 2 ) ) PUNCT ejpam-7001 164 1 = = SYM ejpam-7001 164 2 ∫ ∫ PROPN ejpam-7001 165 1 ∞ ∞ NOUN ejpam-7001 165 2 0 0 NUM ejpam-7001 166 1 etxf(x)dx etxf(x)dx NOUN ejpam-7001 166 2 . . PUNCT ejpam-7001 167 1 therefore therefore ADV ejpam-7001 167 2 , , PUNCT ejpam-7001 167 3 the the DET ejpam-7001 167 4 mgf mgf PROPN ejpam-7001 167 5 of of ADP ejpam-7001 167 6 the the DET ejpam-7001 167 7 crtfw crtfw NOUN ejpam-7001 167 8 distribution distribution NOUN ejpam-7001 167 9 is be AUX ejpam-7001 167 10 obtained obtain VERB ejpam-7001 167 11 as as ADP ejpam-7001 167 12 mx(t mx(t NOUN ejpam-7001 167 13 ) ) PUNCT ejpam-7001 167 14 = = PUNCT ejpam-7001 168 1 ∞∑ ∞∑ NUM ejpam-7001 168 2 r=0 r=0 NUM ejpam-7001 168 3 tr tr NOUN ejpam-7001 168 4 r r NOUN ejpam-7001 168 5 ! ! PUNCT ejpam-7001 168 6 mrβ mrβ NOUN ejpam-7001 168 7 r r NOUN ejpam-7001 168 8 kγ(1− kγ(1− PROPN ejpam-7001 168 9 r r NOUN ejpam-7001 168 10 αk αk NOUN ejpam-7001 168 11 ) ) PUNCT ejpam-7001 168 12 6 6 NUM ejpam-7001 168 13 r r NOUN ejpam-7001 168 14 αk αk NOUN ejpam-7001 168 15 [ [ PUNCT ejpam-7001 168 16 6 6 NUM ejpam-7001 168 17 r r NOUN ejpam-7001 168 18 αk αk NOUN ejpam-7001 168 19 λ1 λ1 ADJ ejpam-7001 168 20 + + CCONJ ejpam-7001 168 21 3 3 NUM ejpam-7001 168 22 r r NOUN ejpam-7001 168 23 αk αk NOUN ejpam-7001 168 24 ( ( PUNCT ejpam-7001 168 25 λ2 λ2 NOUN ejpam-7001 168 26 − − PROPN ejpam-7001 168 27 λ1 λ1 PROPN ejpam-7001 168 28 ) ) PUNCT ejpam-7001 169 1 + + CCONJ ejpam-7001 169 2 2 2 NUM ejpam-7001 169 3 r r NOUN ejpam-7001 169 4 αk αk NOUN ejpam-7001 169 5 ( ( PUNCT ejpam-7001 169 6 1− 1− NUM ejpam-7001 169 7 λ2 λ2 NOUN ejpam-7001 169 8 ) ) PUNCT ejpam-7001 169 9 ] ] PUNCT ejpam-7001 169 10 . . PUNCT ejpam-7001 170 1 imliyangba imliyangba PROPN ejpam-7001 170 2 et et PROPN ejpam-7001 170 3 al al PROPN ejpam-7001 170 4 . . PUNCT ejpam-7001 170 5 / / SYM ejpam-7001 170 6 eur eur PROPN ejpam-7001 170 7 . . PUNCT ejpam-7001 171 1 j. j. PROPN ejpam-7001 171 2 pure pure PROPN ejpam-7001 171 3 appl appl PROPN ejpam-7001 171 4 . . PROPN ejpam-7001 171 5 math math PROPN ejpam-7001 171 6 , , PUNCT ejpam-7001 171 7 18 18 NUM ejpam-7001 171 8 ( ( PUNCT ejpam-7001 171 9 4 4 NUM ejpam-7001 171 10 ) ) PUNCT ejpam-7001 171 11 ( ( PUNCT ejpam-7001 171 12 2025 2025 NUM ejpam-7001 171 13 ) ) PUNCT ejpam-7001 171 14 , , PUNCT ejpam-7001 171 15 7001 7001 NUM ejpam-7001 171 16 11 11 NUM ejpam-7001 171 17 of of ADP ejpam-7001 171 18 27 27 NUM ejpam-7001 171 19 the the DET ejpam-7001 171 20 characteristic characteristic ADJ ejpam-7001 171 21 function function NOUN ejpam-7001 171 22 of of ADP ejpam-7001 171 23 a a DET ejpam-7001 171 24 crtfw crtfw NOUN ejpam-7001 171 25 distribution distribution NOUN ejpam-7001 171 26 is be AUX ejpam-7001 171 27 derived derive VERB ejpam-7001 171 28 in in ADP ejpam-7001 171 29 the the DET ejpam-7001 171 30 following following ADJ ejpam-7001 171 31 way way NOUN ejpam-7001 171 32 : : PUNCT ejpam-7001 171 33 φ(t φ(t NUM ejpam-7001 171 34 ) ) PUNCT ejpam-7001 171 35 = = PUNCT ejpam-7001 172 1 ∞∑ ∞∑ NUM ejpam-7001 172 2 r=0 r=0 PROPN ejpam-7001 172 3 ( ( PUNCT ejpam-7001 172 4 it)r it)r PROPN ejpam-7001 172 5 r r NOUN ejpam-7001 172 6 ! ! PUNCT ejpam-7001 172 7 mrβ mrβ NOUN ejpam-7001 172 8 r r NOUN ejpam-7001 172 9 kγ(1− kγ(1− PROPN ejpam-7001 172 10 r r NOUN ejpam-7001 172 11 αk αk NOUN ejpam-7001 172 12 ) ) PUNCT ejpam-7001 172 13 6 6 NUM ejpam-7001 172 14 r r NOUN ejpam-7001 172 15 αk αk NOUN ejpam-7001 172 16 [ [ PUNCT ejpam-7001 172 17 6 6 NUM ejpam-7001 172 18 r r NOUN ejpam-7001 172 19 αk αk NOUN ejpam-7001 172 20 λ1 λ1 ADJ ejpam-7001 172 21 + + CCONJ ejpam-7001 172 22 3 3 NUM ejpam-7001 172 23 r r NOUN ejpam-7001 172 24 αk αk NOUN ejpam-7001 172 25 ( ( PUNCT ejpam-7001 172 26 λ2 λ2 NOUN ejpam-7001 172 27 − − PROPN ejpam-7001 172 28 λ1 λ1 PROPN ejpam-7001 172 29 ) ) PUNCT ejpam-7001 173 1 + + CCONJ ejpam-7001 173 2 2 2 NUM ejpam-7001 173 3 r r NOUN ejpam-7001 173 4 αk αk NOUN ejpam-7001 173 5 ( ( PUNCT ejpam-7001 173 6 1− 1− NUM ejpam-7001 173 7 λ2 λ2 NOUN ejpam-7001 173 8 ) ) PUNCT ejpam-7001 173 9 ] ] PUNCT ejpam-7001 173 10 . . PUNCT ejpam-7001 174 1 5 5 X ejpam-7001 174 2 . . X ejpam-7001 174 3 reliability reliability NOUN ejpam-7001 174 4 measures measure NOUN ejpam-7001 174 5 , , PUNCT ejpam-7001 174 6 entropy entropy NOUN ejpam-7001 174 7 , , PUNCT ejpam-7001 174 8 and and CCONJ ejpam-7001 174 9 order order NOUN ejpam-7001 174 10 statistics statistic NOUN ejpam-7001 174 11 of of ADP ejpam-7001 174 12 the the DET ejpam-7001 174 13 cubic cubic ADJ ejpam-7001 174 14 rank rank NOUN ejpam-7001 174 15 transmuted transmute VERB ejpam-7001 174 16 fréchet fréchet NOUN ejpam-7001 174 17 - - PUNCT ejpam-7001 174 18 weibull weibull NOUN ejpam-7001 174 19 distribution distribution NOUN ejpam-7001 174 20 5.1 5.1 NUM ejpam-7001 174 21 . . PUNCT ejpam-7001 175 1 hazard hazard NOUN ejpam-7001 175 2 rate rate NOUN ejpam-7001 175 3 function function VERB ejpam-7001 175 4 the the DET ejpam-7001 175 5 hazard hazard NOUN ejpam-7001 175 6 rate rate NOUN ejpam-7001 175 7 function function NOUN ejpam-7001 175 8 ( ( PUNCT ejpam-7001 175 9 hrf hrf PROPN ejpam-7001 175 10 ) ) PUNCT ejpam-7001 175 11 of of ADP ejpam-7001 175 12 a a DET ejpam-7001 175 13 distribution distribution NOUN ejpam-7001 175 14 is be AUX ejpam-7001 175 15 closely closely ADV ejpam-7001 175 16 related relate VERB ejpam-7001 175 17 to to ADP ejpam-7001 175 18 its its PRON ejpam-7001 175 19 survival survival NOUN ejpam-7001 175 20 function function NOUN ejpam-7001 175 21 . . PUNCT ejpam-7001 176 1 for for ADP ejpam-7001 176 2 the the DET ejpam-7001 176 3 crtfw crtfw NOUN ejpam-7001 176 4 distribution distribution NOUN ejpam-7001 176 5 , , PUNCT ejpam-7001 176 6 the the DET ejpam-7001 176 7 survival survival NOUN ejpam-7001 176 8 function function PROPN ejpam-7001 176 9 s(t s(t PROPN ejpam-7001 176 10 ) ) PUNCT ejpam-7001 176 11 is be AUX ejpam-7001 176 12 defined define VERB ejpam-7001 176 13 as as ADP ejpam-7001 176 14 the the DET ejpam-7001 176 15 probability probability NOUN ejpam-7001 176 16 that that SCONJ ejpam-7001 176 17 the the DET ejpam-7001 176 18 lifetime lifetime NOUN ejpam-7001 176 19 t t PROPN ejpam-7001 176 20 exceeds exceed VERB ejpam-7001 176 21 a a DET ejpam-7001 176 22 given give VERB ejpam-7001 176 23 time time NOUN ejpam-7001 176 24 t. t. PROPN ejpam-7001 176 25 thus thus ADV ejpam-7001 176 26 , , PUNCT ejpam-7001 176 27 the the DET ejpam-7001 176 28 survival survival NOUN ejpam-7001 176 29 function function NOUN ejpam-7001 176 30 of of ADP ejpam-7001 176 31 the the DET ejpam-7001 176 32 crtfw crtfw NOUN ejpam-7001 176 33 distribution distribution NOUN ejpam-7001 176 34 is be AUX ejpam-7001 176 35 given give VERB ejpam-7001 176 36 by by ADP ejpam-7001 176 37 s(t s(t PROPN ejpam-7001 176 38 ) ) PUNCT ejpam-7001 176 39 = = SYM ejpam-7001 177 1 1− 1− NUM ejpam-7001 177 2 { { PUNCT ejpam-7001 177 3 λ1e λ1e X ejpam-7001 177 4 −βα(m −βα(m NOUN ejpam-7001 177 5 / / SYM ejpam-7001 177 6 t)αk t)αk PROPN ejpam-7001 177 7 + + CCONJ ejpam-7001 177 8 ( ( PUNCT ejpam-7001 177 9 λ2 λ2 NOUN ejpam-7001 177 10 − − PROPN ejpam-7001 177 11 λ1 λ1 PROPN ejpam-7001 177 12 ) ) PUNCT ejpam-7001 177 13 [ [ PUNCT ejpam-7001 177 14 e−βα(m e−βα(m PROPN ejpam-7001 177 15 / / SYM ejpam-7001 177 16 t)αk]2 t)αk]2 NOUN ejpam-7001 177 17 + + CCONJ ejpam-7001 177 18 ( ( PUNCT ejpam-7001 177 19 1− 1− NUM ejpam-7001 177 20 λ1 λ1 ADJ ejpam-7001 177 21 ) ) PUNCT ejpam-7001 177 22 [ [ PUNCT ejpam-7001 177 23 e−βα(m e−βα(m NOUN ejpam-7001 177 24 / / SYM ejpam-7001 177 25 t)αk]3 t)αk]3 NOUN ejpam-7001 177 26 } } PUNCT ejpam-7001 177 27 . . PUNCT ejpam-7001 178 1 correspondingly correspondingly ADV ejpam-7001 178 2 , , PUNCT ejpam-7001 178 3 the the DET ejpam-7001 178 4 hazard hazard NOUN ejpam-7001 178 5 rate rate NOUN ejpam-7001 178 6 function function NOUN ejpam-7001 178 7 ( ( PUNCT ejpam-7001 178 8 hrf hrf PROPN ejpam-7001 178 9 ) ) PUNCT ejpam-7001 178 10 is be AUX ejpam-7001 178 11 obtained obtain VERB ejpam-7001 178 12 as as ADP ejpam-7001 178 13 h(t h(t PROPN ejpam-7001 178 14 ) ) PUNCT ejpam-7001 179 1 = = PRON ejpam-7001 179 2 { { PUNCT ejpam-7001 179 3 λ1 λ1 PROPN ejpam-7001 179 4 + + NUM ejpam-7001 179 5 2(λ2 2(λ2 NUM ejpam-7001 179 6 − − NOUN ejpam-7001 179 7 λ1)e λ1)e NOUN ejpam-7001 179 8 −βα(m −βα(m NOUN ejpam-7001 179 9 / / SYM ejpam-7001 179 10 t)αk t)αk PROPN ejpam-7001 179 11 + + NUM ejpam-7001 179 12 3(1− 3(1− NUM ejpam-7001 179 13 λ1 λ1 NUM ejpam-7001 179 14 ) ) PUNCT ejpam-7001 179 15 [ [ PUNCT ejpam-7001 179 16 e−βα(m e−βα(m PROPN ejpam-7001 179 17 / / SYM ejpam-7001 179 18 t)αk]2 t)αk]2 NOUN ejpam-7001 179 19 } } PUNCT ejpam-7001 179 20 αkβαmαkt−1−αke−βα(m αkβαmαkt−1−αke−βα(m NOUN ejpam-7001 179 21 / / SYM ejpam-7001 179 22 t)αk t)αk PROPN ejpam-7001 179 23 1− 1− NUM ejpam-7001 179 24 { { PUNCT ejpam-7001 179 25 λ1e−βα(m λ1e−βα(m NOUN ejpam-7001 179 26 / / SYM ejpam-7001 179 27 t)αk t)αk PROPN ejpam-7001 179 28 + + CCONJ ejpam-7001 179 29 ( ( PUNCT ejpam-7001 179 30 λ2 λ2 NOUN ejpam-7001 179 31 − − PROPN ejpam-7001 179 32 λ1 λ1 PROPN ejpam-7001 179 33 ) ) PUNCT ejpam-7001 179 34 [ [ PUNCT ejpam-7001 179 35 e−βα(m e−βα(m NOUN ejpam-7001 179 36 / / SYM ejpam-7001 179 37 t)αk t)αk PROPN ejpam-7001 179 38 ] ] SYM ejpam-7001 179 39 2 2 NUM ejpam-7001 179 40 + + CCONJ ejpam-7001 179 41 ( ( PUNCT ejpam-7001 179 42 1− 1− NUM ejpam-7001 179 43 λ1 λ1 ADJ ejpam-7001 179 44 ) ) PUNCT ejpam-7001 179 45 [ [ PUNCT ejpam-7001 179 46 e−βα(m e−βα(m NOUN ejpam-7001 179 47 / / SYM ejpam-7001 179 48 t)αk t)αk PROPN ejpam-7001 179 49 ] ] SYM ejpam-7001 179 50 3 3 NUM ejpam-7001 179 51 } } PUNCT ejpam-7001 179 52 . . PUNCT ejpam-7001 180 1 figures figure NOUN ejpam-7001 180 2 6 6 NUM ejpam-7001 180 3 and and CCONJ ejpam-7001 180 4 7 7 NUM ejpam-7001 180 5 illustrate illustrate VERB ejpam-7001 180 6 the the DET ejpam-7001 180 7 possible possible ADJ ejpam-7001 180 8 shapes shape NOUN ejpam-7001 180 9 of of ADP ejpam-7001 180 10 the the DET ejpam-7001 180 11 survival survival NOUN ejpam-7001 180 12 function function PROPN ejpam-7001 180 13 s(t s(t PROPN ejpam-7001 180 14 ) ) PUNCT ejpam-7001 180 15 and and CCONJ ejpam-7001 180 16 the the DET ejpam-7001 180 17 hazard hazard NOUN ejpam-7001 180 18 figure figure NOUN ejpam-7001 180 19 6 6 NUM ejpam-7001 180 20 : : PUNCT ejpam-7001 180 21 survival survival NOUN ejpam-7001 180 22 function function NOUN ejpam-7001 180 23 of of ADP ejpam-7001 180 24 the the DET ejpam-7001 180 25 crtfw crtfw NOUN ejpam-7001 180 26 distribution distribution NOUN ejpam-7001 180 27 for for ADP ejpam-7001 180 28 selected select VERB ejpam-7001 180 29 values value NOUN ejpam-7001 180 30 of of ADP ejpam-7001 180 31 m m PROPN ejpam-7001 180 32 and and CCONJ ejpam-7001 180 33 k. k. PROPN ejpam-7001 180 34 function function PROPN ejpam-7001 180 35 h(t h(t PROPN ejpam-7001 180 36 ) ) PUNCT ejpam-7001 180 37 , , PUNCT ejpam-7001 180 38 respectively respectively ADV ejpam-7001 180 39 . . PUNCT ejpam-7001 181 1 figure figure NOUN ejpam-7001 181 2 6(left 6(left PROPN ejpam-7001 181 3 ) ) PUNCT ejpam-7001 181 4 shows show VERB ejpam-7001 181 5 the the DET ejpam-7001 181 6 effect effect NOUN ejpam-7001 181 7 of of ADP ejpam-7001 181 8 varying vary VERB ejpam-7001 181 9 the the DET ejpam-7001 181 10 parameter parameter NOUN ejpam-7001 181 11 m m PROPN ejpam-7001 181 12 on on ADP ejpam-7001 181 13 imliyangba imliyangba PROPN ejpam-7001 181 14 et et PROPN ejpam-7001 181 15 al al PROPN ejpam-7001 181 16 . . PUNCT ejpam-7001 181 17 / / SYM ejpam-7001 181 18 eur eur PROPN ejpam-7001 181 19 . . PUNCT ejpam-7001 182 1 j. j. PROPN ejpam-7001 182 2 pure pure PROPN ejpam-7001 182 3 appl appl PROPN ejpam-7001 182 4 . . PROPN ejpam-7001 182 5 math math PROPN ejpam-7001 182 6 , , PUNCT ejpam-7001 182 7 18 18 NUM ejpam-7001 182 8 ( ( PUNCT ejpam-7001 182 9 4 4 NUM ejpam-7001 182 10 ) ) PUNCT ejpam-7001 182 11 ( ( PUNCT ejpam-7001 182 12 2025 2025 NUM ejpam-7001 182 13 ) ) PUNCT ejpam-7001 182 14 , , PUNCT ejpam-7001 182 15 7001 7001 NUM ejpam-7001 182 16 12 12 NUM ejpam-7001 182 17 of of ADP ejpam-7001 182 18 27 27 NUM ejpam-7001 182 19 s(t s(t NUM ejpam-7001 182 20 ) ) PUNCT ejpam-7001 182 21 , , PUNCT ejpam-7001 182 22 with with ADP ejpam-7001 182 23 λ1 λ1 PROPN ejpam-7001 182 24 = = SYM ejpam-7001 182 25 1 1 NUM ejpam-7001 182 26 , , PUNCT ejpam-7001 182 27 λ2 λ2 NOUN ejpam-7001 182 28 = = SYM ejpam-7001 182 29 1 1 NUM ejpam-7001 182 30 , , PUNCT ejpam-7001 182 31 α α NOUN ejpam-7001 182 32 = = SYM ejpam-7001 182 33 0.5 0.5 NUM ejpam-7001 182 34 , , PUNCT ejpam-7001 182 35 β β X ejpam-7001 182 36 = = SYM ejpam-7001 182 37 0.5 0.5 NUM ejpam-7001 182 38 , , PUNCT ejpam-7001 182 39 and and CCONJ ejpam-7001 182 40 k k NOUN ejpam-7001 182 41 = = SYM ejpam-7001 182 42 1 1 NUM ejpam-7001 182 43 , , PUNCT ejpam-7001 182 44 while while SCONJ ejpam-7001 182 45 figure figure NOUN ejpam-7001 182 46 6(right 6(right NOUN ejpam-7001 182 47 ) ) PUNCT ejpam-7001 182 48 illustrates illustrate VERB ejpam-7001 182 49 the the DET ejpam-7001 182 50 influence influence NOUN ejpam-7001 182 51 of of ADP ejpam-7001 182 52 the the DET ejpam-7001 182 53 parameter parameter NOUN ejpam-7001 182 54 k k PROPN ejpam-7001 182 55 on on ADP ejpam-7001 182 56 s(t s(t PROPN ejpam-7001 182 57 ) ) PUNCT ejpam-7001 182 58 , , PUNCT ejpam-7001 182 59 setting set VERB ejpam-7001 182 60 λ1 λ1 ADJ ejpam-7001 182 61 = = SYM ejpam-7001 182 62 1 1 NUM ejpam-7001 182 63 , , PUNCT ejpam-7001 182 64 λ2 λ2 NOUN ejpam-7001 182 65 = = SYM ejpam-7001 182 66 1 1 NUM ejpam-7001 182 67 , , PUNCT ejpam-7001 182 68 α α NOUN ejpam-7001 182 69 = = SYM ejpam-7001 182 70 0.5 0.5 NUM ejpam-7001 182 71 , , PUNCT ejpam-7001 182 72 β β X ejpam-7001 182 73 = = SYM ejpam-7001 182 74 1.5 1.5 NUM ejpam-7001 182 75 , , PUNCT ejpam-7001 182 76 and and CCONJ ejpam-7001 182 77 m m PROPN ejpam-7001 182 78 = = NOUN ejpam-7001 182 79 0.5 0.5 NUM ejpam-7001 182 80 . . PUNCT ejpam-7001 182 81 figure figure NOUN ejpam-7001 182 82 7(left 7(left NUM ejpam-7001 182 83 ) ) PUNCT ejpam-7001 182 84 shows show VERB ejpam-7001 182 85 that that SCONJ ejpam-7001 182 86 h(t h(t PROPN ejpam-7001 182 87 ) ) PUNCT ejpam-7001 182 88 is be AUX ejpam-7001 182 89 a a DET ejpam-7001 182 90 decreasing decrease VERB ejpam-7001 182 91 function function NOUN ejpam-7001 182 92 for for ADP ejpam-7001 182 93 selected select VERB ejpam-7001 182 94 values value NOUN ejpam-7001 182 95 of of ADP ejpam-7001 182 96 m m PROPN ejpam-7001 182 97 with with ADP ejpam-7001 182 98 λ1 λ1 PROPN ejpam-7001 182 99 = = SYM ejpam-7001 182 100 0.5 0.5 NUM ejpam-7001 182 101 , , PUNCT ejpam-7001 182 102 λ2 λ2 NOUN ejpam-7001 182 103 = = SYM ejpam-7001 182 104 0.5 0.5 NUM ejpam-7001 182 105 , , PUNCT ejpam-7001 182 106 α α NOUN ejpam-7001 182 107 = = SYM ejpam-7001 182 108 0.5 0.5 NUM ejpam-7001 182 109 , , PUNCT ejpam-7001 182 110 β β X ejpam-7001 182 111 = = SYM ejpam-7001 182 112 0.1 0.1 NUM ejpam-7001 182 113 , , PUNCT ejpam-7001 182 114 and and CCONJ ejpam-7001 182 115 k k X ejpam-7001 182 116 = = NOUN ejpam-7001 182 117 0.5 0.5 NUM ejpam-7001 182 118 , , PUNCT ejpam-7001 182 119 whereas whereas SCONJ ejpam-7001 182 120 figure figure NOUN ejpam-7001 182 121 7(right 7(right NUM ejpam-7001 182 122 ) ) PUNCT ejpam-7001 182 123 demonstrates demonstrate VERB ejpam-7001 182 124 an an DET ejpam-7001 182 125 upside upside NOUN ejpam-7001 182 126 - - PUNCT ejpam-7001 182 127 down down ADP ejpam-7001 182 128 bathtub bathtub NOUN ejpam-7001 182 129 shape shape NOUN ejpam-7001 182 130 for for ADP ejpam-7001 182 131 h(t h(t PROPN ejpam-7001 182 132 ) ) PUNCT ejpam-7001 182 133 when when SCONJ ejpam-7001 182 134 k k PROPN ejpam-7001 182 135 = = PROPN ejpam-7001 182 136 0.8 0.8 NUM ejpam-7001 182 137 , , PUNCT ejpam-7001 182 138 0.85 0.85 NUM ejpam-7001 182 139 , , PUNCT ejpam-7001 182 140 1.25 1.25 NUM ejpam-7001 182 141 , , PUNCT ejpam-7001 182 142 and and CCONJ ejpam-7001 182 143 1.75 1.75 NUM ejpam-7001 182 144 with with ADP ejpam-7001 182 145 λ1 λ1 PROPN ejpam-7001 182 146 = = NOUN ejpam-7001 182 147 0.01 0.01 NUM ejpam-7001 182 148 , , PUNCT ejpam-7001 182 149 λ2 λ2 NOUN ejpam-7001 182 150 = = SYM ejpam-7001 182 151 0.5 0.5 NUM ejpam-7001 182 152 , , PUNCT ejpam-7001 182 153 α α NOUN ejpam-7001 182 154 = = PUNCT ejpam-7001 182 155 0.8 0.8 NUM ejpam-7001 182 156 , , PUNCT ejpam-7001 182 157 β β X ejpam-7001 182 158 = = PUNCT ejpam-7001 182 159 0.15 0.15 NUM ejpam-7001 182 160 , , PUNCT ejpam-7001 182 161 and and CCONJ ejpam-7001 182 162 m m PROPN ejpam-7001 182 163 = = NOUN ejpam-7001 182 164 0.75 0.75 NUM ejpam-7001 182 165 . . PUNCT ejpam-7001 183 1 figure figure VERB ejpam-7001 183 2 7 7 NUM ejpam-7001 183 3 : : PUNCT ejpam-7001 183 4 the the DET ejpam-7001 183 5 hrf hrf PROPN ejpam-7001 183 6 of of ADP ejpam-7001 183 7 the the DET ejpam-7001 183 8 crtfw crtfw NOUN ejpam-7001 183 9 distribution distribution NOUN ejpam-7001 183 10 for for ADP ejpam-7001 183 11 selected select VERB ejpam-7001 183 12 values value NOUN ejpam-7001 183 13 of of ADP ejpam-7001 183 14 m m PROPN ejpam-7001 183 15 and and CCONJ ejpam-7001 183 16 k. k. PROPN ejpam-7001 183 17 5.2 5.2 NUM ejpam-7001 183 18 . . PUNCT ejpam-7001 184 1 entropy entropy PROPN ejpam-7001 184 2 entropy entropy PROPN ejpam-7001 184 3 is be AUX ejpam-7001 184 4 a a DET ejpam-7001 184 5 state state NOUN ejpam-7001 184 6 function function NOUN ejpam-7001 184 7 that that PRON ejpam-7001 184 8 is be AUX ejpam-7001 184 9 often often ADV ejpam-7001 184 10 misinterpreted misinterpret VERB ejpam-7001 184 11 as as ADP ejpam-7001 184 12 the the DET ejpam-7001 184 13 disorder disorder NOUN ejpam-7001 184 14 of of ADP ejpam-7001 184 15 a a DET ejpam-7001 184 16 system system NOUN ejpam-7001 184 17 . . PUNCT ejpam-7001 185 1 more more ADV ejpam-7001 185 2 precisely precisely ADV ejpam-7001 185 3 , , PUNCT ejpam-7001 185 4 entropy entropy NOUN ejpam-7001 185 5 measures measure VERB ejpam-7001 185 6 the the DET ejpam-7001 185 7 uncertainty uncertainty NOUN ejpam-7001 185 8 associated associate VERB ejpam-7001 185 9 with with ADP ejpam-7001 185 10 a a DET ejpam-7001 185 11 random random ADJ ejpam-7001 185 12 variable variable NOUN ejpam-7001 185 13 and and CCONJ ejpam-7001 185 14 plays play VERB ejpam-7001 185 15 a a DET ejpam-7001 185 16 key key ADJ ejpam-7001 185 17 role role NOUN ejpam-7001 185 18 in in ADP ejpam-7001 185 19 thermodynamics thermodynamic NOUN ejpam-7001 185 20 and and CCONJ ejpam-7001 185 21 statistical statistical ADJ ejpam-7001 185 22 mechanics mechanic NOUN ejpam-7001 185 23 . . PUNCT ejpam-7001 186 1 in in ADP ejpam-7001 186 2 1948 1948 NUM ejpam-7001 186 3 , , PUNCT ejpam-7001 186 4 claude claude PROPN ejpam-7001 186 5 shannon shannon PROPN ejpam-7001 186 6 introduced introduce VERB ejpam-7001 186 7 the the DET ejpam-7001 186 8 concept concept NOUN ejpam-7001 186 9 of of ADP ejpam-7001 186 10 information information NOUN ejpam-7001 186 11 entropy entropy NOUN ejpam-7001 186 12 , , PUNCT ejpam-7001 186 13 also also ADV ejpam-7001 186 14 called call VERB ejpam-7001 186 15 shannon shannon PROPN ejpam-7001 186 16 entropy entropy PROPN ejpam-7001 187 1 [ [ X ejpam-7001 187 2 35 35 NUM ejpam-7001 187 3 ] ] PUNCT ejpam-7001 187 4 . . PUNCT ejpam-7001 188 1 subsequently subsequently ADV ejpam-7001 188 2 , , PUNCT ejpam-7001 188 3 several several ADJ ejpam-7001 188 4 generalizations generalization NOUN ejpam-7001 188 5 of of ADP ejpam-7001 188 6 shannon shannon PROPN ejpam-7001 188 7 entropy entropy PROPN ejpam-7001 188 8 were be AUX ejpam-7001 188 9 developed develop VERB ejpam-7001 188 10 , , PUNCT ejpam-7001 188 11 such such ADJ ejpam-7001 188 12 as as ADP ejpam-7001 188 13 rényi rényi PROPN ejpam-7001 188 14 and and CCONJ ejpam-7001 188 15 tsallis tsalli VERB ejpam-7001 188 16 entropies entropy NOUN ejpam-7001 188 17 [ [ X ejpam-7001 188 18 36 36 NUM ejpam-7001 188 19 ] ] PUNCT ejpam-7001 188 20 , , PUNCT ejpam-7001 188 21 which which PRON ejpam-7001 188 22 include include VERB ejpam-7001 188 23 shannon shannon PROPN ejpam-7001 188 24 entropy entropy PROPN ejpam-7001 188 25 as as ADP ejpam-7001 188 26 a a DET ejpam-7001 188 27 special special ADJ ejpam-7001 188 28 case case NOUN ejpam-7001 188 29 . . PUNCT ejpam-7001 189 1 for for ADP ejpam-7001 189 2 the the DET ejpam-7001 189 3 crtfw crtfw NOUN ejpam-7001 189 4 distribution distribution NOUN ejpam-7001 189 5 , , PUNCT ejpam-7001 189 6 the the DET ejpam-7001 189 7 entropies entropy NOUN ejpam-7001 189 8 can can AUX ejpam-7001 189 9 be be AUX ejpam-7001 189 10 defined define VERB ejpam-7001 189 11 as as SCONJ ejpam-7001 189 12 follows follow VERB ejpam-7001 189 13 . . PUNCT ejpam-7001 190 1 the the DET ejpam-7001 190 2 rényi rényi PROPN ejpam-7001 190 3 entropy entropy PROPN ejpam-7001 190 4 for for ADP ejpam-7001 190 5 the the DET ejpam-7001 190 6 crtfw crtfw NOUN ejpam-7001 190 7 distribution distribution NOUN ejpam-7001 190 8 is be AUX ejpam-7001 190 9 defined define VERB ejpam-7001 190 10 as as ADP ejpam-7001 190 11 rr(x rr(x NOUN ejpam-7001 190 12 ) ) PUNCT ejpam-7001 190 13 = = SYM ejpam-7001 191 1 1 1 NUM ejpam-7001 191 2 1− 1− NUM ejpam-7001 191 3 r r NOUN ejpam-7001 191 4 log log NOUN ejpam-7001 192 1 [ [ X ejpam-7001 192 2 ( ( PUNCT ejpam-7001 192 3 αk αk INTJ ejpam-7001 192 4 m m NOUN ejpam-7001 192 5 ) ) PUNCT ejpam-7001 193 1 r−1 r−1 PROPN ejpam-7001 193 2 βαr(rβα)− βαr(rβα)− NOUN ejpam-7001 193 3 ( ( PUNCT ejpam-7001 193 4 r r NOUN ejpam-7001 193 5 αk αk NOUN ejpam-7001 193 6 + + NOUN ejpam-7001 193 7 r− r− NOUN ejpam-7001 193 8 1 1 NUM ejpam-7001 193 9 αk αk NOUN ejpam-7001 193 10 ) ) PUNCT ejpam-7001 193 11 γ γ PROPN ejpam-7001 193 12 ( ( PUNCT ejpam-7001 193 13 r r NOUN ejpam-7001 193 14 αk αk NOUN ejpam-7001 193 15 + + CCONJ ejpam-7001 193 16 r r NOUN ejpam-7001 193 17 − − NUM ejpam-7001 193 18 1 1 NUM ejpam-7001 193 19 αk αk NOUN ejpam-7001 193 20 ) ) PUNCT ejpam-7001 193 21 × × NOUN ejpam-7001 193 22 { { PUNCT ejpam-7001 193 23 λr λr ADP ejpam-7001 193 24 1 1 NUM ejpam-7001 193 25 + + SYM ejpam-7001 193 26 2 2 NUM ejpam-7001 193 27 1−r 1−r NUM ejpam-7001 193 28 αk αk NOUN ejpam-7001 193 29 ( ( PUNCT ejpam-7001 193 30 λ2 λ2 NOUN ejpam-7001 193 31 − − PROPN ejpam-7001 193 32 λ1 λ1 PROPN ejpam-7001 193 33 ) ) PUNCT ejpam-7001 193 34 r r NOUN ejpam-7001 193 35 + + NUM ejpam-7001 193 36 3 3 NUM ejpam-7001 193 37 1−r 1−r NUM ejpam-7001 193 38 αk αk NOUN ejpam-7001 193 39 ( ( PUNCT ejpam-7001 193 40 1− 1− NUM ejpam-7001 193 41 λ2 λ2 NOUN ejpam-7001 193 42 ) ) PUNCT ejpam-7001 193 43 r r NOUN ejpam-7001 193 44 } } PUNCT ejpam-7001 193 45 ] ] PUNCT ejpam-7001 193 46 . . PUNCT ejpam-7001 194 1 imliyangba imliyangba PROPN ejpam-7001 194 2 et et PROPN ejpam-7001 194 3 al al PROPN ejpam-7001 194 4 . . PUNCT ejpam-7001 194 5 / / SYM ejpam-7001 194 6 eur eur PROPN ejpam-7001 194 7 . . PUNCT ejpam-7001 195 1 j. j. PROPN ejpam-7001 195 2 pure pure PROPN ejpam-7001 195 3 appl appl PROPN ejpam-7001 195 4 . . PROPN ejpam-7001 195 5 math math PROPN ejpam-7001 195 6 , , PUNCT ejpam-7001 195 7 18 18 NUM ejpam-7001 195 8 ( ( PUNCT ejpam-7001 195 9 4 4 NUM ejpam-7001 195 10 ) ) PUNCT ejpam-7001 195 11 ( ( PUNCT ejpam-7001 195 12 2025 2025 NUM ejpam-7001 195 13 ) ) PUNCT ejpam-7001 195 14 , , PUNCT ejpam-7001 195 15 7001 7001 NUM ejpam-7001 195 16 13 13 NUM ejpam-7001 195 17 of of ADP ejpam-7001 195 18 27 27 NUM ejpam-7001 195 19 similarly similarly ADV ejpam-7001 195 20 , , PUNCT ejpam-7001 195 21 the the DET ejpam-7001 195 22 tsallis tsalli NOUN ejpam-7001 195 23 entropy entropy VERB ejpam-7001 195 24 for for SCONJ ejpam-7001 195 25 the the DET ejpam-7001 195 26 crtfw crtfw NOUN ejpam-7001 195 27 distribution distribution NOUN ejpam-7001 195 28 is be AUX ejpam-7001 195 29 defined define VERB ejpam-7001 195 30 as as ADP ejpam-7001 195 31 tr(x tr(x PRON ejpam-7001 195 32 ) ) PUNCT ejpam-7001 195 33 = = PUNCT ejpam-7001 196 1 1 1 NUM ejpam-7001 196 2 1− 1− NUM ejpam-7001 196 3 r r NOUN ejpam-7001 196 4 [ [ X ejpam-7001 196 5 ( ( PUNCT ejpam-7001 196 6 αk αk INTJ ejpam-7001 196 7 m m NOUN ejpam-7001 196 8 ) ) PUNCT ejpam-7001 197 1 r−1 r−1 PROPN ejpam-7001 197 2 βαr(rβα)− βαr(rβα)− NOUN ejpam-7001 197 3 ( ( PUNCT ejpam-7001 197 4 r r NOUN ejpam-7001 197 5 αk αk NOUN ejpam-7001 197 6 + + NOUN ejpam-7001 197 7 r− r− NOUN ejpam-7001 197 8 1 1 NUM ejpam-7001 197 9 αk αk NOUN ejpam-7001 197 10 ) ) PUNCT ejpam-7001 197 11 γ γ PROPN ejpam-7001 197 12 ( ( PUNCT ejpam-7001 197 13 r r NOUN ejpam-7001 197 14 αk αk NOUN ejpam-7001 197 15 + + CCONJ ejpam-7001 197 16 r r NOUN ejpam-7001 197 17 − − NUM ejpam-7001 197 18 1 1 NUM ejpam-7001 197 19 αk αk NOUN ejpam-7001 197 20 ) ) PUNCT ejpam-7001 197 21 × × NOUN ejpam-7001 197 22 { { PUNCT ejpam-7001 197 23 λr λr ADP ejpam-7001 197 24 1 1 NUM ejpam-7001 197 25 + + SYM ejpam-7001 197 26 2 2 NUM ejpam-7001 197 27 1−r 1−r NUM ejpam-7001 197 28 αk αk NOUN ejpam-7001 197 29 ( ( PUNCT ejpam-7001 197 30 λ2 λ2 NOUN ejpam-7001 197 31 − − PROPN ejpam-7001 197 32 λ1 λ1 PROPN ejpam-7001 197 33 ) ) PUNCT ejpam-7001 197 34 r r NOUN ejpam-7001 197 35 + + NUM ejpam-7001 197 36 3 3 NUM ejpam-7001 197 37 1−r 1−r NUM ejpam-7001 197 38 αk αk NOUN ejpam-7001 197 39 ( ( PUNCT ejpam-7001 197 40 1− 1− NUM ejpam-7001 197 41 λ2 λ2 NOUN ejpam-7001 197 42 ) ) PUNCT ejpam-7001 197 43 r r NOUN ejpam-7001 197 44 } } PUNCT ejpam-7001 197 45 − − PROPN ejpam-7001 197 46 1 1 NUM ejpam-7001 197 47 ] ] PUNCT ejpam-7001 197 48 . . PUNCT ejpam-7001 198 1 finally finally ADV ejpam-7001 198 2 , , PUNCT ejpam-7001 198 3 the the DET ejpam-7001 198 4 shannon shannon PROPN ejpam-7001 198 5 entropy entropy PROPN ejpam-7001 198 6 for for ADP ejpam-7001 198 7 the the DET ejpam-7001 198 8 crtfw crtfw NOUN ejpam-7001 198 9 distribution distribution NOUN ejpam-7001 198 10 is be AUX ejpam-7001 198 11 given give VERB ejpam-7001 198 12 by by ADP ejpam-7001 198 13 sh(x sh(x NOUN ejpam-7001 198 14 ) ) PUNCT ejpam-7001 198 15 = = PUNCT ejpam-7001 198 16 log log NOUN ejpam-7001 198 17 ( ( PUNCT ejpam-7001 198 18 mβ1 mβ1 PROPN ejpam-7001 198 19 / / SYM ejpam-7001 198 20 k k NOUN ejpam-7001 198 21 αk αk NOUN ejpam-7001 198 22 ) ) PUNCT ejpam-7001 199 1 + + CCONJ ejpam-7001 199 2 1 1 NUM ejpam-7001 199 3 + + CCONJ ejpam-7001 199 4 αk αk INTJ ejpam-7001 199 5 αk αk INTJ ejpam-7001 199 6 { { PUNCT ejpam-7001 199 7 γ γ X ejpam-7001 199 8 + + CCONJ ejpam-7001 199 9 ( ( PUNCT ejpam-7001 199 10 λ2 λ2 PROPN ejpam-7001 199 11 − − PROPN ejpam-7001 199 12 λ1 λ1 PROPN ejpam-7001 199 13 ) ) PUNCT ejpam-7001 199 14 log log NOUN ejpam-7001 199 15 2 2 NUM ejpam-7001 199 16 + + CCONJ ejpam-7001 199 17 ( ( PUNCT ejpam-7001 199 18 1− 1− NUM ejpam-7001 199 19 λ2 λ2 NOUN ejpam-7001 199 20 ) ) PUNCT ejpam-7001 199 21 log log VERB ejpam-7001 199 22 3 3 NUM ejpam-7001 199 23 } } PUNCT ejpam-7001 199 24 + + NUM ejpam-7001 199 25 3λ1 3λ1 NUM ejpam-7001 200 1 + + CCONJ ejpam-7001 200 2 λ2 λ2 NOUN ejpam-7001 200 3 − − NOUN ejpam-7001 200 4 2 2 NUM ejpam-7001 200 5 6 6 NUM ejpam-7001 200 6 − − PROPN ejpam-7001 200 7 ∫ ∫ PROPN ejpam-7001 200 8 ∞ ∞ PROPN ejpam-7001 200 9 0 0 NUM ejpam-7001 200 10 { { PUNCT ejpam-7001 200 11 λ1 λ1 PROPN ejpam-7001 200 12 + + NUM ejpam-7001 200 13 2(λ2 2(λ2 NUM ejpam-7001 200 14 − − NOUN ejpam-7001 200 15 λ1)e λ1)e NOUN ejpam-7001 200 16 −βα(m −βα(m PROPN ejpam-7001 200 17 / / SYM ejpam-7001 200 18 x)αk x)αk PROPN ejpam-7001 200 19 +3(1− +3(1− PROPN ejpam-7001 200 20 λ1 λ1 PROPN ejpam-7001 200 21 ) ) PUNCT ejpam-7001 200 22 [ [ PUNCT ejpam-7001 200 23 e−βα(m e−βα(m PROPN ejpam-7001 200 24 / / SYM ejpam-7001 200 25 x)αk x)αk PROPN ejpam-7001 200 26 ] ] PUNCT ejpam-7001 200 27 2 2 X ejpam-7001 200 28 } } PUNCT ejpam-7001 200 29 αkβαmαkx−1−αke−βα(m αkβαmαkx−1−αke−βα(m PROPN ejpam-7001 200 30 / / SYM ejpam-7001 200 31 x)αk x)αk PROPN ejpam-7001 200 32 × × NOUN ejpam-7001 200 33 log log NOUN ejpam-7001 200 34 { { PUNCT ejpam-7001 200 35 λ1 λ1 PROPN ejpam-7001 200 36 + + NUM ejpam-7001 200 37 2(λ2 2(λ2 NUM ejpam-7001 200 38 − − NOUN ejpam-7001 200 39 λ1)e λ1)e NOUN ejpam-7001 200 40 −βα(m −βα(m PROPN ejpam-7001 200 41 / / SYM ejpam-7001 200 42 x)αk x)αk PROPN ejpam-7001 200 43 + + CCONJ ejpam-7001 201 1 3(1− 3(1− NUM ejpam-7001 201 2 λ1 λ1 NUM ejpam-7001 201 3 ) ) PUNCT ejpam-7001 201 4 [ [ PUNCT ejpam-7001 201 5 e−βα(m e−βα(m PROPN ejpam-7001 201 6 / / SYM ejpam-7001 201 7 x)αk x)αk PROPN ejpam-7001 201 8 ] ] PUNCT ejpam-7001 201 9 2 2 X ejpam-7001 201 10 } } PUNCT ejpam-7001 201 11 dx dx PROPN ejpam-7001 201 12 , , PUNCT ejpam-7001 201 13 where where SCONJ ejpam-7001 201 14 γ γ X ejpam-7001 201 15 = = SYM ejpam-7001 201 16 − − PROPN ejpam-7001 201 17 ∫∞ ∫∞ NOUN ejpam-7001 201 18 0 0 NUM ejpam-7001 201 19 e−x e−x NOUN ejpam-7001 201 20 ln(x ln(x X ejpam-7001 201 21 ) ) PUNCT ejpam-7001 201 22 dx dx PROPN ejpam-7001 201 23 denotes denote VERB ejpam-7001 201 24 the the DET ejpam-7001 201 25 euler euler PROPN ejpam-7001 201 26 - - PUNCT ejpam-7001 201 27 mascheroni mascheroni NOUN ejpam-7001 201 28 constant constant ADJ ejpam-7001 201 29 . . PUNCT ejpam-7001 202 1 5.3 5.3 NUM ejpam-7001 202 2 . . PUNCT ejpam-7001 202 3 order order NOUN ejpam-7001 202 4 statistics statistic VERB ejpam-7001 202 5 the the DET ejpam-7001 202 6 study study NOUN ejpam-7001 202 7 of of ADP ejpam-7001 202 8 order order NOUN ejpam-7001 202 9 statistics statistic NOUN ejpam-7001 202 10 deals deal NOUN ejpam-7001 202 11 with with ADP ejpam-7001 202 12 the the DET ejpam-7001 202 13 properties property NOUN ejpam-7001 202 14 and and CCONJ ejpam-7001 202 15 applications application NOUN ejpam-7001 202 16 of of ADP ejpam-7001 202 17 ordered order VERB ejpam-7001 202 18 random random ADJ ejpam-7001 202 19 variables variable NOUN ejpam-7001 202 20 and and CCONJ ejpam-7001 202 21 their their PRON ejpam-7001 202 22 functions function NOUN ejpam-7001 202 23 . . PUNCT ejpam-7001 203 1 order order NOUN ejpam-7001 203 2 statistics statistic NOUN ejpam-7001 203 3 also also ADV ejpam-7001 203 4 play play VERB ejpam-7001 203 5 an an DET ejpam-7001 203 6 important important ADJ ejpam-7001 203 7 role role NOUN ejpam-7001 203 8 in in ADP ejpam-7001 203 9 the the DET ejpam-7001 203 10 estimation estimation NOUN ejpam-7001 203 11 of of ADP ejpam-7001 203 12 the the DET ejpam-7001 203 13 location location NOUN ejpam-7001 203 14 and and CCONJ ejpam-7001 203 15 scale scale NOUN ejpam-7001 203 16 parameters parameter NOUN ejpam-7001 203 17 of of ADP ejpam-7001 203 18 a a DET ejpam-7001 203 19 distribution distribution NOUN ejpam-7001 203 20 . . PUNCT ejpam-7001 204 1 here here ADV ejpam-7001 204 2 we we PRON ejpam-7001 204 3 have have AUX ejpam-7001 204 4 obtained obtain VERB ejpam-7001 204 5 the the DET ejpam-7001 204 6 pdf pdf NOUN ejpam-7001 204 7 of of ADP ejpam-7001 204 8 a a DET ejpam-7001 204 9 single single ADJ ejpam-7001 204 10 - - PUNCT ejpam-7001 204 11 order order NOUN ejpam-7001 204 12 statistic statistic NOUN ejpam-7001 204 13 and and CCONJ ejpam-7001 204 14 joint joint ADJ ejpam-7001 204 15 - - PUNCT ejpam-7001 204 16 order order NOUN ejpam-7001 204 17 statistics statistic NOUN ejpam-7001 204 18 . . PUNCT ejpam-7001 205 1 according accord VERB ejpam-7001 205 2 to to ADP ejpam-7001 205 3 [ [ X ejpam-7001 205 4 37 37 NUM ejpam-7001 205 5 ] ] PUNCT ejpam-7001 205 6 , , PUNCT ejpam-7001 205 7 we we PRON ejpam-7001 205 8 have have VERB ejpam-7001 205 9 the the DET ejpam-7001 205 10 density density NOUN ejpam-7001 205 11 function function NOUN ejpam-7001 205 12 of of ADP ejpam-7001 205 13 the the DET ejpam-7001 205 14 rth rth PROPN ejpam-7001 205 15 order order NOUN ejpam-7001 205 16 statistic statistic NOUN ejpam-7001 205 17 as as ADP ejpam-7001 205 18 : : PUNCT ejpam-7001 205 19 fr(x fr(x X ejpam-7001 205 20 ) ) PUNCT ejpam-7001 205 21 = = SYM ejpam-7001 205 22 n n X ejpam-7001 205 23 ! ! PUNCT ejpam-7001 206 1 ( ( PUNCT ejpam-7001 206 2 r r NOUN ejpam-7001 206 3 − − PROPN ejpam-7001 206 4 1)!(n− 1)!(n− NUM ejpam-7001 206 5 r r NOUN ejpam-7001 206 6 ) ) PUNCT ejpam-7001 206 7 ! ! PUNCT ejpam-7001 207 1 f(x)[f f(x)[f NOUN ejpam-7001 207 2 ( ( PUNCT ejpam-7001 207 3 x)]r−1[1− x)]r−1[1− PROPN ejpam-7001 207 4 f f PROPN ejpam-7001 207 5 ( ( PUNCT ejpam-7001 207 6 x)]n−r x)]n−r PROPN ejpam-7001 207 7 . . PROPN ejpam-7001 208 1 ( ( PUNCT ejpam-7001 208 2 13 13 NUM ejpam-7001 208 3 ) ) PUNCT ejpam-7001 208 4 the the DET ejpam-7001 208 5 pdf pdf NOUN ejpam-7001 208 6 of of ADP ejpam-7001 208 7 the the DET ejpam-7001 208 8 rth rth PROPN ejpam-7001 208 9 order order NOUN ejpam-7001 208 10 statistic statistic NOUN ejpam-7001 208 11 for for ADP ejpam-7001 208 12 the the DET ejpam-7001 208 13 crtfw crtfw NOUN ejpam-7001 208 14 distribution distribution NOUN ejpam-7001 208 15 is be AUX ejpam-7001 208 16 obtained obtain VERB ejpam-7001 208 17 as as ADP ejpam-7001 208 18 : : PUNCT ejpam-7001 208 19 fxr fxr NOUN ejpam-7001 208 20 : : PUNCT ejpam-7001 208 21 n(x n(x ADJ ejpam-7001 208 22 ) ) PUNCT ejpam-7001 208 23 = = SYM ejpam-7001 208 24 n n X ejpam-7001 208 25 ! ! PUNCT ejpam-7001 209 1 ( ( PUNCT ejpam-7001 209 2 r r NOUN ejpam-7001 209 3 − − PROPN ejpam-7001 209 4 1)!(n− 1)!(n− NUM ejpam-7001 209 5 r r NOUN ejpam-7001 209 6 ) ) PUNCT ejpam-7001 209 7 ! ! PUNCT ejpam-7001 210 1 [ [ PUNCT ejpam-7001 210 2 λ1e λ1e X ejpam-7001 210 3 −βα(mx −βα(mx X ejpam-7001 210 4 ) ) PUNCT ejpam-7001 211 1 αk αk CCONJ ejpam-7001 211 2 + + CCONJ ejpam-7001 211 3 ( ( PUNCT ejpam-7001 211 4 λ2 λ2 NOUN ejpam-7001 211 5 − − PROPN ejpam-7001 211 6 λ1 λ1 PROPN ejpam-7001 211 7 ) ) PUNCT ejpam-7001 211 8 { { PUNCT ejpam-7001 211 9 e−βα(mx e−βα(mx PROPN ejpam-7001 211 10 ) ) PUNCT ejpam-7001 212 1 αk αk CCONJ ejpam-7001 212 2 } } SYM ejpam-7001 212 3 2 2 NUM ejpam-7001 212 4 + + NOUN ejpam-7001 212 5 ( ( PUNCT ejpam-7001 212 6 1− 1− NUM ejpam-7001 212 7 λ1 λ1 ADJ ejpam-7001 212 8 ) ) PUNCT ejpam-7001 212 9 { { PUNCT ejpam-7001 212 10 e−βα(mx e−βα(mx PROPN ejpam-7001 212 11 ) ) PUNCT ejpam-7001 212 12 αk αk CCONJ ejpam-7001 212 13 } } SYM ejpam-7001 212 14 3 3 NUM ejpam-7001 212 15 ] ] PUNCT ejpam-7001 212 16 r−1 r−1 PROPN ejpam-7001 212 17 × × NOUN ejpam-7001 212 18 [ [ PUNCT ejpam-7001 212 19 1− 1− NUM ejpam-7001 212 20 λ1e λ1e NOUN ejpam-7001 212 21 −βα(mx −βα(mx X ejpam-7001 212 22 ) ) PUNCT ejpam-7001 213 1 αk αk CCONJ ejpam-7001 213 2 + + CCONJ ejpam-7001 213 3 ( ( PUNCT ejpam-7001 213 4 λ2 λ2 NOUN ejpam-7001 213 5 − − PROPN ejpam-7001 213 6 λ1 λ1 PROPN ejpam-7001 213 7 ) ) PUNCT ejpam-7001 213 8 { { PUNCT ejpam-7001 213 9 e−βα(mx e−βα(mx PROPN ejpam-7001 213 10 ) ) PUNCT ejpam-7001 214 1 αk αk CCONJ ejpam-7001 214 2 } } SYM ejpam-7001 214 3 2 2 NUM ejpam-7001 214 4 + + CCONJ ejpam-7001 214 5 ( ( PUNCT ejpam-7001 214 6 1− 1− NUM ejpam-7001 214 7 λ1 λ1 ADJ ejpam-7001 214 8 ) ) PUNCT ejpam-7001 214 9 { { PUNCT ejpam-7001 214 10 e−βα(mx e−βα(mx PROPN ejpam-7001 214 11 ) ) PUNCT ejpam-7001 214 12 αk αk CCONJ ejpam-7001 214 13 } } SYM ejpam-7001 214 14 3 3 NUM ejpam-7001 214 15 ] ] PUNCT ejpam-7001 214 16 n−r n−r NOUN ejpam-7001 214 17 × × NOUN ejpam-7001 214 18 { { PUNCT ejpam-7001 214 19 λ1 λ1 PROPN ejpam-7001 214 20 + + NUM ejpam-7001 214 21 2(λ2 2(λ2 NUM ejpam-7001 214 22 − − NOUN ejpam-7001 214 23 λ1)e λ1)e NOUN ejpam-7001 214 24 −βα(mx −βα(mx PUNCT ejpam-7001 214 25 ) ) PUNCT ejpam-7001 214 26 αk αk CCONJ ejpam-7001 215 1 + + CCONJ ejpam-7001 215 2 3(1− 3(1− NUM ejpam-7001 215 3 λ1 λ1 NUM ejpam-7001 215 4 ) ) PUNCT ejpam-7001 215 5 [ [ PUNCT ejpam-7001 215 6 e−βα(mx e−βα(mx PROPN ejpam-7001 215 7 ) ) PUNCT ejpam-7001 216 1 αk αk CCONJ ejpam-7001 216 2 ] ] SYM ejpam-7001 216 3 2 2 X ejpam-7001 216 4 } } PUNCT ejpam-7001 216 5 imliyangba imliyangba PROPN ejpam-7001 216 6 et et PROPN ejpam-7001 216 7 al al PROPN ejpam-7001 216 8 . . PUNCT ejpam-7001 216 9 / / SYM ejpam-7001 216 10 eur eur PROPN ejpam-7001 216 11 . . PUNCT ejpam-7001 217 1 j. j. PROPN ejpam-7001 217 2 pure pure PROPN ejpam-7001 217 3 appl appl PROPN ejpam-7001 217 4 . . PROPN ejpam-7001 217 5 math math PROPN ejpam-7001 217 6 , , PUNCT ejpam-7001 217 7 18 18 NUM ejpam-7001 217 8 ( ( PUNCT ejpam-7001 217 9 4 4 NUM ejpam-7001 217 10 ) ) PUNCT ejpam-7001 217 11 ( ( PUNCT ejpam-7001 217 12 2025 2025 NUM ejpam-7001 217 13 ) ) PUNCT ejpam-7001 217 14 , , PUNCT ejpam-7001 217 15 7001 7001 NUM ejpam-7001 217 16 14 14 NUM ejpam-7001 217 17 of of ADP ejpam-7001 217 18 27 27 NUM ejpam-7001 217 19 ×αkβαmαkx−1−αke−βα(mx ×αkβαmαkx−1−αke−βα(mx NUM ejpam-7001 217 20 ) ) PUNCT ejpam-7001 218 1 αk αk INTJ ejpam-7001 218 2 , , PUNCT ejpam-7001 218 3 where where SCONJ ejpam-7001 218 4 r r NOUN ejpam-7001 218 5 = = SYM ejpam-7001 218 6 1 1 NUM ejpam-7001 218 7 , , PUNCT ejpam-7001 218 8 2 2 NUM ejpam-7001 218 9 , , PUNCT ejpam-7001 218 10 . . PUNCT ejpam-7001 218 11 . . PUNCT ejpam-7001 218 12 . . PUNCT ejpam-7001 219 1 , , PUNCT ejpam-7001 219 2 n. n. PROPN ejpam-7001 219 3 therefore therefore ADV ejpam-7001 219 4 , , PUNCT ejpam-7001 219 5 for for ADP ejpam-7001 219 6 r r NOUN ejpam-7001 219 7 = = SYM ejpam-7001 219 8 1 1 NUM ejpam-7001 219 9 and and CCONJ ejpam-7001 219 10 r r NOUN ejpam-7001 219 11 = = SYM ejpam-7001 219 12 n n CCONJ ejpam-7001 219 13 , , PUNCT ejpam-7001 219 14 we we PRON ejpam-7001 219 15 have have VERB ejpam-7001 219 16 the the DET ejpam-7001 219 17 pdf pdf NOUN ejpam-7001 219 18 of of ADP ejpam-7001 219 19 the the DET ejpam-7001 219 20 smallest small ADJ ejpam-7001 219 21 order order NOUN ejpam-7001 219 22 statistic statistic NOUN ejpam-7001 219 23 and and CCONJ ejpam-7001 219 24 largest large ADJ ejpam-7001 219 25 order order NOUN ejpam-7001 219 26 statistic statistic NOUN ejpam-7001 219 27 , , PUNCT ejpam-7001 219 28 respectively respectively ADV ejpam-7001 219 29 , , PUNCT ejpam-7001 219 30 as as ADP ejpam-7001 219 31 : : PUNCT ejpam-7001 219 32 fx1 fx1 ADJ ejpam-7001 219 33 : : PUNCT ejpam-7001 219 34 n(x n(x ADJ ejpam-7001 219 35 ) ) PUNCT ejpam-7001 219 36 = = SYM ejpam-7001 220 1 n n PROPN ejpam-7001 220 2 [ [ PUNCT ejpam-7001 220 3 1− 1− NUM ejpam-7001 220 4 λ1e λ1e X ejpam-7001 220 5 −βα(mx −βα(mx X ejpam-7001 220 6 ) ) PUNCT ejpam-7001 221 1 αk αk CCONJ ejpam-7001 221 2 + + CCONJ ejpam-7001 221 3 ( ( PUNCT ejpam-7001 221 4 λ2 λ2 NOUN ejpam-7001 221 5 − − PROPN ejpam-7001 221 6 λ1 λ1 PROPN ejpam-7001 221 7 ) ) PUNCT ejpam-7001 221 8 { { PUNCT ejpam-7001 221 9 e−βα(mx e−βα(mx PROPN ejpam-7001 221 10 ) ) PUNCT ejpam-7001 222 1 αk αk CCONJ ejpam-7001 222 2 } } SYM ejpam-7001 222 3 2 2 NUM ejpam-7001 222 4 + + CCONJ ejpam-7001 222 5 ( ( PUNCT ejpam-7001 222 6 1− 1− NUM ejpam-7001 222 7 λ1 λ1 ADJ ejpam-7001 222 8 ) ) PUNCT ejpam-7001 222 9 { { PUNCT ejpam-7001 222 10 e−βα(mx e−βα(mx PROPN ejpam-7001 222 11 ) ) PUNCT ejpam-7001 222 12 αk αk CCONJ ejpam-7001 222 13 } } SYM ejpam-7001 222 14 3 3 NUM ejpam-7001 222 15 ] ] PUNCT ejpam-7001 222 16 n−1 n−1 PROPN ejpam-7001 222 17 × × NOUN ejpam-7001 222 18 { { PUNCT ejpam-7001 222 19 λ1 λ1 PROPN ejpam-7001 222 20 + + NUM ejpam-7001 222 21 2(λ2 2(λ2 NUM ejpam-7001 222 22 − − NOUN ejpam-7001 222 23 λ1)e λ1)e NOUN ejpam-7001 222 24 −βα(mx −βα(mx PUNCT ejpam-7001 222 25 ) ) PUNCT ejpam-7001 222 26 αk αk CCONJ ejpam-7001 223 1 + + CCONJ ejpam-7001 223 2 3(1− 3(1− NUM ejpam-7001 223 3 λ1 λ1 NUM ejpam-7001 223 4 ) ) PUNCT ejpam-7001 223 5 [ [ PUNCT ejpam-7001 223 6 e−βα(mx e−βα(mx PROPN ejpam-7001 223 7 ) ) PUNCT ejpam-7001 224 1 αk αk CCONJ ejpam-7001 224 2 ] ] SYM ejpam-7001 224 3 2 2 NUM ejpam-7001 224 4 } } SYM ejpam-7001 224 5 × × NOUN ejpam-7001 224 6 αkβαmαkx−1−αke−βα(mx αkβαmαkx−1−αke−βα(mx NOUN ejpam-7001 224 7 ) ) PUNCT ejpam-7001 224 8 αk αk CCONJ ejpam-7001 224 9 , , PUNCT ejpam-7001 224 10 and and CCONJ ejpam-7001 224 11 fxn fxn NOUN ejpam-7001 224 12 : : PUNCT ejpam-7001 224 13 n(x n(x ADJ ejpam-7001 224 14 ) ) PUNCT ejpam-7001 224 15 = = SYM ejpam-7001 225 1 n n CCONJ ejpam-7001 225 2 [ [ PUNCT ejpam-7001 225 3 λ1e λ1e X ejpam-7001 225 4 −βα(mx −βα(mx X ejpam-7001 225 5 ) ) PUNCT ejpam-7001 226 1 αk αk CCONJ ejpam-7001 226 2 + + CCONJ ejpam-7001 226 3 ( ( PUNCT ejpam-7001 226 4 λ2 λ2 NOUN ejpam-7001 226 5 − − PROPN ejpam-7001 226 6 λ1 λ1 PROPN ejpam-7001 226 7 ) ) PUNCT ejpam-7001 226 8 { { PUNCT ejpam-7001 226 9 e−βα(mx e−βα(mx PROPN ejpam-7001 226 10 ) ) PUNCT ejpam-7001 227 1 αk αk CCONJ ejpam-7001 227 2 } } SYM ejpam-7001 227 3 2 2 NUM ejpam-7001 227 4 + + CCONJ ejpam-7001 227 5 ( ( PUNCT ejpam-7001 227 6 1− 1− NUM ejpam-7001 227 7 λ1 λ1 ADJ ejpam-7001 227 8 ) ) PUNCT ejpam-7001 227 9 { { PUNCT ejpam-7001 227 10 e−βα(mx e−βα(mx PROPN ejpam-7001 227 11 ) ) PUNCT ejpam-7001 227 12 αk αk CCONJ ejpam-7001 227 13 } } SYM ejpam-7001 227 14 3 3 NUM ejpam-7001 227 15 ] ] PUNCT ejpam-7001 227 16 n−1 n−1 PROPN ejpam-7001 227 17 × × NOUN ejpam-7001 227 18 { { PUNCT ejpam-7001 227 19 λ1 λ1 PROPN ejpam-7001 227 20 + + NUM ejpam-7001 227 21 2(λ2 2(λ2 NUM ejpam-7001 227 22 − − NOUN ejpam-7001 227 23 λ1)e λ1)e NOUN ejpam-7001 227 24 −βα(mx −βα(mx PUNCT ejpam-7001 227 25 ) ) PUNCT ejpam-7001 227 26 αk αk CCONJ ejpam-7001 228 1 + + CCONJ ejpam-7001 228 2 3(1− 3(1− NUM ejpam-7001 228 3 λ1 λ1 NUM ejpam-7001 228 4 ) ) PUNCT ejpam-7001 228 5 [ [ PUNCT ejpam-7001 228 6 e−βα(mx e−βα(mx PROPN ejpam-7001 228 7 ) ) PUNCT ejpam-7001 229 1 αk αk CCONJ ejpam-7001 229 2 ] ] SYM ejpam-7001 229 3 2 2 NUM ejpam-7001 229 4 } } SYM ejpam-7001 229 5 ×αkβαmαkx−1−αke−βα(mx ×αkβαmαkx−1−αke−βα(mx NUM ejpam-7001 229 6 ) ) PUNCT ejpam-7001 229 7 αk αk INTJ ejpam-7001 229 8 . . PUNCT ejpam-7001 230 1 the the DET ejpam-7001 230 2 joint joint ADJ ejpam-7001 230 3 distribution distribution NOUN ejpam-7001 230 4 of of ADP ejpam-7001 230 5 the the DET ejpam-7001 230 6 rth rth NOUN ejpam-7001 230 7 and and CCONJ ejpam-7001 230 8 sth sth PROPN ejpam-7001 230 9 order order NOUN ejpam-7001 230 10 statistics statistic NOUN ejpam-7001 230 11 from from ADP ejpam-7001 230 12 the the DET ejpam-7001 230 13 crtfw crtfw NOUN ejpam-7001 230 14 distribution distribution NOUN ejpam-7001 230 15 is be AUX ejpam-7001 230 16 defined define VERB ejpam-7001 230 17 as as ADP ejpam-7001 230 18 : : PUNCT ejpam-7001 230 19 fr fr NOUN ejpam-7001 230 20 : : PUNCT ejpam-7001 230 21 s s X ejpam-7001 230 22 : : PUNCT ejpam-7001 230 23 n(x n(x PROPN ejpam-7001 230 24 , , PUNCT ejpam-7001 230 25 y y NOUN ejpam-7001 230 26 ) ) PUNCT ejpam-7001 231 1 = = NOUN ejpam-7001 231 2 c[f c[f NOUN ejpam-7001 231 3 ( ( PUNCT ejpam-7001 231 4 x)]r−1[f x)]r−1[f PRON ejpam-7001 231 5 ( ( PUNCT ejpam-7001 231 6 y)− y)− PROPN ejpam-7001 231 7 f f X ejpam-7001 231 8 ( ( PUNCT ejpam-7001 231 9 x)]s−r−1[1− x)]s−r−1[1− PROPN ejpam-7001 231 10 f f PROPN ejpam-7001 231 11 ( ( PUNCT ejpam-7001 231 12 y)]n−sf(x)f(y y)]n−sf(x)f(y NUM ejpam-7001 231 13 ) ) PUNCT ejpam-7001 231 14 , , PUNCT ejpam-7001 231 15 ( ( PUNCT ejpam-7001 231 16 14 14 NUM ejpam-7001 231 17 ) ) PUNCT ejpam-7001 231 18 where where SCONJ ejpam-7001 231 19 c c NOUN ejpam-7001 231 20 = = SYM ejpam-7001 231 21 n n X ejpam-7001 231 22 ! ! PUNCT ejpam-7001 232 1 ( ( PUNCT ejpam-7001 232 2 r r NOUN ejpam-7001 232 3 − − PROPN ejpam-7001 232 4 1)!(s− 1)!(s− NUM ejpam-7001 232 5 r r NOUN ejpam-7001 232 6 − − PROPN ejpam-7001 232 7 1)!(n− 1)!(n− NUM ejpam-7001 232 8 s s NOUN ejpam-7001 232 9 ) ) PUNCT ejpam-7001 232 10 ! ! PUNCT ejpam-7001 232 11 . . PUNCT ejpam-7001 233 1 the the DET ejpam-7001 233 2 joint joint ADJ ejpam-7001 233 3 pdf pdf NOUN ejpam-7001 233 4 of of ADP ejpam-7001 233 5 the the DET ejpam-7001 233 6 smallest small ADJ ejpam-7001 233 7 and and CCONJ ejpam-7001 233 8 largest large ADJ ejpam-7001 233 9 order order NOUN ejpam-7001 233 10 statistics statistic NOUN ejpam-7001 233 11 for for ADP ejpam-7001 233 12 the the DET ejpam-7001 233 13 crtfw crtfw NOUN ejpam-7001 233 14 distribution distribution NOUN ejpam-7001 233 15 can can AUX ejpam-7001 233 16 be be AUX ejpam-7001 233 17 easily easily ADV ejpam-7001 233 18 obtained obtain VERB ejpam-7001 233 19 from from ADP ejpam-7001 233 20 equation equation NOUN ejpam-7001 233 21 ( ( PUNCT ejpam-7001 233 22 14 14 NUM ejpam-7001 233 23 ) ) PUNCT ejpam-7001 233 24 by by ADP ejpam-7001 233 25 using use VERB ejpam-7001 233 26 r r NOUN ejpam-7001 233 27 = = SYM ejpam-7001 233 28 1 1 NUM ejpam-7001 233 29 and and CCONJ ejpam-7001 233 30 s s NOUN ejpam-7001 233 31 = = PROPN ejpam-7001 233 32 n. n. NOUN ejpam-7001 233 33 note note NOUN ejpam-7001 233 34 that that SCONJ ejpam-7001 233 35 if if SCONJ ejpam-7001 233 36 λ1 λ1 PROPN ejpam-7001 233 37 = = SYM ejpam-7001 233 38 λ2 λ2 NOUN ejpam-7001 233 39 = = SYM ejpam-7001 233 40 1 1 NUM ejpam-7001 233 41 , , PUNCT ejpam-7001 233 42 then then ADV ejpam-7001 233 43 we we PRON ejpam-7001 233 44 have have VERB ejpam-7001 233 45 the the DET ejpam-7001 233 46 pdf pdf NOUN ejpam-7001 233 47 of of ADP ejpam-7001 233 48 the the DET ejpam-7001 233 49 rth rth PROPN ejpam-7001 233 50 order order NOUN ejpam-7001 233 51 statistic statistic NOUN ejpam-7001 233 52 for for ADP ejpam-7001 233 53 the the DET ejpam-7001 233 54 fréchet fréchet PROPN ejpam-7001 233 55 – – PUNCT ejpam-7001 233 56 weibull weibull NOUN ejpam-7001 233 57 distribution distribution NOUN ejpam-7001 233 58 as as SCONJ ejpam-7001 233 59 follows follow VERB ejpam-7001 233 60 : : PUNCT ejpam-7001 233 61 gxr gxr NOUN ejpam-7001 233 62 : : PUNCT ejpam-7001 233 63 n(x n(x ADJ ejpam-7001 233 64 ) ) PUNCT ejpam-7001 233 65 = = SYM ejpam-7001 234 1 n n X ejpam-7001 234 2 ! ! PUNCT ejpam-7001 235 1 ( ( PUNCT ejpam-7001 235 2 r r NOUN ejpam-7001 235 3 − − PROPN ejpam-7001 235 4 1)!(n− 1)!(n− NUM ejpam-7001 235 5 r r NOUN ejpam-7001 235 6 ) ) PUNCT ejpam-7001 235 7 ! ! PUNCT ejpam-7001 235 8 { { PUNCT ejpam-7001 236 1 αkβαmαkx−1−αke αkβαmαkx−1−αke NUM ejpam-7001 236 2 −rβα −rβα NOUN ejpam-7001 236 3 ( ( PUNCT ejpam-7001 236 4 λ λ X ejpam-7001 236 5 x x NOUN ejpam-7001 236 6 ) ) PUNCT ejpam-7001 236 7 αk αk ADP ejpam-7001 236 8 } } PUNCT ejpam-7001 236 9 [ [ PUNCT ejpam-7001 236 10 1− 1− NUM ejpam-7001 236 11 e e X ejpam-7001 236 12 −βα −βα PROPN ejpam-7001 236 13 ( ( PUNCT ejpam-7001 236 14 λ λ X ejpam-7001 236 15 x x SYM ejpam-7001 236 16 ) ) PUNCT ejpam-7001 236 17 αk]n−r αk]n−r NOUN ejpam-7001 236 18 . . PUNCT ejpam-7001 237 1 6 6 NUM ejpam-7001 237 2 . . X ejpam-7001 237 3 parameter parameter NOUN ejpam-7001 237 4 estimation estimation NOUN ejpam-7001 237 5 this this DET ejpam-7001 237 6 section section NOUN ejpam-7001 237 7 is be AUX ejpam-7001 237 8 devoted devote VERB ejpam-7001 237 9 to to ADP ejpam-7001 237 10 the the DET ejpam-7001 237 11 estimation estimation NOUN ejpam-7001 237 12 of of ADP ejpam-7001 237 13 the the DET ejpam-7001 237 14 parameters parameter NOUN ejpam-7001 237 15 of of ADP ejpam-7001 237 16 the the DET ejpam-7001 237 17 proposed propose VERB ejpam-7001 237 18 crtfw crtfw NOUN ejpam-7001 237 19 distribution distribution NOUN ejpam-7001 237 20 . . PUNCT ejpam-7001 238 1 for for ADP ejpam-7001 238 2 this this DET ejpam-7001 238 3 purpose purpose NOUN ejpam-7001 238 4 , , PUNCT ejpam-7001 238 5 we we PRON ejpam-7001 238 6 employ employ VERB ejpam-7001 238 7 the the DET ejpam-7001 238 8 method method NOUN ejpam-7001 238 9 of of ADP ejpam-7001 238 10 maximum maximum ADJ ejpam-7001 238 11 likelihood likelihood NOUN ejpam-7001 238 12 estimation estimation NOUN ejpam-7001 238 13 ( ( PUNCT ejpam-7001 238 14 mle mle PROPN ejpam-7001 238 15 ) ) PUNCT ejpam-7001 238 16 , , PUNCT ejpam-7001 238 17 which which PRON ejpam-7001 238 18 is be AUX ejpam-7001 238 19 one one NUM ejpam-7001 238 20 of of ADP ejpam-7001 238 21 the the DET ejpam-7001 238 22 most most ADV ejpam-7001 238 23 widely widely ADV ejpam-7001 238 24 used use VERB ejpam-7001 238 25 and and CCONJ ejpam-7001 238 26 efficient efficient ADJ ejpam-7001 238 27 estimation estimation NOUN ejpam-7001 238 28 techniques technique NOUN ejpam-7001 238 29 in in ADP ejpam-7001 238 30 statistical statistical ADJ ejpam-7001 238 31 inference inference NOUN ejpam-7001 238 32 . . PUNCT ejpam-7001 239 1 let let VERB ejpam-7001 239 2 x1 x1 NUM ejpam-7001 239 3 , , PUNCT ejpam-7001 239 4 x2 x2 PROPN ejpam-7001 239 5 , , PUNCT ejpam-7001 239 6 . . PUNCT ejpam-7001 239 7 . . PUNCT ejpam-7001 240 1 . . PUNCT ejpam-7001 241 1 , , PUNCT ejpam-7001 241 2 xn xn PROPN ejpam-7001 241 3 denote denote VERB ejpam-7001 241 4 a a DET ejpam-7001 241 5 random random ADJ ejpam-7001 241 6 sample sample NOUN ejpam-7001 241 7 of of ADP ejpam-7001 241 8 size size NOUN ejpam-7001 241 9 n n CCONJ ejpam-7001 241 10 drawn draw VERB ejpam-7001 241 11 independently independently ADV ejpam-7001 241 12 imliyangba imliyangba PROPN ejpam-7001 241 13 et et PROPN ejpam-7001 241 14 al al PROPN ejpam-7001 241 15 . . PUNCT ejpam-7001 241 16 / / SYM ejpam-7001 241 17 eur eur PROPN ejpam-7001 241 18 . . PUNCT ejpam-7001 242 1 j. j. PROPN ejpam-7001 242 2 pure pure PROPN ejpam-7001 242 3 appl appl PROPN ejpam-7001 242 4 . . PROPN ejpam-7001 242 5 math math PROPN ejpam-7001 242 6 , , PUNCT ejpam-7001 242 7 18 18 NUM ejpam-7001 242 8 ( ( PUNCT ejpam-7001 242 9 4 4 NUM ejpam-7001 242 10 ) ) PUNCT ejpam-7001 242 11 ( ( PUNCT ejpam-7001 242 12 2025 2025 NUM ejpam-7001 242 13 ) ) PUNCT ejpam-7001 242 14 , , PUNCT ejpam-7001 242 15 7001 7001 NUM ejpam-7001 242 16 15 15 NUM ejpam-7001 242 17 of of ADP ejpam-7001 242 18 27 27 NUM ejpam-7001 242 19 from from ADP ejpam-7001 242 20 the the DET ejpam-7001 242 21 crtfw crtfw NOUN ejpam-7001 242 22 distribution distribution NOUN ejpam-7001 242 23 with with ADP ejpam-7001 242 24 probability probability NOUN ejpam-7001 242 25 density density NOUN ejpam-7001 242 26 function function VERB ejpam-7001 242 27 f(x f(x PROPN ejpam-7001 242 28 ) ) PUNCT ejpam-7001 242 29 . . PUNCT ejpam-7001 243 1 the the DET ejpam-7001 243 2 corresponding corresponding ADJ ejpam-7001 243 3 log log NOUN ejpam-7001 243 4 - - PUNCT ejpam-7001 243 5 likelihood likelihood NOUN ejpam-7001 243 6 function function NOUN ejpam-7001 243 7 can can AUX ejpam-7001 243 8 be be AUX ejpam-7001 243 9 expressed express VERB ejpam-7001 243 10 as as ADP ejpam-7001 243 11 logl(x logl(x PROPN ejpam-7001 243 12 ) ) PUNCT ejpam-7001 243 13 = = NOUN ejpam-7001 243 14 { { PUNCT ejpam-7001 243 15 n n CCONJ ejpam-7001 243 16 log log VERB ejpam-7001 243 17 λ1 λ1 PROPN ejpam-7001 243 18 − − PROPN ejpam-7001 243 19 2(λ2 2(λ2 NUM ejpam-7001 243 20 − − NOUN ejpam-7001 243 21 λ1)β λ1)β ADJ ejpam-7001 243 22 α α PROPN ejpam-7001 244 1 n∑ n∑ NOUN ejpam-7001 244 2 i=1 i=1 PROPN ejpam-7001 245 1 ( ( PUNCT ejpam-7001 245 2 m m AUX ejpam-7001 245 3 xi xi X ejpam-7001 245 4 ) ) PUNCT ejpam-7001 245 5 αk αk CCONJ ejpam-7001 245 6 − − PROPN ejpam-7001 245 7 6(1− 6(1− NUM ejpam-7001 245 8 λ1)β λ1)β VERB ejpam-7001 245 9 α α NOUN ejpam-7001 246 1 n∑ n∑ NOUN ejpam-7001 246 2 i=1 i=1 PROPN ejpam-7001 247 1 ( ( PUNCT ejpam-7001 247 2 m m PROPN ejpam-7001 247 3 xi xi X ejpam-7001 247 4 ) ) PUNCT ejpam-7001 247 5 αk αk ADP ejpam-7001 247 6 } } PUNCT ejpam-7001 247 7 + + CCONJ ejpam-7001 247 8 n n PRON ejpam-7001 247 9 log(αk log(αk ADJ ejpam-7001 247 10 ) ) PUNCT ejpam-7001 248 1 + + CCONJ ejpam-7001 248 2 nα nα X ejpam-7001 248 3 log(β log(β NUM ejpam-7001 248 4 ) ) PUNCT ejpam-7001 249 1 + + CCONJ ejpam-7001 249 2 nαk nαk NOUN ejpam-7001 249 3 log(m)− log(m)− PROPN ejpam-7001 249 4 ( ( PUNCT ejpam-7001 249 5 1− 1− NUM ejpam-7001 249 6 αk αk NOUN ejpam-7001 249 7 ) ) PUNCT ejpam-7001 249 8 n∑ n∑ NOUN ejpam-7001 249 9 i=1 i=1 PROPN ejpam-7001 249 10 log(xi)− log(xi)− PROPN ejpam-7001 249 11 βα βα PROPN ejpam-7001 250 1 n∑ n∑ PROPN ejpam-7001 250 2 i=1 i=1 PROPN ejpam-7001 251 1 ( ( PUNCT ejpam-7001 251 2 m m PROPN ejpam-7001 251 3 xi xi X ejpam-7001 251 4 ) ) PUNCT ejpam-7001 251 5 αk αk NOUN ejpam-7001 251 6 . . PUNCT ejpam-7001 252 1 ( ( PUNCT ejpam-7001 252 2 15 15 NUM ejpam-7001 252 3 ) ) PUNCT ejpam-7001 252 4 the the DET ejpam-7001 252 5 likelihood likelihood NOUN ejpam-7001 252 6 equations equation NOUN ejpam-7001 252 7 are be AUX ejpam-7001 252 8 obtained obtain VERB ejpam-7001 252 9 by by ADP ejpam-7001 252 10 differentiating differentiate VERB ejpam-7001 252 11 equation equation NOUN ejpam-7001 252 12 ( ( PUNCT ejpam-7001 252 13 15 15 NUM ejpam-7001 252 14 ) ) PUNCT ejpam-7001 252 15 with with ADP ejpam-7001 252 16 respect respect NOUN ejpam-7001 252 17 to to ADP ejpam-7001 252 18 each each PRON ejpam-7001 252 19 of of ADP ejpam-7001 252 20 the the DET ejpam-7001 252 21 parameters parameter NOUN ejpam-7001 252 22 α α NOUN ejpam-7001 252 23 , , PUNCT ejpam-7001 252 24 β β NOUN ejpam-7001 252 25 , , PUNCT ejpam-7001 252 26 λ1 λ1 ADJ ejpam-7001 252 27 , , PUNCT ejpam-7001 252 28 λ2 λ2 PROPN ejpam-7001 252 29 , , PUNCT ejpam-7001 252 30 m m PROPN ejpam-7001 252 31 , , PUNCT ejpam-7001 252 32 and and CCONJ ejpam-7001 252 33 k k NOUN ejpam-7001 252 34 , , PUNCT ejpam-7001 252 35 and and CCONJ ejpam-7001 252 36 then then ADV ejpam-7001 252 37 equating equate VERB ejpam-7001 252 38 the the DET ejpam-7001 252 39 derivatives derivative NOUN ejpam-7001 252 40 to to ADP ejpam-7001 252 41 zero zero NUM ejpam-7001 252 42 . . PUNCT ejpam-7001 253 1 the the DET ejpam-7001 253 2 resulting result VERB ejpam-7001 253 3 score score NOUN ejpam-7001 253 4 functions function NOUN ejpam-7001 253 5 are be AUX ejpam-7001 253 6 given give VERB ejpam-7001 253 7 below below ADP ejpam-7001 253 8 : : PUNCT ejpam-7001 254 1 ∂ ∂ NUM ejpam-7001 254 2 logl(x logl(x PROPN ejpam-7001 254 3 ) ) PUNCT ejpam-7001 254 4 ∂α ∂α PROPN ejpam-7001 254 5 = = PUNCT ejpam-7001 254 6 { { PUNCT ejpam-7001 254 7 n n NOUN ejpam-7001 254 8 α α NOUN ejpam-7001 254 9 − − PROPN ejpam-7001 254 10 ( ( PUNCT ejpam-7001 254 11 7− 7− NUM ejpam-7001 254 12 2λ1 2λ1 NUM ejpam-7001 255 1 − − NUM ejpam-7001 256 1 4λ2)β 4λ2)β INTJ ejpam-7001 257 1 αk αk INTJ ejpam-7001 257 2 n∑ n∑ NOUN ejpam-7001 257 3 i=1 i=1 PROPN ejpam-7001 258 1 ( ( PUNCT ejpam-7001 258 2 m m PROPN ejpam-7001 258 3 xi xi X ejpam-7001 258 4 ) ) PUNCT ejpam-7001 259 1 αk αk NOUN ejpam-7001 260 1 + + CCONJ ejpam-7001 260 2 log log VERB ejpam-7001 260 3 β β PROPN ejpam-7001 260 4 n∑ n∑ NOUN ejpam-7001 260 5 i=1 i=1 PROPN ejpam-7001 260 6 ( ( PUNCT ejpam-7001 260 7 m m PROPN ejpam-7001 260 8 xi xi X ejpam-7001 260 9 ) ) PUNCT ejpam-7001 260 10 αk αk CCONJ ejpam-7001 260 11 + + NOUN ejpam-7001 260 12 n n PRON ejpam-7001 260 13 log(β log(β PROPN ejpam-7001 260 14 ) ) PUNCT ejpam-7001 261 1 + + CCONJ ejpam-7001 261 2 nk nk PROPN ejpam-7001 261 3 log(m)− log(m)− PROPN ejpam-7001 262 1 k k PROPN ejpam-7001 262 2 n∑ n∑ PROPN ejpam-7001 262 3 i=1 i=1 PROPN ejpam-7001 262 4 log(xi log(xi X ejpam-7001 262 5 ) ) PUNCT ejpam-7001 262 6 } } PUNCT ejpam-7001 263 1 = = SYM ejpam-7001 263 2 0 0 NUM ejpam-7001 263 3 , , PUNCT ejpam-7001 263 4 ∂ ∂ NUM ejpam-7001 263 5 logl(x logl(x PROPN ejpam-7001 263 6 ) ) PUNCT ejpam-7001 263 7 ∂β ∂β PROPN ejpam-7001 264 1 = = PUNCT ejpam-7001 264 2 { { PUNCT ejpam-7001 264 3 nα nα NOUN ejpam-7001 264 4 β β X ejpam-7001 264 5 − − X ejpam-7001 264 6 αβα−1(7− αβα−1(7− PROPN ejpam-7001 264 7 2λ1 2λ1 NUM ejpam-7001 264 8 − − NUM ejpam-7001 264 9 4λ2 4λ2 NUM ejpam-7001 264 10 ) ) PUNCT ejpam-7001 265 1 n∑ n∑ NOUN ejpam-7001 265 2 i=1 i=1 PROPN ejpam-7001 266 1 ( ( PUNCT ejpam-7001 266 2 m m PROPN ejpam-7001 266 3 xi xi X ejpam-7001 266 4 ) ) PUNCT ejpam-7001 266 5 αk αk NOUN ejpam-7001 266 6 } } PUNCT ejpam-7001 266 7 = = SYM ejpam-7001 266 8 0 0 NUM ejpam-7001 266 9 , , PUNCT ejpam-7001 266 10 ∂ ∂ NUM ejpam-7001 267 1 logl(x logl(x PROPN ejpam-7001 267 2 ) ) PUNCT ejpam-7001 267 3 ∂λ1 ∂λ1 NOUN ejpam-7001 267 4 = = SYM ejpam-7001 267 5 { { PUNCT ejpam-7001 267 6 n n CCONJ ejpam-7001 267 7 λ1 λ1 PROPN ejpam-7001 267 8 − − PROPN ejpam-7001 267 9 2βα 2βα NOUN ejpam-7001 267 10 n∑ n∑ PROPN ejpam-7001 267 11 i=1 i=1 PROPN ejpam-7001 268 1 ( ( PUNCT ejpam-7001 268 2 m m PROPN ejpam-7001 268 3 xi xi X ejpam-7001 268 4 ) ) PUNCT ejpam-7001 268 5 αk αk NOUN ejpam-7001 268 6 } } PUNCT ejpam-7001 268 7 = = SYM ejpam-7001 268 8 0 0 NUM ejpam-7001 268 9 , , PUNCT ejpam-7001 268 10 ∂ ∂ NUM ejpam-7001 269 1 logl(x logl(x PROPN ejpam-7001 269 2 ) ) PUNCT ejpam-7001 270 1 ∂λ2 ∂λ2 PROPN ejpam-7001 270 2 = = PUNCT ejpam-7001 270 3 { { PUNCT ejpam-7001 270 4 4βα 4βα PROPN ejpam-7001 270 5 n∑ n∑ PROPN ejpam-7001 271 1 i=1 i=1 PROPN ejpam-7001 271 2 ( ( PUNCT ejpam-7001 271 3 m m PROPN ejpam-7001 271 4 xi xi X ejpam-7001 271 5 ) ) PUNCT ejpam-7001 271 6 αk αk NOUN ejpam-7001 271 7 } } PUNCT ejpam-7001 271 8 = = SYM ejpam-7001 271 9 0 0 NUM ejpam-7001 271 10 , , PUNCT ejpam-7001 271 11 ∂ ∂ NUM ejpam-7001 271 12 logl(x logl(x PROPN ejpam-7001 271 13 ) ) PUNCT ejpam-7001 271 14 ∂m ∂m PROPN ejpam-7001 272 1 = = PUNCT ejpam-7001 272 2 { { PUNCT ejpam-7001 272 3 nαk nαk NOUN ejpam-7001 272 4 m m VERB ejpam-7001 272 5 − − NOUN ejpam-7001 272 6 βα(7− βα(7− ADJ ejpam-7001 272 7 2λ1 2λ1 NUM ejpam-7001 272 8 − − NUM ejpam-7001 272 9 4λ2 4λ2 NUM ejpam-7001 272 10 ) ) PUNCT ejpam-7001 273 1 n∑ n∑ NOUN ejpam-7001 273 2 i=1 i=1 PROPN ejpam-7001 274 1 ( ( PUNCT ejpam-7001 274 2 m m PROPN ejpam-7001 274 3 xi xi X ejpam-7001 274 4 ) ) PUNCT ejpam-7001 274 5 αk αk CCONJ ejpam-7001 274 6 αkm(αk−1 αkm(αk−1 PROPN ejpam-7001 274 7 ) ) PUNCT ejpam-7001 274 8 } } PUNCT ejpam-7001 275 1 = = SYM ejpam-7001 275 2 0 0 NUM ejpam-7001 275 3 , , PUNCT ejpam-7001 275 4 ∂ ∂ NUM ejpam-7001 275 5 logl(x logl(x NOUN ejpam-7001 275 6 ) ) PUNCT ejpam-7001 275 7 ∂k ∂k PROPN ejpam-7001 275 8 = = X ejpam-7001 275 9 { { PUNCT ejpam-7001 275 10 n n NOUN ejpam-7001 275 11 k k NOUN ejpam-7001 275 12 − − PROPN ejpam-7001 276 1 βα(7− βα(7− PROPN ejpam-7001 276 2 2λ1 2λ1 NUM ejpam-7001 276 3 − − NUM ejpam-7001 277 1 4λ2)α 4λ2)α NUM ejpam-7001 278 1 n∑ n∑ NOUN ejpam-7001 278 2 i=1 i=1 PROPN ejpam-7001 279 1 ( ( PUNCT ejpam-7001 279 2 m m PROPN ejpam-7001 279 3 xi xi X ejpam-7001 279 4 ) ) PUNCT ejpam-7001 280 1 αk αk NOUN ejpam-7001 280 2 log log NOUN ejpam-7001 280 3 ( ( PUNCT ejpam-7001 280 4 m m NOUN ejpam-7001 280 5 xi xi X ejpam-7001 280 6 ) ) PUNCT ejpam-7001 281 1 + + ADP ejpam-7001 281 2 nα nα ADP ejpam-7001 281 3 log(m)− log(m)− PROPN ejpam-7001 281 4 α α NUM ejpam-7001 281 5 n∑ n∑ PROPN ejpam-7001 281 6 i=1 i=1 PROPN ejpam-7001 281 7 log(xi log(xi X ejpam-7001 281 8 ) ) PUNCT ejpam-7001 281 9 } } PUNCT ejpam-7001 281 10 = = PUNCT ejpam-7001 281 11 0 0 X ejpam-7001 281 12 . . PUNCT ejpam-7001 281 13 imliyangba imliyangba PROPN ejpam-7001 281 14 et et PROPN ejpam-7001 281 15 al al PROPN ejpam-7001 281 16 . . PUNCT ejpam-7001 281 17 / / SYM ejpam-7001 281 18 eur eur PROPN ejpam-7001 281 19 . . PUNCT ejpam-7001 282 1 j. j. PROPN ejpam-7001 282 2 pure pure PROPN ejpam-7001 282 3 appl appl PROPN ejpam-7001 282 4 . . PROPN ejpam-7001 282 5 math math PROPN ejpam-7001 282 6 , , PUNCT ejpam-7001 282 7 18 18 NUM ejpam-7001 282 8 ( ( PUNCT ejpam-7001 282 9 4 4 NUM ejpam-7001 282 10 ) ) PUNCT ejpam-7001 282 11 ( ( PUNCT ejpam-7001 282 12 2025 2025 NUM ejpam-7001 282 13 ) ) PUNCT ejpam-7001 282 14 , , PUNCT ejpam-7001 282 15 7001 7001 NUM ejpam-7001 282 16 16 16 NUM ejpam-7001 282 17 of of ADP ejpam-7001 282 18 27 27 NUM ejpam-7001 282 19 in in ADP ejpam-7001 282 20 principle principle NOUN ejpam-7001 282 21 , , PUNCT ejpam-7001 282 22 the the DET ejpam-7001 282 23 maximum maximum ADJ ejpam-7001 282 24 likelihood likelihood NOUN ejpam-7001 282 25 estimates estimate NOUN ejpam-7001 282 26 ( ( PUNCT ejpam-7001 282 27 mles mle NOUN ejpam-7001 282 28 ) ) PUNCT ejpam-7001 282 29 of of ADP ejpam-7001 282 30 the the DET ejpam-7001 282 31 parameters parameter NOUN ejpam-7001 282 32 α α NOUN ejpam-7001 282 33 , , PUNCT ejpam-7001 282 34 β β NOUN ejpam-7001 282 35 , , PUNCT ejpam-7001 282 36 λ1 λ1 ADJ ejpam-7001 282 37 , , PUNCT ejpam-7001 282 38 λ2 λ2 PROPN ejpam-7001 282 39 , , PUNCT ejpam-7001 282 40 m m PRON ejpam-7001 282 41 , , PUNCT ejpam-7001 282 42 and and CCONJ ejpam-7001 282 43 k k PROPN ejpam-7001 282 44 can can AUX ejpam-7001 282 45 be be AUX ejpam-7001 282 46 derived derive VERB ejpam-7001 282 47 from from ADP ejpam-7001 282 48 the the DET ejpam-7001 282 49 aforementioned aforementioned ADJ ejpam-7001 282 50 system system NOUN ejpam-7001 282 51 of of ADP ejpam-7001 282 52 nonlinear nonlinear ADJ ejpam-7001 282 53 equations equation NOUN ejpam-7001 282 54 . . PUNCT ejpam-7001 283 1 nonetheless nonetheless ADV ejpam-7001 283 2 , , PUNCT ejpam-7001 283 3 analytically analytically ADV ejpam-7001 283 4 solving solve VERB ejpam-7001 283 5 these these DET ejpam-7001 283 6 equations equation NOUN ejpam-7001 283 7 in in ADP ejpam-7001 283 8 closed closed ADJ ejpam-7001 283 9 form form NOUN ejpam-7001 283 10 is be AUX ejpam-7001 283 11 exceedingly exceedingly ADV ejpam-7001 283 12 challenging challenging ADJ ejpam-7001 283 13 due due ADJ ejpam-7001 283 14 to to ADP ejpam-7001 283 15 their their PRON ejpam-7001 283 16 nonlinear nonlinear ADJ ejpam-7001 283 17 and and CCONJ ejpam-7001 283 18 interrelated interrelated ADJ ejpam-7001 283 19 nature nature NOUN ejpam-7001 283 20 . . PUNCT ejpam-7001 284 1 consequently consequently ADV ejpam-7001 284 2 , , PUNCT ejpam-7001 284 3 an an DET ejpam-7001 284 4 iterative iterative NOUN ejpam-7001 284 5 numerical numerical ADJ ejpam-7001 284 6 technique technique NOUN ejpam-7001 284 7 like like ADP ejpam-7001 284 8 the the DET ejpam-7001 284 9 newton newton PROPN ejpam-7001 284 10 – – PUNCT ejpam-7001 284 11 raphson raphson NOUN ejpam-7001 284 12 algorithm algorithm NOUN ejpam-7001 284 13 is be AUX ejpam-7001 284 14 typically typically ADV ejpam-7001 284 15 utilized utilize VERB ejpam-7001 284 16 to to PART ejpam-7001 284 17 get get VERB ejpam-7001 284 18 approximate approximate ADJ ejpam-7001 284 19 solutions solution NOUN ejpam-7001 284 20 . . PUNCT ejpam-7001 285 1 statistical statistical ADJ ejpam-7001 285 2 software software NOUN ejpam-7001 285 3 packages package NOUN ejpam-7001 285 4 ( ( PUNCT ejpam-7001 285 5 e.g. e.g. ADV ejpam-7001 285 6 , , PUNCT ejpam-7001 285 7 r r NOUN ejpam-7001 285 8 , , PUNCT ejpam-7001 285 9 matlab matlab PROPN ejpam-7001 285 10 , , PUNCT ejpam-7001 285 11 or or CCONJ ejpam-7001 285 12 python python NOUN ejpam-7001 285 13 ) ) PUNCT ejpam-7001 285 14 are be AUX ejpam-7001 285 15 employed employ VERB ejpam-7001 285 16 to to PART ejpam-7001 285 17 compute compute VERB ejpam-7001 285 18 the the DET ejpam-7001 285 19 maximum maximum ADJ ejpam-7001 285 20 likelihood likelihood NOUN ejpam-7001 285 21 estimates estimate NOUN ejpam-7001 285 22 efficiently efficiently ADV ejpam-7001 285 23 . . PUNCT ejpam-7001 286 1 section section NOUN ejpam-7001 286 2 7 7 NUM ejpam-7001 286 3 offers offer VERB ejpam-7001 286 4 a a DET ejpam-7001 286 5 comprehensive comprehensive ADJ ejpam-7001 286 6 examination examination NOUN ejpam-7001 286 7 of of ADP ejpam-7001 286 8 the the DET ejpam-7001 286 9 estimating estimate VERB ejpam-7001 286 10 technique technique NOUN ejpam-7001 286 11 , , PUNCT ejpam-7001 286 12 encompassing encompass VERB ejpam-7001 286 13 a a DET ejpam-7001 286 14 simulation simulation NOUN ejpam-7001 286 15 study study NOUN ejpam-7001 286 16 and and CCONJ ejpam-7001 286 17 applications application NOUN ejpam-7001 286 18 involving involve VERB ejpam-7001 286 19 real real ADJ ejpam-7001 286 20 data datum NOUN ejpam-7001 286 21 . . PUNCT ejpam-7001 287 1 7 7 X ejpam-7001 287 2 . . X ejpam-7001 287 3 simulation simulation NOUN ejpam-7001 287 4 - - PUNCT ejpam-7001 287 5 based base VERB ejpam-7001 287 6 analysis analysis NOUN ejpam-7001 287 7 of of ADP ejpam-7001 287 8 estimator estimator NOUN ejpam-7001 287 9 properties property NOUN ejpam-7001 287 10 we we PRON ejpam-7001 287 11 performed perform VERB ejpam-7001 287 12 a a DET ejpam-7001 287 13 simulation simulation NOUN ejpam-7001 287 14 research research NOUN ejpam-7001 287 15 to to PART ejpam-7001 287 16 assess assess VERB ejpam-7001 287 17 the the DET ejpam-7001 287 18 efficacy efficacy NOUN ejpam-7001 287 19 of of ADP ejpam-7001 287 20 the the DET ejpam-7001 287 21 maximum maximum ADJ ejpam-7001 287 22 likelihood likelihood NOUN ejpam-7001 287 23 estimates estimate NOUN ejpam-7001 287 24 ( ( PUNCT ejpam-7001 287 25 mles mle NOUN ejpam-7001 287 26 ) ) PUNCT ejpam-7001 287 27 . . PUNCT ejpam-7001 288 1 in in ADP ejpam-7001 288 2 this this DET ejpam-7001 288 3 simulation simulation NOUN ejpam-7001 288 4 study study NOUN ejpam-7001 288 5 , , PUNCT ejpam-7001 288 6 mles mle NOUN ejpam-7001 288 7 were be AUX ejpam-7001 288 8 computed compute VERB ejpam-7001 288 9 for for ADP ejpam-7001 288 10 random random ADJ ejpam-7001 288 11 samples sample NOUN ejpam-7001 288 12 from from ADP ejpam-7001 288 13 different different ADJ ejpam-7001 288 14 sizes size NOUN ejpam-7001 288 15 , , PUNCT ejpam-7001 288 16 which which PRON ejpam-7001 288 17 were be AUX ejpam-7001 288 18 drawn draw VERB ejpam-7001 288 19 from from ADP ejpam-7001 288 20 the the DET ejpam-7001 288 21 crtfw crtfw NOUN ejpam-7001 288 22 distribution distribution NOUN ejpam-7001 288 23 . . PUNCT ejpam-7001 289 1 the the DET ejpam-7001 289 2 simulation simulation NOUN ejpam-7001 289 3 algorithm algorithm NOUN ejpam-7001 289 4 is be AUX ejpam-7001 289 5 given give VERB ejpam-7001 289 6 below below ADP ejpam-7001 289 7 : : PUNCT ejpam-7001 289 8 • • NUM ejpam-7001 289 9 step step NOUN ejpam-7001 289 10 1 1 NUM ejpam-7001 289 11 : : PUNCT ejpam-7001 289 12 generate generate VERB ejpam-7001 289 13 random random ADJ ejpam-7001 289 14 samples sample NOUN ejpam-7001 289 15 of of ADP ejpam-7001 289 16 sizes size NOUN ejpam-7001 289 17 n n NOUN ejpam-7001 289 18 = = SYM ejpam-7001 289 19 50 50 NUM ejpam-7001 289 20 , , PUNCT ejpam-7001 289 21 80 80 NUM ejpam-7001 289 22 , , PUNCT ejpam-7001 289 23 100 100 NUM ejpam-7001 289 24 , , PUNCT ejpam-7001 289 25 200 200 NUM ejpam-7001 289 26 , , PUNCT ejpam-7001 289 27 500 500 NUM ejpam-7001 289 28 , , PUNCT ejpam-7001 289 29 and and CCONJ ejpam-7001 289 30 600 600 NUM ejpam-7001 289 31 from from ADP ejpam-7001 289 32 the the DET ejpam-7001 289 33 crtfw crtfw NOUN ejpam-7001 289 34 distribution distribution NOUN ejpam-7001 289 35 by by ADP ejpam-7001 289 36 utilizing utilize VERB ejpam-7001 289 37 the the DET ejpam-7001 289 38 parameter parameter NOUN ejpam-7001 289 39 values value NOUN ejpam-7001 289 40 α α X ejpam-7001 289 41 = = SYM ejpam-7001 289 42 0.5 0.5 NUM ejpam-7001 289 43 , , PUNCT ejpam-7001 289 44 β β X ejpam-7001 289 45 = = SYM ejpam-7001 289 46 0.5 0.5 NUM ejpam-7001 289 47 , , PUNCT ejpam-7001 289 48 λ1 λ1 NOUN ejpam-7001 289 49 = = NOUN ejpam-7001 289 50 0.01 0.01 NUM ejpam-7001 289 51 , , PUNCT ejpam-7001 289 52 λ2 λ2 NOUN ejpam-7001 289 53 = = SYM ejpam-7001 289 54 0.1 0.1 NUM ejpam-7001 289 55 , , PUNCT ejpam-7001 289 56 m m VERB ejpam-7001 289 57 = = NOUN ejpam-7001 289 58 0.5 0.5 NUM ejpam-7001 289 59 , , PUNCT ejpam-7001 289 60 and and CCONJ ejpam-7001 289 61 k k X ejpam-7001 289 62 = = SYM ejpam-7001 289 63 0.5 0.5 NUM ejpam-7001 289 64 . . NOUN ejpam-7001 289 65 • • NUM ejpam-7001 289 66 step step NOUN ejpam-7001 289 67 2 2 NUM ejpam-7001 289 68 : : PUNCT ejpam-7001 289 69 evaluate evaluate VERB ejpam-7001 289 70 parameter parameter NOUN ejpam-7001 289 71 estimates estimate NOUN ejpam-7001 289 72 for for ADP ejpam-7001 289 73 each each DET ejpam-7001 289 74 sample sample NOUN ejpam-7001 289 75 of of ADP ejpam-7001 289 76 a a DET ejpam-7001 289 77 specific specific ADJ ejpam-7001 289 78 size size NOUN ejpam-7001 289 79 . . PUNCT ejpam-7001 290 1 • • NUM ejpam-7001 290 2 step step NOUN ejpam-7001 290 3 3 3 NUM ejpam-7001 290 4 : : PUNCT ejpam-7001 290 5 repeat repeat NOUN ejpam-7001 290 6 step step NOUN ejpam-7001 290 7 1 1 NUM ejpam-7001 290 8 and and CCONJ ejpam-7001 290 9 step step NOUN ejpam-7001 290 10 2 2 NUM ejpam-7001 290 11 for for ADP ejpam-7001 290 12 1,000 1,000 NUM ejpam-7001 290 13 times time NOUN ejpam-7001 290 14 . . PUNCT ejpam-7001 291 1 • • NUM ejpam-7001 291 2 step step NOUN ejpam-7001 291 3 4 4 NUM ejpam-7001 291 4 : : PUNCT ejpam-7001 291 5 to to PART ejpam-7001 291 6 calculate calculate VERB ejpam-7001 291 7 the the DET ejpam-7001 291 8 average average ADJ ejpam-7001 291 9 bias bias NOUN ejpam-7001 291 10 and and CCONJ ejpam-7001 291 11 mean mean VERB ejpam-7001 291 12 square square ADJ ejpam-7001 291 13 error error NOUN ejpam-7001 291 14 ( ( PUNCT ejpam-7001 291 15 mse mse NOUN ejpam-7001 291 16 ) ) PUNCT ejpam-7001 291 17 of of ADP ejpam-7001 291 18 the the DET ejpam-7001 291 19 parameters parameter NOUN ejpam-7001 291 20 , , PUNCT ejpam-7001 291 21 i.e. i.e. X ejpam-7001 291 22 , , PUNCT ejpam-7001 291 23 α α NOUN ejpam-7001 291 24 , , PUNCT ejpam-7001 291 25 β β NOUN ejpam-7001 291 26 , , PUNCT ejpam-7001 291 27 λ1 λ1 ADJ ejpam-7001 291 28 , , PUNCT ejpam-7001 291 29 λ2 λ2 PROPN ejpam-7001 291 30 , , PUNCT ejpam-7001 291 31 m m PROPN ejpam-7001 291 32 , , PUNCT ejpam-7001 291 33 and and CCONJ ejpam-7001 291 34 k k NOUN ejpam-7001 291 35 , , PUNCT ejpam-7001 291 36 represented represent VERB ejpam-7001 291 37 by by ADP ejpam-7001 291 38 q q PROPN ejpam-7001 291 39 we we PRON ejpam-7001 291 40 used use VERB ejpam-7001 291 41 the the DET ejpam-7001 291 42 following follow VERB ejpam-7001 291 43 formulae formulae NOUN ejpam-7001 291 44 . . PUNCT ejpam-7001 292 1 let let VERB ejpam-7001 292 2 q∗ q∗ NOUN ejpam-7001 292 3 be be AUX ejpam-7001 292 4 the the DET ejpam-7001 292 5 true true ADJ ejpam-7001 292 6 values value NOUN ejpam-7001 292 7 of of ADP ejpam-7001 292 8 parameters parameter NOUN ejpam-7001 292 9 q. q. VERB ejpam-7001 292 10 then then ADV ejpam-7001 292 11 , , PUNCT ejpam-7001 292 12 the the DET ejpam-7001 292 13 bias bias NOUN ejpam-7001 292 14 and and CCONJ ejpam-7001 292 15 mse mse NOUN ejpam-7001 292 16 from from ADP ejpam-7001 292 17 true true ADJ ejpam-7001 292 18 values value NOUN ejpam-7001 292 19 of of ADP ejpam-7001 292 20 parameters parameter NOUN ejpam-7001 292 21 q∗ q∗ NOUN ejpam-7001 292 22 are be AUX ejpam-7001 292 23 defined define VERB ejpam-7001 292 24 as as ADP ejpam-7001 292 25 : : PUNCT ejpam-7001 292 26 bias(q̂ bias(q̂ NUM ejpam-7001 292 27 ) ) PUNCT ejpam-7001 292 28 = = SYM ejpam-7001 293 1 1 1 NUM ejpam-7001 293 2 n n NUM ejpam-7001 293 3 n∑ n∑ NOUN ejpam-7001 293 4 i=1 i=1 PROPN ejpam-7001 293 5 ( ( PUNCT ejpam-7001 293 6 q̂−q∗ q̂−q∗ PROPN ejpam-7001 293 7 ) ) PUNCT ejpam-7001 293 8 , , PUNCT ejpam-7001 293 9 mse(q̂ mse(q̂ PROPN ejpam-7001 293 10 ) ) PUNCT ejpam-7001 293 11 = = SYM ejpam-7001 294 1 1 1 NUM ejpam-7001 294 2 n n NUM ejpam-7001 294 3 n∑ n∑ NOUN ejpam-7001 294 4 i=1 i=1 PROPN ejpam-7001 294 5 ( ( PUNCT ejpam-7001 294 6 q̂−q∗)2 q̂−q∗)2 INTJ ejpam-7001 294 7 where where SCONJ ejpam-7001 294 8 n n PRON ejpam-7001 294 9 is be AUX ejpam-7001 294 10 the the DET ejpam-7001 294 11 number number NOUN ejpam-7001 294 12 of of ADP ejpam-7001 294 13 replications replication NOUN ejpam-7001 294 14 and and CCONJ ejpam-7001 294 15 q q NOUN ejpam-7001 294 16 represents represent VERB ejpam-7001 294 17 the the DET ejpam-7001 294 18 parameters parameter NOUN ejpam-7001 294 19 i.e. i.e. X ejpam-7001 294 20 , , PUNCT ejpam-7001 294 21 α α X ejpam-7001 294 22 , , PUNCT ejpam-7001 294 23 β β NOUN ejpam-7001 294 24 , , PUNCT ejpam-7001 294 25 λ1 λ1 ADJ ejpam-7001 294 26 , , PUNCT ejpam-7001 294 27 λ2 λ2 PROPN ejpam-7001 294 28 , , PUNCT ejpam-7001 294 29 m m PRON ejpam-7001 294 30 , , PUNCT ejpam-7001 294 31 and and CCONJ ejpam-7001 294 32 k. k. NOUN ejpam-7001 294 33 for for ADP ejpam-7001 294 34 each each DET ejpam-7001 294 35 replication replication NOUN ejpam-7001 294 36 , , PUNCT ejpam-7001 294 37 we we PRON ejpam-7001 294 38 calculated calculate VERB ejpam-7001 294 39 the the DET ejpam-7001 294 40 mean mean ADJ ejpam-7001 294 41 , , PUNCT ejpam-7001 294 42 bias bias NOUN ejpam-7001 294 43 , , PUNCT ejpam-7001 294 44 and and CCONJ ejpam-7001 294 45 mean mean VERB ejpam-7001 294 46 square square ADJ ejpam-7001 294 47 error error NOUN ejpam-7001 294 48 ( ( PUNCT ejpam-7001 294 49 mse mse NOUN ejpam-7001 294 50 ) ) PUNCT ejpam-7001 294 51 of of ADP ejpam-7001 294 52 the the DET ejpam-7001 294 53 parameter parameter NOUN ejpam-7001 294 54 estimates estimate NOUN ejpam-7001 294 55 , , PUNCT ejpam-7001 294 56 with with ADP ejpam-7001 294 57 the the DET ejpam-7001 294 58 summary summary NOUN ejpam-7001 294 59 results result NOUN ejpam-7001 294 60 presented present VERB ejpam-7001 294 61 in in ADP ejpam-7001 294 62 table table NOUN ejpam-7001 294 63 2 2 NUM ejpam-7001 294 64 . . PUNCT ejpam-7001 295 1 the the DET ejpam-7001 295 2 results result NOUN ejpam-7001 295 3 demonstrate demonstrate VERB ejpam-7001 295 4 that that SCONJ ejpam-7001 295 5 , , PUNCT ejpam-7001 295 6 with with ADP ejpam-7001 295 7 an an DET ejpam-7001 295 8 increase increase NOUN ejpam-7001 295 9 in in ADP ejpam-7001 295 10 sample sample NOUN ejpam-7001 295 11 size size NOUN ejpam-7001 295 12 , , PUNCT ejpam-7001 295 13 the the DET ejpam-7001 295 14 estimated estimate VERB ejpam-7001 295 15 values value NOUN ejpam-7001 295 16 approach approach VERB ejpam-7001 295 17 the the DET ejpam-7001 295 18 actual actual ADJ ejpam-7001 295 19 parameter parameter NOUN ejpam-7001 295 20 values value NOUN ejpam-7001 295 21 . . PUNCT ejpam-7001 296 1 furthermore furthermore ADV ejpam-7001 296 2 , , PUNCT ejpam-7001 296 3 both both CCONJ ejpam-7001 296 4 the the DET ejpam-7001 296 5 bias bias NOUN ejpam-7001 296 6 and and CCONJ ejpam-7001 296 7 the the DET ejpam-7001 296 8 mean mean ADJ ejpam-7001 296 9 squared square VERB ejpam-7001 296 10 error error NOUN ejpam-7001 296 11 diminish diminish NOUN ejpam-7001 296 12 and and CCONJ ejpam-7001 296 13 converge converge VERB ejpam-7001 296 14 to to ADP ejpam-7001 296 15 zero zero NUM ejpam-7001 296 16 with with ADP ejpam-7001 296 17 increasing increase VERB ejpam-7001 296 18 sample sample NOUN ejpam-7001 296 19 sizes size NOUN ejpam-7001 296 20 , , PUNCT ejpam-7001 296 21 so so ADV ejpam-7001 296 22 validating validate VERB ejpam-7001 296 23 the the DET ejpam-7001 296 24 appropriateness appropriateness NOUN ejpam-7001 296 25 and and CCONJ ejpam-7001 296 26 consistency consistency NOUN ejpam-7001 296 27 of of ADP ejpam-7001 296 28 the the DET ejpam-7001 296 29 maximum maximum ADJ ejpam-7001 296 30 likelihood likelihood NOUN ejpam-7001 296 31 estimation estimation NOUN ejpam-7001 296 32 method method NOUN ejpam-7001 296 33 for for ADP ejpam-7001 296 34 the the DET ejpam-7001 296 35 crtfw crtfw NOUN ejpam-7001 296 36 distribution distribution NOUN ejpam-7001 296 37 . . PUNCT ejpam-7001 297 1 imliyangba imliyangba PROPN ejpam-7001 297 2 et et PROPN ejpam-7001 297 3 al al PROPN ejpam-7001 297 4 . . PUNCT ejpam-7001 297 5 / / SYM ejpam-7001 297 6 eur eur PROPN ejpam-7001 297 7 . . PUNCT ejpam-7001 298 1 j. j. PROPN ejpam-7001 298 2 pure pure PROPN ejpam-7001 298 3 appl appl PROPN ejpam-7001 298 4 . . PROPN ejpam-7001 298 5 math math PROPN ejpam-7001 298 6 , , PUNCT ejpam-7001 298 7 18 18 NUM ejpam-7001 298 8 ( ( PUNCT ejpam-7001 298 9 4 4 NUM ejpam-7001 298 10 ) ) PUNCT ejpam-7001 298 11 ( ( PUNCT ejpam-7001 298 12 2025 2025 NUM ejpam-7001 298 13 ) ) PUNCT ejpam-7001 298 14 , , PUNCT ejpam-7001 298 15 7001 7001 NUM ejpam-7001 298 16 17 17 NUM ejpam-7001 298 17 of of ADP ejpam-7001 298 18 27 27 NUM ejpam-7001 298 19 table table NOUN ejpam-7001 298 20 2 2 NUM ejpam-7001 298 21 : : PUNCT ejpam-7001 298 22 average average ADJ ejpam-7001 298 23 estimates estimate NOUN ejpam-7001 298 24 of of ADP ejpam-7001 298 25 parameters parameter NOUN ejpam-7001 298 26 , , PUNCT ejpam-7001 298 27 bias bias NOUN ejpam-7001 298 28 , , PUNCT ejpam-7001 298 29 and and CCONJ ejpam-7001 298 30 mse mse NOUN ejpam-7001 298 31 for for ADP ejpam-7001 298 32 crtfw crtfw NOUN ejpam-7001 298 33 distribution distribution NOUN ejpam-7001 298 34 . . PUNCT ejpam-7001 299 1 size size NOUN ejpam-7001 299 2 n n PROPN ejpam-7001 299 3 α̂ α̂ NUM ejpam-7001 299 4 β̂ β̂ ADP ejpam-7001 300 1 λ̂1 λ̂1 X ejpam-7001 300 2 λ̂2 λ̂2 PROPN ejpam-7001 300 3 m̂ m̂ PROPN ejpam-7001 300 4 k̂ k̂ X ejpam-7001 300 5 estimate estimate VERB ejpam-7001 300 6 50 50 NUM ejpam-7001 300 7 0.995089 0.995089 NUM ejpam-7001 300 8 0.850162 0.850162 NUM ejpam-7001 300 9 0.059021 0.059021 NUM ejpam-7001 300 10 0.597612 0.597612 NUM ejpam-7001 300 11 0.805081 0.805081 NUM ejpam-7001 300 12 0.852239 0.852239 NUM ejpam-7001 300 13 80 80 NUM ejpam-7001 300 14 0.924812 0.924812 NUM ejpam-7001 300 15 0.751471 0.751471 NUM ejpam-7001 300 16 0.086000 0.086000 NUM ejpam-7001 300 17 0.534561 0.534561 NUM ejpam-7001 300 18 0.712205 0.712205 NUM ejpam-7001 300 19 0.828724 0.828724 NUM ejpam-7001 300 20 100 100 NUM ejpam-7001 300 21 0.887845 0.887845 NUM ejpam-7001 300 22 0.626945 0.626945 NUM ejpam-7001 300 23 0.057691 0.057691 NUM ejpam-7001 300 24 0.467345 0.467345 NUM ejpam-7001 300 25 0.711295 0.711295 NUM ejpam-7001 300 26 0.766432 0.766432 NUM ejpam-7001 300 27 200 200 NUM ejpam-7001 300 28 0.856031 0.856031 NUM ejpam-7001 300 29 0.664595 0.664595 NUM ejpam-7001 300 30 0.040832 0.040832 NUM ejpam-7001 300 31 0.312545 0.312545 NUM ejpam-7001 300 32 0.698012 0.698012 NUM ejpam-7001 300 33 0.735124 0.735124 NUM ejpam-7001 300 34 500 500 NUM ejpam-7001 300 35 0.552406 0.552406 NUM ejpam-7001 300 36 0.528823 0.528823 NUM ejpam-7001 300 37 0.03677 0.03677 NUM ejpam-7001 300 38 0.296969 0.296969 NUM ejpam-7001 300 39 0.648339 0.648339 NUM ejpam-7001 300 40 0.564601 0.564601 NUM ejpam-7001 300 41 600 600 NUM ejpam-7001 300 42 0.505899 0.505899 NUM ejpam-7001 300 43 0.517074 0.517074 NUM ejpam-7001 300 44 0.014722 0.014722 NUM ejpam-7001 300 45 0.186874 0.186874 NUM ejpam-7001 300 46 0.609673 0.609673 NUM ejpam-7001 300 47 0.508491 0.508491 NUM ejpam-7001 300 48 bias bias NOUN ejpam-7001 300 49 50 50 NUM ejpam-7001 300 50 0.495089 0.495089 NUM ejpam-7001 300 51 0.350162 0.350162 NUM ejpam-7001 300 52 0.049021 0.049021 NUM ejpam-7001 300 53 0.497612 0.497612 NUM ejpam-7001 300 54 0.305081 0.305081 NUM ejpam-7001 300 55 0.352239 0.352239 NUM ejpam-7001 300 56 80 80 NUM ejpam-7001 300 57 0.424812 0.424812 NUM ejpam-7001 300 58 0.251471 0.251471 NUM ejpam-7001 300 59 0.076 0.076 NUM ejpam-7001 300 60 0.434561 0.434561 NUM ejpam-7001 300 61 0.212205 0.212205 NUM ejpam-7001 300 62 0.328724 0.328724 NUM ejpam-7001 300 63 100 100 NUM ejpam-7001 300 64 0.387845 0.387845 NUM ejpam-7001 301 1 0.126945 0.126945 NUM ejpam-7001 301 2 0.047691 0.047691 NUM ejpam-7001 301 3 0.367345 0.367345 NUM ejpam-7001 301 4 0.211295 0.211295 NUM ejpam-7001 301 5 0.266432 0.266432 NUM ejpam-7001 301 6 200 200 NUM ejpam-7001 301 7 0.356031 0.356031 NUM ejpam-7001 301 8 0.164595 0.164595 NUM ejpam-7001 301 9 0.030832 0.030832 NUM ejpam-7001 301 10 0.212545 0.212545 NUM ejpam-7001 301 11 0.198012 0.198012 NUM ejpam-7001 301 12 0.235124 0.235124 NUM ejpam-7001 301 13 500 500 NUM ejpam-7001 301 14 0.052406 0.052406 NUM ejpam-7001 301 15 0.028823 0.028823 NUM ejpam-7001 301 16 0.02677 0.02677 NUM ejpam-7001 301 17 0.196969 0.196969 NUM ejpam-7001 301 18 0.148339 0.148339 NUM ejpam-7001 301 19 0.064601 0.064601 NUM ejpam-7001 301 20 600 600 NUM ejpam-7001 301 21 0.005899 0.005899 NUM ejpam-7001 301 22 0.017074 0.017074 NUM ejpam-7001 301 23 0.004722 0.004722 NUM ejpam-7001 301 24 0.086874 0.086874 NUM ejpam-7001 301 25 0.109673 0.109673 NUM ejpam-7001 301 26 0.008491 0.008491 NUM ejpam-7001 301 27 mse mse NOUN ejpam-7001 301 28 50 50 NUM ejpam-7001 301 29 15.33271 15.33271 NUM ejpam-7001 301 30 17.12075 17.12075 NUM ejpam-7001 301 31 0.654881 0.654881 NUM ejpam-7001 301 32 0.732761 0.732761 NUM ejpam-7001 301 33 21.96745 21.96745 NUM ejpam-7001 301 34 2.455233 2.455233 NUM ejpam-7001 301 35 80 80 NUM ejpam-7001 301 36 10.58112 10.58112 NUM ejpam-7001 301 37 12.59183 12.59183 NUM ejpam-7001 301 38 0.460856 0.460856 NUM ejpam-7001 301 39 0.514562 0.514562 NUM ejpam-7001 301 40 18.87466 18.87466 NUM ejpam-7001 301 41 1.989642 1.989642 NUM ejpam-7001 301 42 100 100 NUM ejpam-7001 301 43 7.543545 7.543545 NUM ejpam-7001 301 44 10.73492 10.73492 NUM ejpam-7001 301 45 0.214024 0.214024 NUM ejpam-7001 301 46 0.612900 0.612900 NUM ejpam-7001 301 47 15.71612 15.71612 NUM ejpam-7001 301 48 0.669543 0.669543 NUM ejpam-7001 301 49 200 200 NUM ejpam-7001 301 50 5.139154 5.139154 NUM ejpam-7001 301 51 13.54455 13.54455 NUM ejpam-7001 301 52 0.188822 0.188822 NUM ejpam-7001 301 53 0.388841 0.388841 NUM ejpam-7001 301 54 15.58835 15.58835 NUM ejpam-7001 301 55 0.603745 0.603745 NUM ejpam-7001 301 56 500 500 NUM ejpam-7001 301 57 1.692579 1.692579 NUM ejpam-7001 301 58 9.84899 9.84899 NUM ejpam-7001 301 59 0.112303 0.112303 NUM ejpam-7001 301 60 0.198201 0.198201 NUM ejpam-7001 301 61 14.71857 14.71857 NUM ejpam-7001 301 62 0.640984 0.640984 NUM ejpam-7001 301 63 600 600 NUM ejpam-7001 301 64 1.341729 1.341729 NUM ejpam-7001 301 65 1.240959 1.240959 NUM ejpam-7001 301 66 0.065385 0.065385 NUM ejpam-7001 301 67 0.035882 0.035882 NUM ejpam-7001 301 68 13.62887 13.62887 NUM ejpam-7001 301 69 0.578568 0.578568 NUM ejpam-7001 301 70 8 8 NUM ejpam-7001 301 71 . . PUNCT ejpam-7001 302 1 evaluating evaluate VERB ejpam-7001 302 2 model model NOUN ejpam-7001 302 3 fit fit ADJ ejpam-7001 302 4 in in ADP ejpam-7001 302 5 sustainability sustainability NOUN ejpam-7001 302 6 data datum NOUN ejpam-7001 302 7 analysis analysis NOUN ejpam-7001 302 8 this this DET ejpam-7001 302 9 section section NOUN ejpam-7001 302 10 evaluates evaluate VERB ejpam-7001 302 11 the the DET ejpam-7001 302 12 proposed propose VERB ejpam-7001 302 13 crtfw crtfw NOUN ejpam-7001 302 14 distribution distribution NOUN ejpam-7001 302 15 using use VERB ejpam-7001 302 16 two two NUM ejpam-7001 302 17 real real ADJ ejpam-7001 302 18 lifetime lifetime NOUN ejpam-7001 302 19 datasets dataset NOUN ejpam-7001 302 20 to to PART ejpam-7001 302 21 determine determine VERB ejpam-7001 302 22 its its PRON ejpam-7001 302 23 goodness goodness NOUN ejpam-7001 302 24 - - PUNCT ejpam-7001 302 25 of of ADP ejpam-7001 302 26 - - PUNCT ejpam-7001 302 27 fit fit NOUN ejpam-7001 302 28 and and CCONJ ejpam-7001 302 29 adaptability adaptability NOUN ejpam-7001 302 30 . . PUNCT ejpam-7001 303 1 the the DET ejpam-7001 303 2 performance performance NOUN ejpam-7001 303 3 of of ADP ejpam-7001 303 4 the the DET ejpam-7001 303 5 crtfw crtfw NOUN ejpam-7001 303 6 model model NOUN ejpam-7001 303 7 is be AUX ejpam-7001 303 8 assessed assess VERB ejpam-7001 303 9 in in ADP ejpam-7001 303 10 comparison comparison NOUN ejpam-7001 303 11 to to ADP ejpam-7001 303 12 several several ADJ ejpam-7001 303 13 established establish VERB ejpam-7001 303 14 competing compete VERB ejpam-7001 303 15 distributions distribution NOUN ejpam-7001 303 16 , , PUNCT ejpam-7001 303 17 including include VERB ejpam-7001 303 18 the the DET ejpam-7001 303 19 weibull weibull NOUN ejpam-7001 303 20 ( ( PUNCT ejpam-7001 303 21 w w NOUN ejpam-7001 303 22 ) ) PUNCT ejpam-7001 303 23 , , PUNCT ejpam-7001 303 24 fréchet fréchet NOUN ejpam-7001 303 25 ( ( PUNCT ejpam-7001 303 26 f f NOUN ejpam-7001 303 27 ) ) PUNCT ejpam-7001 303 28 , , PUNCT ejpam-7001 303 29 fréchet fréchet PROPN ejpam-7001 303 30 – – PUNCT ejpam-7001 303 31 weibull weibull NOUN ejpam-7001 303 32 ( ( PUNCT ejpam-7001 303 33 fw fw ADJ ejpam-7001 303 34 ) ) PUNCT ejpam-7001 303 35 , , PUNCT ejpam-7001 303 36 and and CCONJ ejpam-7001 303 37 qrtfw qrtfw NOUN ejpam-7001 303 38 distributions distribution NOUN ejpam-7001 303 39 . . PUNCT ejpam-7001 304 1 following follow VERB ejpam-7001 304 2 this this DET ejpam-7001 304 3 preliminary preliminary ADJ ejpam-7001 304 4 assessment assessment NOUN ejpam-7001 304 5 , , PUNCT ejpam-7001 304 6 we we PRON ejpam-7001 304 7 broaden broaden VERB ejpam-7001 304 8 the the DET ejpam-7001 304 9 research research NOUN ejpam-7001 304 10 to to PART ejpam-7001 304 11 include include VERB ejpam-7001 304 12 sustainability sustainability NOUN ejpam-7001 304 13 - - PUNCT ejpam-7001 304 14 related relate VERB ejpam-7001 304 15 data datum NOUN ejpam-7001 304 16 to to PART ejpam-7001 304 17 examine examine VERB ejpam-7001 304 18 the the DET ejpam-7001 304 19 significance significance NOUN ejpam-7001 304 20 of of ADP ejpam-7001 304 21 the the DET ejpam-7001 304 22 crtfw crtfw NOUN ejpam-7001 304 23 distribution distribution NOUN ejpam-7001 304 24 in in ADP ejpam-7001 304 25 modeling model VERB ejpam-7001 304 26 environmental environmental ADJ ejpam-7001 304 27 and and CCONJ ejpam-7001 304 28 sustainability sustainability NOUN ejpam-7001 304 29 variables variable NOUN ejpam-7001 304 30 . . PUNCT ejpam-7001 305 1 this this PRON ejpam-7001 305 2 yields yield VERB ejpam-7001 305 3 a a DET ejpam-7001 305 4 focused focused ADJ ejpam-7001 305 5 evaluation evaluation NOUN ejpam-7001 305 6 of of ADP ejpam-7001 305 7 model model NOUN ejpam-7001 305 8 fit fit ADJ ejpam-7001 305 9 in in ADP ejpam-7001 305 10 sustainability sustainability NOUN ejpam-7001 305 11 data datum NOUN ejpam-7001 305 12 analysis analysis NOUN ejpam-7001 305 13 , , PUNCT ejpam-7001 305 14 highlighting highlight VERB ejpam-7001 305 15 the the DET ejpam-7001 305 16 efficacy efficacy NOUN ejpam-7001 305 17 of of ADP ejpam-7001 305 18 the the DET ejpam-7001 305 19 suggested suggest VERB ejpam-7001 305 20 distribution distribution NOUN ejpam-7001 305 21 in in ADP ejpam-7001 305 22 depicting depict VERB ejpam-7001 305 23 the the DET ejpam-7001 305 24 essential essential ADJ ejpam-7001 305 25 trends trend NOUN ejpam-7001 305 26 in in ADP ejpam-7001 305 27 real real ADJ ejpam-7001 305 28 sustainability sustainability NOUN ejpam-7001 305 29 measures measure NOUN ejpam-7001 305 30 . . PUNCT ejpam-7001 306 1 8.1 8.1 NUM ejpam-7001 306 2 . . PUNCT ejpam-7001 307 1 dataset dataset VERB ejpam-7001 307 2 i i NOUN ejpam-7001 307 3 : : PUNCT ejpam-7001 307 4 water water NOUN ejpam-7001 307 5 quality quality NOUN ejpam-7001 307 6 data datum NOUN ejpam-7001 307 7 to to PART ejpam-7001 307 8 assess assess VERB ejpam-7001 307 9 the the DET ejpam-7001 307 10 relevance relevance NOUN ejpam-7001 307 11 of of ADP ejpam-7001 307 12 the the DET ejpam-7001 307 13 crtfw crtfw NOUN ejpam-7001 307 14 distribution distribution NOUN ejpam-7001 307 15 in in ADP ejpam-7001 307 16 environmental environmental ADJ ejpam-7001 307 17 sciences science NOUN ejpam-7001 307 18 , , PUNCT ejpam-7001 307 19 we we PRON ejpam-7001 307 20 analyze analyze VERB ejpam-7001 307 21 a a DET ejpam-7001 307 22 dataset dataset NOUN ejpam-7001 307 23 of of ADP ejpam-7001 307 24 seasonal seasonal ADJ ejpam-7001 307 25 estimated estimate VERB ejpam-7001 307 26 boron boron NOUN ejpam-7001 307 27 ( ( PUNCT ejpam-7001 307 28 b b NOUN ejpam-7001 307 29 ) ) PUNCT ejpam-7001 307 30 concentrations concentration NOUN ejpam-7001 307 31 ( ( PUNCT ejpam-7001 307 32 mg mg PROPN ejpam-7001 307 33 / / SYM ejpam-7001 307 34 l l NOUN ejpam-7001 307 35 ) ) PUNCT ejpam-7001 307 36 in in ADP ejpam-7001 307 37 groundwater groundwater NOUN ejpam-7001 307 38 samples sample NOUN ejpam-7001 307 39 from from ADP ejpam-7001 307 40 rungagora rungagora PROPN ejpam-7001 307 41 te te PROPN ejpam-7001 307 42 belt belt NOUN ejpam-7001 307 43 , , PUNCT ejpam-7001 307 44 golaghat golaghat NOUN ejpam-7001 307 45 district district NOUN ejpam-7001 307 46 , , PUNCT ejpam-7001 307 47 assam assam PROPN ejpam-7001 307 48 , , PUNCT ejpam-7001 307 49 india india PROPN ejpam-7001 307 50 . . PUNCT ejpam-7001 308 1 the the DET ejpam-7001 308 2 measurements measurement NOUN ejpam-7001 308 3 were be AUX ejpam-7001 308 4 obtained obtain VERB ejpam-7001 308 5 from from ADP ejpam-7001 308 6 april april PROPN ejpam-7001 308 7 1 1 NUM ejpam-7001 308 8 , , PUNCT ejpam-7001 308 9 2009 2009 NUM ejpam-7001 308 10 , , PUNCT ejpam-7001 308 11 to to ADP ejpam-7001 308 12 march march PROPN ejpam-7001 308 13 31 31 NUM ejpam-7001 308 14 , , PUNCT ejpam-7001 308 15 2010 2010 NUM ejpam-7001 308 16 . . PUNCT ejpam-7001 309 1 the the DET ejpam-7001 309 2 dataset dataset NOUN ejpam-7001 309 3 was be AUX ejpam-7001 309 4 utilized utilize VERB ejpam-7001 309 5 with with ADP ejpam-7001 309 6 the the DET ejpam-7001 309 7 author author NOUN ejpam-7001 309 8 ’s ’s PART ejpam-7001 309 9 prior prior ADJ ejpam-7001 309 10 consent consent NOUN ejpam-7001 309 11 from from ADP ejpam-7001 309 12 the the DET ejpam-7001 309 13 ph.d ph.d PROPN ejpam-7001 309 14 . . PUNCT ejpam-7001 310 1 thesis thesis NOUN ejpam-7001 310 2 , , PUNCT ejpam-7001 310 3 department department NOUN ejpam-7001 310 4 of of ADP ejpam-7001 310 5 chemistry chemistry NOUN ejpam-7001 310 6 , , PUNCT ejpam-7001 310 7 gauhati gauhati PROPN ejpam-7001 310 8 university university PROPN ejpam-7001 310 9 , , PUNCT ejpam-7001 310 10 assam assam PROPN ejpam-7001 310 11 . . PUNCT ejpam-7001 311 1 the the DET ejpam-7001 311 2 recorded record VERB ejpam-7001 311 3 values value NOUN ejpam-7001 311 4 are be AUX ejpam-7001 311 5 as as SCONJ ejpam-7001 311 6 follows follow VERB ejpam-7001 311 7 : : PUNCT ejpam-7001 311 8 0.56 0.56 NUM ejpam-7001 311 9 , , PUNCT ejpam-7001 311 10 0.67 0.67 NUM ejpam-7001 311 11 , , PUNCT ejpam-7001 311 12 1.09 1.09 NUM ejpam-7001 311 13 , , PUNCT ejpam-7001 311 14 1.35 1.35 NUM ejpam-7001 311 15 , , PUNCT ejpam-7001 311 16 0.12 0.12 NUM ejpam-7001 311 17 , , PUNCT ejpam-7001 311 18 0.27 0.27 NUM ejpam-7001 311 19 , , PUNCT ejpam-7001 311 20 0.56 0.56 NUM ejpam-7001 311 21 , , PUNCT ejpam-7001 312 1 imliyangba imliyangba PROPN ejpam-7001 312 2 et et PROPN ejpam-7001 312 3 al al PROPN ejpam-7001 312 4 . . PUNCT ejpam-7001 312 5 / / SYM ejpam-7001 312 6 eur eur PROPN ejpam-7001 312 7 . . PUNCT ejpam-7001 313 1 j. j. PROPN ejpam-7001 313 2 pure pure PROPN ejpam-7001 313 3 appl appl PROPN ejpam-7001 313 4 . . PROPN ejpam-7001 313 5 math math PROPN ejpam-7001 313 6 , , PUNCT ejpam-7001 313 7 18 18 NUM ejpam-7001 313 8 ( ( PUNCT ejpam-7001 313 9 4 4 NUM ejpam-7001 313 10 ) ) PUNCT ejpam-7001 313 11 ( ( PUNCT ejpam-7001 313 12 2025 2025 NUM ejpam-7001 313 13 ) ) PUNCT ejpam-7001 313 14 , , PUNCT ejpam-7001 313 15 7001 7001 NUM ejpam-7001 313 16 18 18 NUM ejpam-7001 313 17 of of ADP ejpam-7001 313 18 27 27 NUM ejpam-7001 313 19 0.12 0.12 NUM ejpam-7001 313 20 , , PUNCT ejpam-7001 313 21 1.09 1.09 NUM ejpam-7001 313 22 , , PUNCT ejpam-7001 313 23 0.56 0.56 NUM ejpam-7001 313 24 , , PUNCT ejpam-7001 313 25 0.36 0.36 NUM ejpam-7001 313 26 , , PUNCT ejpam-7001 313 27 0.29 0.29 NUM ejpam-7001 313 28 , , PUNCT ejpam-7001 313 29 0.45 0.45 NUM ejpam-7001 313 30 , , PUNCT ejpam-7001 313 31 0.06 0.06 NUM ejpam-7001 313 32 , , PUNCT ejpam-7001 313 33 0.11 0.11 NUM ejpam-7001 313 34 , , PUNCT ejpam-7001 313 35 0.09 0.09 NUM ejpam-7001 313 36 , , PUNCT ejpam-7001 313 37 0.89 0.89 NUM ejpam-7001 313 38 , , PUNCT ejpam-7001 313 39 0.38 0.38 NUM ejpam-7001 313 40 , , PUNCT ejpam-7001 313 41 0.77 0.77 NUM ejpam-7001 313 42 , , PUNCT ejpam-7001 313 43 0.87 0.87 NUM ejpam-7001 313 44 , , PUNCT ejpam-7001 313 45 0.09 0.09 NUM ejpam-7001 313 46 , , PUNCT ejpam-7001 313 47 0.12 0.12 NUM ejpam-7001 313 48 , , PUNCT ejpam-7001 313 49 0.45 0.45 NUM ejpam-7001 313 50 , , PUNCT ejpam-7001 313 51 0.23 0.23 NUM ejpam-7001 313 52 , , PUNCT ejpam-7001 313 53 1.03 1.03 NUM ejpam-7001 313 54 , , PUNCT ejpam-7001 313 55 1.23 1.23 NUM ejpam-7001 313 56 , , PUNCT ejpam-7001 313 57 0.98 0.98 NUM ejpam-7001 313 58 , , PUNCT ejpam-7001 313 59 0.78 0.78 NUM ejpam-7001 313 60 , , PUNCT ejpam-7001 313 61 0.19 0.19 NUM ejpam-7001 313 62 , , PUNCT ejpam-7001 313 63 0.11 0.11 NUM ejpam-7001 313 64 , , PUNCT ejpam-7001 313 65 0.13 0.13 NUM ejpam-7001 313 66 , , PUNCT ejpam-7001 313 67 0.28 0.28 NUM ejpam-7001 313 68 , , PUNCT ejpam-7001 313 69 0.56 0.56 NUM ejpam-7001 313 70 , , PUNCT ejpam-7001 313 71 0.47 0.47 NUM ejpam-7001 313 72 , , PUNCT ejpam-7001 313 73 0.39 0.39 NUM ejpam-7001 313 74 , , PUNCT ejpam-7001 313 75 0.41 0.41 NUM ejpam-7001 313 76 , , PUNCT ejpam-7001 313 77 0.17 0.17 NUM ejpam-7001 313 78 , , PUNCT ejpam-7001 313 79 0.19 0.19 NUM ejpam-7001 313 80 , , PUNCT ejpam-7001 313 81 0.11 0.11 NUM ejpam-7001 313 82 , , PUNCT ejpam-7001 313 83 0.21 0.21 NUM ejpam-7001 313 84 , , PUNCT ejpam-7001 313 85 0.34 0.34 NUM ejpam-7001 313 86 , , PUNCT ejpam-7001 313 87 0.67 0.67 NUM ejpam-7001 313 88 , , PUNCT ejpam-7001 313 89 0.17 0.17 NUM ejpam-7001 313 90 , , PUNCT ejpam-7001 313 91 0.20 0.20 NUM ejpam-7001 313 92 , , PUNCT ejpam-7001 313 93 0.09 0.09 NUM ejpam-7001 313 94 , , PUNCT ejpam-7001 313 95 0.10 0.10 NUM ejpam-7001 313 96 , , PUNCT ejpam-7001 313 97 0.07 0.07 NUM ejpam-7001 313 98 , , PUNCT ejpam-7001 313 99 0.09 0.09 NUM ejpam-7001 313 100 . . PUNCT ejpam-7001 313 101 figure figure NOUN ejpam-7001 313 102 8 8 NUM ejpam-7001 313 103 : : PUNCT ejpam-7001 313 104 non non ADJ ejpam-7001 313 105 parametric parametric ADJ ejpam-7001 313 106 plots plot NOUN ejpam-7001 313 107 for for ADP ejpam-7001 313 108 water water NOUN ejpam-7001 313 109 quality quality NOUN ejpam-7001 313 110 data datum NOUN ejpam-7001 313 111 . . PUNCT ejpam-7001 314 1 figure figure NOUN ejpam-7001 314 2 8 8 NUM ejpam-7001 314 3 represents represent VERB ejpam-7001 314 4 the the DET ejpam-7001 314 5 non non ADJ ejpam-7001 314 6 - - ADJ ejpam-7001 314 7 parametric parametric ADJ ejpam-7001 314 8 plots plot NOUN ejpam-7001 314 9 for for ADP ejpam-7001 314 10 water water NOUN ejpam-7001 314 11 quality quality NOUN ejpam-7001 314 12 data datum NOUN ejpam-7001 314 13 . . PUNCT ejpam-7001 315 1 the the DET ejpam-7001 315 2 ttt ttt PROPN ejpam-7001 315 3 plot plot NOUN ejpam-7001 315 4 indicates indicate VERB ejpam-7001 315 5 an an DET ejpam-7001 315 6 increasing increase VERB ejpam-7001 315 7 behavior behavior NOUN ejpam-7001 315 8 , , PUNCT ejpam-7001 315 9 kernel kernel PROPN ejpam-7001 315 10 density density PROPN ejpam-7001 315 11 plot plot NOUN ejpam-7001 315 12 indicates indicate VERB ejpam-7001 315 13 a a DET ejpam-7001 315 14 right right NOUN ejpam-7001 315 15 - - PUNCT ejpam-7001 315 16 skewness skewness NOUN ejpam-7001 315 17 and and CCONJ ejpam-7001 315 18 the the DET ejpam-7001 315 19 violin violin NOUN ejpam-7001 315 20 plot plot NOUN ejpam-7001 315 21 shows show VERB ejpam-7001 315 22 asymmetry asymmetry NOUN ejpam-7001 315 23 . . PUNCT ejpam-7001 316 1 thus thus ADV ejpam-7001 316 2 , , PUNCT ejpam-7001 316 3 the the DET ejpam-7001 316 4 proposed propose VERB ejpam-7001 316 5 distribution distribution NOUN ejpam-7001 316 6 is be AUX ejpam-7001 316 7 appropriate appropriate ADJ ejpam-7001 316 8 for for ADP ejpam-7001 316 9 fitting fit VERB ejpam-7001 316 10 the the DET ejpam-7001 316 11 water water NOUN ejpam-7001 316 12 quality quality NOUN ejpam-7001 316 13 dataset dataset NOUN ejpam-7001 316 14 . . PUNCT ejpam-7001 317 1 table table NOUN ejpam-7001 317 2 3 3 NUM ejpam-7001 317 3 : : PUNCT ejpam-7001 318 1 estimated estimate VERB ejpam-7001 318 2 values value NOUN ejpam-7001 318 3 of of ADP ejpam-7001 318 4 aic aic PROPN ejpam-7001 318 5 , , PUNCT ejpam-7001 318 6 caic caic PROPN ejpam-7001 318 7 , , PUNCT ejpam-7001 318 8 bic bic PROPN ejpam-7001 318 9 , , PUNCT ejpam-7001 318 10 − − PROPN ejpam-7001 318 11 log log NOUN ejpam-7001 318 12 l l NOUN ejpam-7001 318 13 , , PUNCT ejpam-7001 318 14 w w PROPN ejpam-7001 318 15 , , PUNCT ejpam-7001 318 16 a a PRON ejpam-7001 318 17 , , PUNCT ejpam-7001 318 18 ks ks NOUN ejpam-7001 318 19 , , PUNCT ejpam-7001 318 20 and and CCONJ ejpam-7001 318 21 p p NOUN ejpam-7001 318 22 - - PUNCT ejpam-7001 318 23 value value NOUN ejpam-7001 318 24 for for ADP ejpam-7001 318 25 water water NOUN ejpam-7001 318 26 quality quality NOUN ejpam-7001 318 27 data datum NOUN ejpam-7001 318 28 . . PUNCT ejpam-7001 319 1 distribution distribution NOUN ejpam-7001 319 2 aic aic PROPN ejpam-7001 319 3 caic caic PROPN ejpam-7001 319 4 bic bic PROPN ejpam-7001 319 5 − − PROPN ejpam-7001 319 6 log log NOUN ejpam-7001 319 7 l l PROPN ejpam-7001 319 8 w w NOUN ejpam-7001 319 9 a a DET ejpam-7001 319 10 ks ks NOUN ejpam-7001 319 11 p p NOUN ejpam-7001 319 12 - - PUNCT ejpam-7001 319 13 value value NOUN ejpam-7001 319 14 w w PROPN ejpam-7001 319 15 14.6514 14.6514 NUM ejpam-7001 319 16 14.9180 14.9180 NUM ejpam-7001 319 17 18.3938 18.3938 NUM ejpam-7001 319 18 5.3257 5.3257 NUM ejpam-7001 319 19 0.1245 0.1245 NUM ejpam-7001 319 20 0.8728 0.8728 NUM ejpam-7001 319 21 0.1079 0.1079 NUM ejpam-7001 319 22 0.6308 0.6308 NUM ejpam-7001 319 23 f f PROPN ejpam-7001 319 24 15.2230 15.2230 NUM ejpam-7001 319 25 15.4897 15.4897 NUM ejpam-7001 319 26 18.9654 18.9654 NUM ejpam-7001 319 27 14.0748 14.0748 NUM ejpam-7001 319 28 0.1648 0.1648 NUM ejpam-7001 319 29 1.0297 1.0297 NUM ejpam-7001 319 30 0.1140 0.1140 NUM ejpam-7001 319 31 0.5599 0.5599 NUM ejpam-7001 319 32 fw fw PROPN ejpam-7001 319 33 19.2230 19.2230 NUM ejpam-7001 319 34 20.1532 20.1532 NUM ejpam-7001 319 35 26.7078 26.7078 NUM ejpam-7001 319 36 5.6115 5.6115 NUM ejpam-7001 319 37 0.1648 0.1648 NUM ejpam-7001 319 38 1.0297 1.0297 NUM ejpam-7001 319 39 0.1140 0.1140 NUM ejpam-7001 319 40 0.5600 0.5600 NUM ejpam-7001 319 41 qrtfw qrtfw NOUN ejpam-7001 319 42 20.8403 20.8403 NUM ejpam-7001 319 43 22.2689 22.2689 NUM ejpam-7001 319 44 30.1963 30.1963 NUM ejpam-7001 319 45 5.4202 5.4202 NUM ejpam-7001 319 46 0.1584 0.1584 NUM ejpam-7001 319 47 0.9966 0.9966 NUM ejpam-7001 319 48 0.1087 0.1087 NUM ejpam-7001 319 49 0.6211 0.6211 NUM ejpam-7001 319 50 crtfw crtfw NOUN ejpam-7001 319 51 14.6106 14.6106 NUM ejpam-7001 319 52 16.6594 16.6594 NUM ejpam-7001 319 53 25.8378 25.8378 NUM ejpam-7001 319 54 1.3053 1.3053 NUM ejpam-7001 319 55 0.0503 0.0503 NUM ejpam-7001 319 56 0.3920 0.3920 NUM ejpam-7001 319 57 0.0777 0.0777 NUM ejpam-7001 319 58 0.9343 0.9343 NUM ejpam-7001 319 59 table table NOUN ejpam-7001 319 60 3 3 NUM ejpam-7001 319 61 presents present VERB ejpam-7001 319 62 the the DET ejpam-7001 319 63 goodness goodness NOUN ejpam-7001 319 64 - - PUNCT ejpam-7001 319 65 of of ADP ejpam-7001 319 66 - - PUNCT ejpam-7001 319 67 fit fit ADJ ejpam-7001 319 68 metrics metric NOUN ejpam-7001 319 69 , , PUNCT ejpam-7001 319 70 encompassing encompass VERB ejpam-7001 319 71 the the DET ejpam-7001 319 72 akaike akaike ADJ ejpam-7001 319 73 information information NOUN ejpam-7001 319 74 criterion criterion NOUN ejpam-7001 319 75 ( ( PUNCT ejpam-7001 319 76 aic aic PROPN ejpam-7001 319 77 ) ) PUNCT ejpam-7001 319 78 , , PUNCT ejpam-7001 319 79 consistent consistent ADJ ejpam-7001 319 80 aic aic PROPN ejpam-7001 319 81 ( ( PUNCT ejpam-7001 319 82 caic caic PROPN ejpam-7001 319 83 ) ) PUNCT ejpam-7001 319 84 , , PUNCT ejpam-7001 319 85 bayesian bayesian NOUN ejpam-7001 319 86 information information NOUN ejpam-7001 319 87 criterion criterion NOUN ejpam-7001 319 88 ( ( PUNCT ejpam-7001 319 89 bic bic PROPN ejpam-7001 319 90 ) ) PUNCT ejpam-7001 319 91 , , PUNCT ejpam-7001 319 92 negative negative ADJ ejpam-7001 319 93 log log NOUN ejpam-7001 319 94 - - PUNCT ejpam-7001 319 95 likelihood likelihood NOUN ejpam-7001 319 96 ( ( PUNCT ejpam-7001 319 97 − − PROPN ejpam-7001 319 98 log log NOUN ejpam-7001 319 99 l l NOUN ejpam-7001 319 100 ) ) PUNCT ejpam-7001 319 101 , , PUNCT ejpam-7001 319 102 cramér cramér PROPN ejpam-7001 319 103 – – PUNCT ejpam-7001 319 104 von von PROPN ejpam-7001 319 105 mises mises PROPN ejpam-7001 319 106 statistic statistic PROPN ejpam-7001 319 107 ( ( PUNCT ejpam-7001 319 108 w w PROPN ejpam-7001 319 109 ) ) PUNCT ejpam-7001 319 110 , , PUNCT ejpam-7001 319 111 anderson anderson PROPN ejpam-7001 319 112 – – PUNCT ejpam-7001 319 113 darling darling NOUN ejpam-7001 319 114 statistic statistic NOUN ejpam-7001 319 115 ( ( PUNCT ejpam-7001 319 116 a a NOUN ejpam-7001 319 117 ) ) PUNCT ejpam-7001 319 118 , , PUNCT ejpam-7001 319 119 kolmogorov kolmogorov PROPN ejpam-7001 319 120 – – PUNCT ejpam-7001 319 121 smirnov smirnov ADJ ejpam-7001 319 122 statistic statistic NOUN ejpam-7001 319 123 ( ( PUNCT ejpam-7001 319 124 ks ks NOUN ejpam-7001 319 125 ) ) PUNCT ejpam-7001 319 126 , , PUNCT ejpam-7001 319 127 and and CCONJ ejpam-7001 319 128 the the DET ejpam-7001 319 129 associated associated ADJ ejpam-7001 319 130 p p NOUN ejpam-7001 319 131 - - PUNCT ejpam-7001 319 132 value value NOUN ejpam-7001 319 133 . . PUNCT ejpam-7001 320 1 table table NOUN ejpam-7001 320 2 3 3 NUM ejpam-7001 320 3 clearly clearly ADV ejpam-7001 320 4 demonstrates demonstrate VERB ejpam-7001 320 5 that that SCONJ ejpam-7001 320 6 the the DET ejpam-7001 320 7 crtfw crtfw NOUN ejpam-7001 320 8 distribution distribution NOUN ejpam-7001 320 9 produces produce VERB ejpam-7001 320 10 the the DET ejpam-7001 320 11 lowest low ADJ ejpam-7001 320 12 values value NOUN ejpam-7001 320 13 of of ADP ejpam-7001 320 14 aic aic PROPN ejpam-7001 320 15 , , PUNCT ejpam-7001 320 16 − − PROPN ejpam-7001 320 17 log log NOUN ejpam-7001 320 18 l l NOUN ejpam-7001 320 19 , , PUNCT ejpam-7001 320 20 w w PROPN ejpam-7001 320 21 , , PUNCT ejpam-7001 320 22 a a PRON ejpam-7001 320 23 , , PUNCT ejpam-7001 320 24 and and CCONJ ejpam-7001 320 25 ks ks NOUN ejpam-7001 320 26 , , PUNCT ejpam-7001 320 27 along along ADP ejpam-7001 320 28 with with ADP ejpam-7001 320 29 the the DET ejpam-7001 320 30 highest high ADJ ejpam-7001 320 31 p p NOUN ejpam-7001 320 32 - - PUNCT ejpam-7001 320 33 value value NOUN ejpam-7001 320 34 compared compare VERB ejpam-7001 320 35 to to ADP ejpam-7001 320 36 the the DET ejpam-7001 320 37 other other ADJ ejpam-7001 320 38 models model NOUN ejpam-7001 320 39 , , PUNCT ejpam-7001 320 40 thereby thereby ADV ejpam-7001 320 41 indicating indicate VERB ejpam-7001 320 42 the the DET ejpam-7001 320 43 optimal optimal ADJ ejpam-7001 320 44 fit fit NOUN ejpam-7001 320 45 to to ADP ejpam-7001 320 46 the the DET ejpam-7001 320 47 dataset dataset NOUN ejpam-7001 320 48 . . PUNCT ejpam-7001 321 1 the the DET ejpam-7001 321 2 calculations calculation NOUN ejpam-7001 321 3 were be AUX ejpam-7001 321 4 executed execute VERB ejpam-7001 321 5 with with ADP ejpam-7001 321 6 r r NOUN ejpam-7001 321 7 software software NOUN ejpam-7001 321 8 . . PUNCT ejpam-7001 322 1 table table NOUN ejpam-7001 322 2 4 4 NUM ejpam-7001 322 3 displays display VERB ejpam-7001 322 4 the the DET ejpam-7001 322 5 maximum maximum ADJ ejpam-7001 322 6 likelihood likelihood NOUN ejpam-7001 322 7 estimates estimate NOUN ejpam-7001 322 8 ( ( PUNCT ejpam-7001 322 9 mles mle NOUN ejpam-7001 322 10 ) ) PUNCT ejpam-7001 322 11 of of ADP ejpam-7001 322 12 the the DET ejpam-7001 322 13 parameters parameter NOUN ejpam-7001 322 14 together together ADV ejpam-7001 322 15 with with ADP ejpam-7001 322 16 their their PRON ejpam-7001 322 17 imliyangba imliyangba PROPN ejpam-7001 322 18 et et PROPN ejpam-7001 322 19 al al PROPN ejpam-7001 322 20 . . PUNCT ejpam-7001 322 21 / / SYM ejpam-7001 322 22 eur eur PROPN ejpam-7001 322 23 . . PUNCT ejpam-7001 323 1 j. j. PROPN ejpam-7001 323 2 pure pure PROPN ejpam-7001 323 3 appl appl PROPN ejpam-7001 323 4 . . PROPN ejpam-7001 323 5 math math PROPN ejpam-7001 323 6 , , PUNCT ejpam-7001 323 7 18 18 NUM ejpam-7001 323 8 ( ( PUNCT ejpam-7001 323 9 4 4 NUM ejpam-7001 323 10 ) ) PUNCT ejpam-7001 323 11 ( ( PUNCT ejpam-7001 323 12 2025 2025 NUM ejpam-7001 323 13 ) ) PUNCT ejpam-7001 323 14 , , PUNCT ejpam-7001 323 15 7001 7001 NUM ejpam-7001 323 16 19 19 NUM ejpam-7001 323 17 of of ADP ejpam-7001 323 18 27 27 NUM ejpam-7001 323 19 corresponding correspond VERB ejpam-7001 323 20 standard standard ADJ ejpam-7001 323 21 errors error NOUN ejpam-7001 323 22 ( ( PUNCT ejpam-7001 323 23 ses ses PROPN ejpam-7001 323 24 ) ) PUNCT ejpam-7001 323 25 for for ADP ejpam-7001 323 26 each each DET ejpam-7001 323 27 fitted fit VERB ejpam-7001 323 28 distribution distribution NOUN ejpam-7001 323 29 . . PUNCT ejpam-7001 324 1 figures figure NOUN ejpam-7001 324 2 9 9 NUM ejpam-7001 324 3 and and CCONJ ejpam-7001 324 4 10 10 NUM ejpam-7001 324 5 illustrate illustrate VERB ejpam-7001 324 6 the the DET ejpam-7001 324 7 fitted fit VERB ejpam-7001 324 8 density density NOUN ejpam-7001 324 9 and and CCONJ ejpam-7001 324 10 cumulative cumulative ADJ ejpam-7001 324 11 distribution distribution NOUN ejpam-7001 324 12 functions function NOUN ejpam-7001 324 13 , , PUNCT ejpam-7001 324 14 together together ADV ejpam-7001 324 15 with with ADP ejpam-7001 324 16 the the DET ejpam-7001 324 17 p p NOUN ejpam-7001 324 18 – – PUNCT ejpam-7001 324 19 p p NOUN ejpam-7001 324 20 plots plot NOUN ejpam-7001 324 21 . . PUNCT ejpam-7001 325 1 the the DET ejpam-7001 325 2 crtfw crtfw NOUN ejpam-7001 325 3 distribution distribution NOUN ejpam-7001 325 4 demonstrates demonstrate VERB ejpam-7001 325 5 the the DET ejpam-7001 325 6 highest high ADJ ejpam-7001 325 7 concordance concordance NOUN ejpam-7001 325 8 with with ADP ejpam-7001 325 9 the the DET ejpam-7001 325 10 empirical empirical ADJ ejpam-7001 325 11 data datum NOUN ejpam-7001 325 12 . . PUNCT ejpam-7001 326 1 table table NOUN ejpam-7001 326 2 4 4 NUM ejpam-7001 326 3 : : PUNCT ejpam-7001 326 4 estimates estimate NOUN ejpam-7001 326 5 and and CCONJ ejpam-7001 326 6 ses se NOUN ejpam-7001 326 7 of of ADP ejpam-7001 326 8 parameters parameter NOUN ejpam-7001 326 9 α α X ejpam-7001 326 10 , , PUNCT ejpam-7001 326 11 β β NOUN ejpam-7001 326 12 , , PUNCT ejpam-7001 326 13 λ1 λ1 ADJ ejpam-7001 326 14 , , PUNCT ejpam-7001 326 15 λ2 λ2 PROPN ejpam-7001 326 16 , , PUNCT ejpam-7001 326 17 m m PRON ejpam-7001 326 18 , , PUNCT ejpam-7001 326 19 and and CCONJ ejpam-7001 326 20 k k PROPN ejpam-7001 326 21 for for ADP ejpam-7001 326 22 water water NOUN ejpam-7001 326 23 quality quality NOUN ejpam-7001 326 24 data datum NOUN ejpam-7001 326 25 . . PUNCT ejpam-7001 327 1 distribution distribution NOUN ejpam-7001 327 2 estimated estimate VERB ejpam-7001 327 3 parameter parameter NOUN ejpam-7001 327 4 standard standard NOUN ejpam-7001 327 5 error error NOUN ejpam-7001 327 6 w w NOUN ejpam-7001 327 7 β̂ β̂ PUNCT ejpam-7001 327 8 = = PUNCT ejpam-7001 327 9 2.1660 2.1660 NUM ejpam-7001 327 10 0.2630 0.2630 NUM ejpam-7001 327 11 λ̂ λ̂ X ejpam-7001 328 1 = = PUNCT ejpam-7001 328 2 1.2582 1.2582 NUM ejpam-7001 328 3 0.1412 0.1412 NUM ejpam-7001 328 4 f f NOUN ejpam-7001 328 5 α̂ α̂ NUM ejpam-7001 328 6 = = PUNCT ejpam-7001 329 1 1.2477 1.2477 NUM ejpam-7001 329 2 0.1397 0.1397 NUM ejpam-7001 329 3 β̂ β̂ ADP ejpam-7001 330 1 = = SYM ejpam-7001 330 2 0.1913 0.1913 NUM ejpam-7001 330 3 0.0234 0.0234 NUM ejpam-7001 330 4 fw fw NOUN ejpam-7001 330 5 α̂ α̂ NUM ejpam-7001 330 6 = = SYM ejpam-7001 330 7 1.3971 1.3971 NUM ejpam-7001 330 8 0.9982 0.9982 NUM ejpam-7001 330 9 β̂ β̂ X ejpam-7001 330 10 = = SYM ejpam-7001 330 11 0.3049 0.3049 NUM ejpam-7001 330 12 0.7315 0.7315 NUM ejpam-7001 330 13 λ̂ λ̂ NUM ejpam-7001 330 14 = = SYM ejpam-7001 330 15 0.7233 0.7233 NUM ejpam-7001 330 16 0.2852 0.2852 NUM ejpam-7001 330 17 k̂ k̂ NOUN ejpam-7001 330 18 = = SYM ejpam-7001 330 19 0.8931 0.8931 NUM ejpam-7001 330 20 0.2876 0.2876 NUM ejpam-7001 330 21 qrtfw qrtfw NOUN ejpam-7001 330 22 α̂ α̂ ADP ejpam-7001 330 23 = = PUNCT ejpam-7001 330 24 1.5224 1.5224 NUM ejpam-7001 330 25 0.1934 0.1934 NUM ejpam-7001 330 26 β̂ β̂ PUNCT ejpam-7001 330 27 = = SYM ejpam-7001 330 28 0.4755 0.4755 NUM ejpam-7001 330 29 0.2919 0.2919 NUM ejpam-7001 330 30 λ̂ λ̂ X ejpam-7001 331 1 = = PUNCT ejpam-7001 331 2 0.7236 0.7236 NUM ejpam-7001 331 3 0.4358 0.4358 NUM ejpam-7001 331 4 m̂ m̂ X ejpam-7001 332 1 = = SYM ejpam-7001 332 2 0.4022 0.4022 NUM ejpam-7001 332 3 0.2114 0.2114 NUM ejpam-7001 332 4 k̂ k̂ NOUN ejpam-7001 333 1 = = PUNCT ejpam-7001 333 2 0.8583 0.8583 NUM ejpam-7001 333 3 1.0902 1.0902 NUM ejpam-7001 333 4 crtfw crtfw NOUN ejpam-7001 333 5 α̂ α̂ NUM ejpam-7001 333 6 = = SYM ejpam-7001 333 7 1.4849 1.4849 NUM ejpam-7001 333 8 0.3549 0.3549 NUM ejpam-7001 333 9 β̂ β̂ PUNCT ejpam-7001 333 10 = = SYM ejpam-7001 333 11 0.1565 0.1565 NUM ejpam-7001 333 12 0.1967 0.1967 NUM ejpam-7001 333 13 λ̂1 λ̂1 NOUN ejpam-7001 333 14 = = PUNCT ejpam-7001 333 15 0.7035 0.7035 NUM ejpam-7001 333 16 0.4026 0.4026 NUM ejpam-7001 333 17 λ̂2 λ̂2 X ejpam-7001 334 1 = = PUNCT ejpam-7001 334 2 −0.4309 −0.4309 NOUN ejpam-7001 334 3 0.5999 0.5999 NUM ejpam-7001 334 4 m̂ m̂ NOUN ejpam-7001 334 5 = = SYM ejpam-7001 335 1 0.7995 0.7995 NUM ejpam-7001 335 2 0.2570 0.2570 NUM ejpam-7001 335 3 k̂ k̂ NOUN ejpam-7001 335 4 = = SYM ejpam-7001 336 1 1.1687 1.1687 NUM ejpam-7001 336 2 0.2794 0.2794 NUM ejpam-7001 336 3 8.2 8.2 NUM ejpam-7001 336 4 . . PUNCT ejpam-7001 337 1 dataset dataset PROPN ejpam-7001 337 2 ii ii PROPN ejpam-7001 337 3 : : PUNCT ejpam-7001 337 4 survival survival PROPN ejpam-7001 337 5 times time NOUN ejpam-7001 337 6 of of ADP ejpam-7001 337 7 patients patient NOUN ejpam-7001 337 8 this this DET ejpam-7001 337 9 section section NOUN ejpam-7001 337 10 examines examine VERB ejpam-7001 337 11 a a DET ejpam-7001 337 12 medical medical ADJ ejpam-7001 337 13 dataset dataset NOUN ejpam-7001 337 14 comprising comprise VERB ejpam-7001 337 15 the the DET ejpam-7001 337 16 survival survival NOUN ejpam-7001 337 17 durations duration NOUN ejpam-7001 337 18 ( ( PUNCT ejpam-7001 337 19 measured measure VERB ejpam-7001 337 20 in in ADP ejpam-7001 337 21 days day NOUN ejpam-7001 337 22 ) ) PUNCT ejpam-7001 337 23 of of ADP ejpam-7001 337 24 44 44 NUM ejpam-7001 337 25 patients patient NOUN ejpam-7001 337 26 diagnosed diagnose VERB ejpam-7001 337 27 with with ADP ejpam-7001 337 28 head head NOUN ejpam-7001 337 29 and and CCONJ ejpam-7001 337 30 neck neck NOUN ejpam-7001 337 31 cancer cancer NOUN ejpam-7001 337 32 . . PUNCT ejpam-7001 338 1 all all DET ejpam-7001 338 2 patients patient NOUN ejpam-7001 338 3 received receive VERB ejpam-7001 338 4 treatment treatment NOUN ejpam-7001 338 5 using use VERB ejpam-7001 338 6 a a DET ejpam-7001 338 7 combination combination NOUN ejpam-7001 338 8 of of ADP ejpam-7001 338 9 radiotherapy radiotherapy NOUN ejpam-7001 338 10 and and CCONJ ejpam-7001 338 11 chemotherapy chemotherapy NOUN ejpam-7001 338 12 ( ( PUNCT ejpam-7001 338 13 rt+ct rt+ct NOUN ejpam-7001 338 14 ) ) PUNCT ejpam-7001 338 15 . . PUNCT ejpam-7001 339 1 the the DET ejpam-7001 339 2 initial initial ADJ ejpam-7001 339 3 dataset dataset NOUN ejpam-7001 339 4 was be AUX ejpam-7001 339 5 documented document VERB ejpam-7001 339 6 by by ADP ejpam-7001 339 7 [ [ X ejpam-7001 339 8 38 38 NUM ejpam-7001 339 9 ] ] PUNCT ejpam-7001 339 10 , , PUNCT ejpam-7001 339 11 and and CCONJ ejpam-7001 339 12 the the DET ejpam-7001 339 13 recorded recorded ADJ ejpam-7001 339 14 survival survival NOUN ejpam-7001 339 15 durations duration NOUN ejpam-7001 339 16 are be AUX ejpam-7001 339 17 as as SCONJ ejpam-7001 339 18 follows follow VERB ejpam-7001 339 19 : : PUNCT ejpam-7001 339 20 12.20 12.20 NUM ejpam-7001 339 21 , , PUNCT ejpam-7001 339 22 23.56 23.56 NUM ejpam-7001 339 23 , , PUNCT ejpam-7001 339 24 23.74 23.74 NUM ejpam-7001 339 25 , , PUNCT ejpam-7001 339 26 25.87 25.87 NUM ejpam-7001 339 27 , , PUNCT ejpam-7001 339 28 31.98 31.98 NUM ejpam-7001 339 29 , , PUNCT ejpam-7001 339 30 37.00 37.00 NUM ejpam-7001 339 31 , , PUNCT ejpam-7001 339 32 41.35 41.35 NUM ejpam-7001 339 33 , , PUNCT ejpam-7001 339 34 47.38 47.38 NUM ejpam-7001 339 35 , , PUNCT ejpam-7001 339 36 55.46 55.46 NUM ejpam-7001 339 37 , , PUNCT ejpam-7001 339 38 58.36 58.36 NUM ejpam-7001 339 39 , , PUNCT ejpam-7001 339 40 63.47 63.47 NUM ejpam-7001 339 41 , , PUNCT ejpam-7001 339 42 68.46 68.46 NUM ejpam-7001 339 43 , , PUNCT ejpam-7001 339 44 74.47 74.47 NUM ejpam-7001 339 45 , , PUNCT ejpam-7001 339 46 78.26 78.26 NUM ejpam-7001 339 47 , , PUNCT ejpam-7001 339 48 81.43 81.43 NUM ejpam-7001 339 49 , , PUNCT ejpam-7001 339 50 84.00 84.00 NUM ejpam-7001 339 51 , , PUNCT ejpam-7001 339 52 92.00 92.00 NUM ejpam-7001 339 53 , , PUNCT ejpam-7001 339 54 94.00 94.00 NUM ejpam-7001 339 55 , , PUNCT ejpam-7001 339 56 110.00 110.00 NUM ejpam-7001 339 57 , , PUNCT ejpam-7001 339 58 112.00 112.00 NUM ejpam-7001 339 59 , , PUNCT ejpam-7001 339 60 119.00 119.00 NUM ejpam-7001 339 61 , , PUNCT ejpam-7001 339 62 127.00 127.00 NUM ejpam-7001 339 63 , , PUNCT ejpam-7001 339 64 130.00 130.00 NUM ejpam-7001 339 65 , , PUNCT ejpam-7001 339 66 133.00 133.00 NUM ejpam-7001 339 67 , , PUNCT ejpam-7001 339 68 140.00 140.00 NUM ejpam-7001 339 69 , , PUNCT ejpam-7001 339 70 146.00 146.00 NUM ejpam-7001 339 71 , , PUNCT ejpam-7001 339 72 155.00 155.00 NUM ejpam-7001 339 73 , , PUNCT ejpam-7001 339 74 159.00 159.00 NUM ejpam-7001 339 75 , , PUNCT ejpam-7001 339 76 173.00 173.00 NUM ejpam-7001 339 77 , , PUNCT ejpam-7001 339 78 179.00 179.00 NUM ejpam-7001 339 79 , , PUNCT ejpam-7001 339 80 194.00 194.00 NUM ejpam-7001 339 81 , , PUNCT ejpam-7001 339 82 195.00 195.00 NUM ejpam-7001 339 83 , , PUNCT ejpam-7001 339 84 209.00 209.00 NUM ejpam-7001 339 85 , , PUNCT ejpam-7001 339 86 249.00 249.00 NUM ejpam-7001 339 87 , , PUNCT ejpam-7001 339 88 281.00 281.00 NUM ejpam-7001 339 89 , , PUNCT ejpam-7001 339 90 319.00 319.00 NUM ejpam-7001 339 91 , , PUNCT ejpam-7001 339 92 339.00 339.00 NUM ejpam-7001 339 93 , , PUNCT ejpam-7001 339 94 432.00 432.00 NUM ejpam-7001 339 95 , , PUNCT ejpam-7001 339 96 469.00 469.00 NUM ejpam-7001 339 97 , , PUNCT ejpam-7001 339 98 519.00 519.00 NUM ejpam-7001 339 99 , , PUNCT ejpam-7001 339 100 633.00 633.00 NUM ejpam-7001 339 101 , , PUNCT ejpam-7001 339 102 725.00 725.00 NUM ejpam-7001 339 103 , , PUNCT ejpam-7001 339 104 817.00 817.00 NUM ejpam-7001 339 105 , , PUNCT ejpam-7001 339 106 1776.00 1776.00 NUM ejpam-7001 339 107 . . PUNCT ejpam-7001 340 1 to to PART ejpam-7001 340 2 assess assess VERB ejpam-7001 340 3 the the DET ejpam-7001 340 4 efficacy efficacy NOUN ejpam-7001 340 5 of of ADP ejpam-7001 340 6 the the DET ejpam-7001 340 7 proposed propose VERB ejpam-7001 340 8 crtfw crtfw NOUN ejpam-7001 340 9 distribution distribution NOUN ejpam-7001 340 10 in in ADP ejpam-7001 340 11 modeling model VERB ejpam-7001 340 12 this this DET ejpam-7001 340 13 survival survival NOUN ejpam-7001 340 14 data datum NOUN ejpam-7001 340 15 , , PUNCT ejpam-7001 340 16 we we PRON ejpam-7001 340 17 fitted fit VERB ejpam-7001 340 18 the the DET ejpam-7001 340 19 crtfw crtfw NOUN ejpam-7001 340 20 model model NOUN ejpam-7001 340 21 in in ADP ejpam-7001 340 22 conjunction conjunction NOUN ejpam-7001 340 23 imliyangba imliyangba PROPN ejpam-7001 340 24 et et PROPN ejpam-7001 340 25 al al PROPN ejpam-7001 340 26 . . PUNCT ejpam-7001 340 27 / / SYM ejpam-7001 340 28 eur eur PROPN ejpam-7001 340 29 . . PUNCT ejpam-7001 341 1 j. j. PROPN ejpam-7001 341 2 pure pure PROPN ejpam-7001 341 3 appl appl PROPN ejpam-7001 341 4 . . PROPN ejpam-7001 341 5 math math PROPN ejpam-7001 341 6 , , PUNCT ejpam-7001 341 7 18 18 NUM ejpam-7001 341 8 ( ( PUNCT ejpam-7001 341 9 4 4 NUM ejpam-7001 341 10 ) ) PUNCT ejpam-7001 341 11 ( ( PUNCT ejpam-7001 341 12 2025 2025 NUM ejpam-7001 341 13 ) ) PUNCT ejpam-7001 341 14 , , PUNCT ejpam-7001 341 15 7001 7001 NUM ejpam-7001 341 16 20 20 NUM ejpam-7001 341 17 of of ADP ejpam-7001 341 18 27 27 NUM ejpam-7001 341 19 figure figure NOUN ejpam-7001 341 20 9 9 NUM ejpam-7001 341 21 : : PUNCT ejpam-7001 341 22 fitted fit VERB ejpam-7001 341 23 density density NOUN ejpam-7001 341 24 and and CCONJ ejpam-7001 341 25 distribution distribution NOUN ejpam-7001 341 26 functions function NOUN ejpam-7001 341 27 of of ADP ejpam-7001 341 28 crtfw crtfw NOUN ejpam-7001 341 29 model model NOUN ejpam-7001 341 30 for for ADP ejpam-7001 341 31 water water NOUN ejpam-7001 341 32 quality quality NOUN ejpam-7001 341 33 data datum NOUN ejpam-7001 341 34 . . PUNCT ejpam-7001 342 1 figure figure VERB ejpam-7001 342 2 10 10 NUM ejpam-7001 342 3 : : PUNCT ejpam-7001 343 1 p p X ejpam-7001 343 2 – – PUNCT ejpam-7001 343 3 p p NOUN ejpam-7001 343 4 plots plot NOUN ejpam-7001 343 5 of of ADP ejpam-7001 343 6 fitted fit VERB ejpam-7001 343 7 distributions distribution NOUN ejpam-7001 343 8 ( ( PUNCT ejpam-7001 343 9 w w NOUN ejpam-7001 343 10 , , PUNCT ejpam-7001 343 11 f f PROPN ejpam-7001 343 12 , , PUNCT ejpam-7001 343 13 fw fw ADJ ejpam-7001 343 14 , , PUNCT ejpam-7001 343 15 qrtfw qrtfw ADJ ejpam-7001 343 16 , , PUNCT ejpam-7001 343 17 crtfw crtfw NOUN ejpam-7001 343 18 ) ) PUNCT ejpam-7001 343 19 for for ADP ejpam-7001 343 20 water water NOUN ejpam-7001 343 21 quality quality NOUN ejpam-7001 343 22 data datum NOUN ejpam-7001 343 23 . . PUNCT ejpam-7001 344 1 with with ADP ejpam-7001 344 2 many many ADJ ejpam-7001 344 3 rival rival ADJ ejpam-7001 344 4 distributions distribution NOUN ejpam-7001 344 5 , , PUNCT ejpam-7001 344 6 including include VERB ejpam-7001 344 7 the the DET ejpam-7001 344 8 w w PROPN ejpam-7001 344 9 , , PUNCT ejpam-7001 344 10 f f PROPN ejpam-7001 344 11 , , PUNCT ejpam-7001 344 12 fw fw ADJ ejpam-7001 344 13 , , PUNCT ejpam-7001 344 14 and and CCONJ ejpam-7001 344 15 crtfw crtfw PROPN ejpam-7001 344 16 distributions distribution NOUN ejpam-7001 344 17 . . PUNCT ejpam-7001 345 1 table table NOUN ejpam-7001 345 2 5 5 NUM ejpam-7001 345 3 provides provide VERB ejpam-7001 345 4 a a DET ejpam-7001 345 5 comprehensive comprehensive ADJ ejpam-7001 345 6 comparison comparison NOUN ejpam-7001 345 7 of of ADP ejpam-7001 345 8 the the DET ejpam-7001 345 9 goodness goodness NOUN ejpam-7001 345 10 - - PUNCT ejpam-7001 345 11 of of ADP ejpam-7001 345 12 - - PUNCT ejpam-7001 345 13 fit fit ADJ ejpam-7001 345 14 metrics metric NOUN ejpam-7001 345 15 , , PUNCT ejpam-7001 345 16 encompassing encompass VERB ejpam-7001 345 17 the the DET ejpam-7001 345 18 aic aic PROPN ejpam-7001 345 19 , , PUNCT ejpam-7001 345 20 caic caic PROPN ejpam-7001 345 21 , , PUNCT ejpam-7001 345 22 bic bic PROPN ejpam-7001 345 23 , , PUNCT ejpam-7001 345 24 − − PROPN ejpam-7001 345 25 log log NOUN ejpam-7001 345 26 l l NOUN ejpam-7001 345 27 , , PUNCT ejpam-7001 345 28 w w PROPN ejpam-7001 345 29 , , PUNCT ejpam-7001 345 30 a a PRON ejpam-7001 345 31 , , PUNCT ejpam-7001 345 32 ks ks NOUN ejpam-7001 345 33 , , PUNCT ejpam-7001 345 34 and and CCONJ ejpam-7001 345 35 the the DET ejpam-7001 345 36 associated associated ADJ ejpam-7001 345 37 p p NOUN ejpam-7001 345 38 - - PUNCT ejpam-7001 345 39 values value NOUN ejpam-7001 345 40 . . PUNCT ejpam-7001 346 1 table table NOUN ejpam-7001 346 2 5 5 NUM ejpam-7001 346 3 demonstrates demonstrate VERB ejpam-7001 346 4 that that SCONJ ejpam-7001 346 5 the the DET ejpam-7001 346 6 crtfw crtfw NOUN ejpam-7001 346 7 distribution distribution NOUN ejpam-7001 346 8 regularly regularly ADV ejpam-7001 346 9 surpasses surpass VERB ejpam-7001 346 10 the the DET ejpam-7001 346 11 other other ADJ ejpam-7001 346 12 distributions distribution NOUN ejpam-7001 346 13 , , PUNCT ejpam-7001 346 14 yielding yield VERB ejpam-7001 346 15 the the DET ejpam-7001 346 16 lowest low ADJ ejpam-7001 346 17 values value NOUN ejpam-7001 346 18 for for ADP ejpam-7001 346 19 aic aic PROPN ejpam-7001 346 20 , , PUNCT ejpam-7001 346 21 − − PROPN ejpam-7001 346 22 log log NOUN ejpam-7001 346 23 l l NOUN ejpam-7001 346 24 , , PUNCT ejpam-7001 346 25 w w PROPN ejpam-7001 346 26 , , PUNCT ejpam-7001 346 27 a a PRON ejpam-7001 346 28 , , PUNCT ejpam-7001 346 29 and and CCONJ ejpam-7001 346 30 ks ks NOUN ejpam-7001 346 31 , , PUNCT ejpam-7001 346 32 while while SCONJ ejpam-7001 346 33 simultaneously simultaneously ADV ejpam-7001 346 34 obtaining obtain VERB ejpam-7001 346 35 the the DET ejpam-7001 346 36 maximum maximum ADJ ejpam-7001 346 37 imliyangba imliyangba PROPN ejpam-7001 346 38 et et PROPN ejpam-7001 346 39 al al PROPN ejpam-7001 346 40 . . PUNCT ejpam-7001 346 41 / / SYM ejpam-7001 346 42 eur eur PROPN ejpam-7001 346 43 . . PUNCT ejpam-7001 347 1 j. j. PROPN ejpam-7001 347 2 pure pure PROPN ejpam-7001 347 3 appl appl PROPN ejpam-7001 347 4 . . PROPN ejpam-7001 347 5 math math PROPN ejpam-7001 347 6 , , PUNCT ejpam-7001 347 7 18 18 NUM ejpam-7001 347 8 ( ( PUNCT ejpam-7001 347 9 4 4 NUM ejpam-7001 347 10 ) ) PUNCT ejpam-7001 347 11 ( ( PUNCT ejpam-7001 347 12 2025 2025 NUM ejpam-7001 347 13 ) ) PUNCT ejpam-7001 347 14 , , PUNCT ejpam-7001 347 15 7001 7001 NUM ejpam-7001 347 16 21 21 NUM ejpam-7001 347 17 of of ADP ejpam-7001 347 18 27 27 NUM ejpam-7001 347 19 p p NOUN ejpam-7001 347 20 - - PUNCT ejpam-7001 347 21 value value NOUN ejpam-7001 347 22 . . PUNCT ejpam-7001 348 1 the the DET ejpam-7001 348 2 results result NOUN ejpam-7001 348 3 demonstrate demonstrate VERB ejpam-7001 348 4 that that SCONJ ejpam-7001 348 5 the the DET ejpam-7001 348 6 crtfw crtfw NOUN ejpam-7001 348 7 distribution distribution NOUN ejpam-7001 348 8 offers offer VERB ejpam-7001 348 9 the the DET ejpam-7001 348 10 optimal optimal ADJ ejpam-7001 348 11 fit fit NOUN ejpam-7001 348 12 for for ADP ejpam-7001 348 13 the the DET ejpam-7001 348 14 survival survival NOUN ejpam-7001 348 15 data data PROPN ejpam-7001 348 16 , , PUNCT ejpam-7001 348 17 effectively effectively ADV ejpam-7001 348 18 reflecting reflect VERB ejpam-7001 348 19 the the DET ejpam-7001 348 20 underlying underlie VERB ejpam-7001 348 21 structure structure NOUN ejpam-7001 348 22 of of ADP ejpam-7001 348 23 the the DET ejpam-7001 348 24 observed observe VERB ejpam-7001 348 25 lifetimes lifetime NOUN ejpam-7001 348 26 compared compare VERB ejpam-7001 348 27 to to ADP ejpam-7001 348 28 alternative alternative ADJ ejpam-7001 348 29 models model NOUN ejpam-7001 348 30 . . PUNCT ejpam-7001 349 1 the the DET ejpam-7001 349 2 maximum maximum ADJ ejpam-7001 349 3 likelihood likelihood NOUN ejpam-7001 349 4 estimates estimate NOUN ejpam-7001 349 5 ( ( PUNCT ejpam-7001 349 6 mles mle NOUN ejpam-7001 349 7 ) ) PUNCT ejpam-7001 349 8 of of ADP ejpam-7001 349 9 the the DET ejpam-7001 349 10 model model NOUN ejpam-7001 349 11 parameters parameter NOUN ejpam-7001 349 12 and and CCONJ ejpam-7001 349 13 their their PRON ejpam-7001 349 14 corresponding corresponding ADJ ejpam-7001 349 15 standard standard ADJ ejpam-7001 349 16 errors error NOUN ejpam-7001 349 17 ( ( PUNCT ejpam-7001 349 18 ses ses PROPN ejpam-7001 349 19 ) ) PUNCT ejpam-7001 349 20 are be AUX ejpam-7001 349 21 presented present VERB ejpam-7001 349 22 in in ADP ejpam-7001 349 23 table table NOUN ejpam-7001 349 24 6 6 NUM ejpam-7001 349 25 . . PUNCT ejpam-7001 350 1 figure figure NOUN ejpam-7001 350 2 11 11 NUM ejpam-7001 350 3 : : PUNCT ejpam-7001 350 4 non non ADJ ejpam-7001 350 5 parametric parametric ADJ ejpam-7001 350 6 plots plot NOUN ejpam-7001 350 7 for for ADP ejpam-7001 350 8 survival survival NOUN ejpam-7001 350 9 data datum NOUN ejpam-7001 350 10 . . PUNCT ejpam-7001 351 1 figure figure NOUN ejpam-7001 351 2 11 11 NUM ejpam-7001 351 3 represents represent VERB ejpam-7001 351 4 the the DET ejpam-7001 351 5 non non ADJ ejpam-7001 351 6 - - ADJ ejpam-7001 351 7 parametric parametric ADJ ejpam-7001 351 8 plots plot NOUN ejpam-7001 351 9 for for ADP ejpam-7001 351 10 survival survival NOUN ejpam-7001 351 11 times time NOUN ejpam-7001 351 12 of of ADP ejpam-7001 351 13 patients patient NOUN ejpam-7001 351 14 ’ ' PUNCT ejpam-7001 351 15 data datum NOUN ejpam-7001 351 16 . . PUNCT ejpam-7001 352 1 the the DET ejpam-7001 352 2 ttt ttt PROPN ejpam-7001 352 3 plot plot NOUN ejpam-7001 352 4 shows show VERB ejpam-7001 352 5 an an DET ejpam-7001 352 6 unimodal unimodal ADJ ejpam-7001 352 7 behavior behavior NOUN ejpam-7001 352 8 , , PUNCT ejpam-7001 352 9 kernel kernel PROPN ejpam-7001 352 10 density density PROPN ejpam-7001 352 11 plot plot NOUN ejpam-7001 352 12 indicates indicate VERB ejpam-7001 352 13 a a DET ejpam-7001 352 14 right right NOUN ejpam-7001 352 15 - - PUNCT ejpam-7001 352 16 skewness skewness NOUN ejpam-7001 352 17 and and CCONJ ejpam-7001 352 18 the the DET ejpam-7001 352 19 violin violin NOUN ejpam-7001 352 20 plot plot NOUN ejpam-7001 352 21 indicate indicate VERB ejpam-7001 352 22 a a DET ejpam-7001 352 23 positive positive ADJ ejpam-7001 352 24 skew skew NOUN ejpam-7001 352 25 . . PUNCT ejpam-7001 353 1 table table NOUN ejpam-7001 353 2 5 5 NUM ejpam-7001 353 3 : : PUNCT ejpam-7001 353 4 estimated estimate VERB ejpam-7001 353 5 values value NOUN ejpam-7001 353 6 of of ADP ejpam-7001 353 7 aic aic PROPN ejpam-7001 353 8 , , PUNCT ejpam-7001 353 9 caic caic PROPN ejpam-7001 353 10 , , PUNCT ejpam-7001 353 11 bic bic PROPN ejpam-7001 353 12 , , PUNCT ejpam-7001 353 13 − − PROPN ejpam-7001 353 14 log log NOUN ejpam-7001 353 15 l l NOUN ejpam-7001 353 16 , , PUNCT ejpam-7001 353 17 w w PROPN ejpam-7001 353 18 , , PUNCT ejpam-7001 353 19 a a PRON ejpam-7001 353 20 , , PUNCT ejpam-7001 353 21 ks ks NOUN ejpam-7001 353 22 , , PUNCT ejpam-7001 353 23 and and CCONJ ejpam-7001 353 24 p p NOUN ejpam-7001 353 25 - - PUNCT ejpam-7001 353 26 value value NOUN ejpam-7001 353 27 for for ADP ejpam-7001 353 28 survival survival NOUN ejpam-7001 353 29 times time NOUN ejpam-7001 353 30 of of ADP ejpam-7001 353 31 patients patient NOUN ejpam-7001 353 32 . . PUNCT ejpam-7001 354 1 distribution distribution NOUN ejpam-7001 354 2 aic aic PROPN ejpam-7001 354 3 caic caic PROPN ejpam-7001 354 4 bic bic PROPN ejpam-7001 354 5 − − PROPN ejpam-7001 354 6 log log NOUN ejpam-7001 354 7 l l PROPN ejpam-7001 354 8 w w NOUN ejpam-7001 354 9 a a DET ejpam-7001 354 10 ks ks NOUN ejpam-7001 354 11 p p NOUN ejpam-7001 354 12 - - PUNCT ejpam-7001 354 13 value value NOUN ejpam-7001 354 14 w w ADP ejpam-7001 354 15 567.689 567.689 NUM ejpam-7001 354 16 567.982 567.982 NUM ejpam-7001 354 17 571.258 571.258 NUM ejpam-7001 354 18 281.845 281.845 NUM ejpam-7001 354 19 0.1410 0.1410 NUM ejpam-7001 354 20 0.8213 0.8213 NUM ejpam-7001 354 21 0.1261 0.1261 NUM ejpam-7001 354 22 0.4499 0.4499 NUM ejpam-7001 354 23 f f X ejpam-7001 354 24 563.141 563.141 NUM ejpam-7001 354 25 563.433 563.433 NUM ejpam-7001 354 26 566.709 566.709 NUM ejpam-7001 354 27 279.570 279.570 NUM ejpam-7001 354 28 0.0771 0.0771 NUM ejpam-7001 354 29 0.4754 0.4754 NUM ejpam-7001 354 30 0.0938 0.0938 NUM ejpam-7001 354 31 0.7999 0.7999 NUM ejpam-7001 354 32 fw fw PROPN ejpam-7001 354 33 567.140 567.140 NUM ejpam-7001 354 34 568.166 568.166 NUM ejpam-7001 354 35 574.277 574.277 NUM ejpam-7001 354 36 279.570 279.570 NUM ejpam-7001 354 37 0.0771 0.0771 NUM ejpam-7001 354 38 0.4754 0.4754 NUM ejpam-7001 355 1 0.0927 0.0927 NUM ejpam-7001 355 2 0.8104 0.8104 NUM ejpam-7001 355 3 qrtfw qrtfw NOUN ejpam-7001 355 4 567.646 567.646 NUM ejpam-7001 355 5 569.225 569.225 NUM ejpam-7001 355 6 576.567 576.567 NUM ejpam-7001 355 7 278.823 278.823 NUM ejpam-7001 355 8 0.0570 0.0570 NUM ejpam-7001 355 9 0.3581 0.3581 NUM ejpam-7001 355 10 0.0829 0.0829 NUM ejpam-7001 355 11 0.8979 0.8979 NUM ejpam-7001 355 12 crtfw crtfw VERB ejpam-7001 355 13 561.953 561.953 NUM ejpam-7001 355 14 569.224 569.224 NUM ejpam-7001 355 15 577.659 577.659 NUM ejpam-7001 355 16 277.477 277.477 NUM ejpam-7001 355 17 0.0119 0.0119 NUM ejpam-7001 355 18 0.1098 0.1098 NUM ejpam-7001 355 19 0.0465 0.0465 NUM ejpam-7001 355 20 0.9870 0.9870 NUM ejpam-7001 355 21 figures figure NOUN ejpam-7001 355 22 12 12 NUM ejpam-7001 355 23 and and CCONJ ejpam-7001 355 24 13 13 NUM ejpam-7001 355 25 depict depict NOUN ejpam-7001 355 26 the the DET ejpam-7001 355 27 fitted fit VERB ejpam-7001 355 28 probability probability NOUN ejpam-7001 355 29 density density NOUN ejpam-7001 355 30 functions function NOUN ejpam-7001 355 31 and and CCONJ ejpam-7001 355 32 cumulative cumulative ADJ ejpam-7001 355 33 distribution distribution NOUN ejpam-7001 355 34 functions function NOUN ejpam-7001 355 35 , , PUNCT ejpam-7001 355 36 respectively respectively ADV ejpam-7001 355 37 , , PUNCT ejpam-7001 355 38 alongside alongside ADP ejpam-7001 355 39 the the DET ejpam-7001 355 40 p p NOUN ejpam-7001 355 41 – – PUNCT ejpam-7001 355 42 p p NOUN ejpam-7001 355 43 plots plot NOUN ejpam-7001 355 44 that that PRON ejpam-7001 355 45 compare compare VERB ejpam-7001 355 46 the the DET ejpam-7001 355 47 empirical empirical ADJ ejpam-7001 355 48 cumulative cumulative ADJ ejpam-7001 355 49 distribution distribution NOUN ejpam-7001 355 50 with with ADP ejpam-7001 355 51 the the DET ejpam-7001 355 52 estimated estimate VERB ejpam-7001 355 53 cumulative cumulative ADJ ejpam-7001 355 54 distributions distribution NOUN ejpam-7001 355 55 derived derive VERB ejpam-7001 355 56 from from ADP ejpam-7001 355 57 the the DET ejpam-7001 355 58 fitted fit VERB ejpam-7001 355 59 models model NOUN ejpam-7001 355 60 . . PUNCT ejpam-7001 356 1 the the DET ejpam-7001 356 2 figures figure NOUN ejpam-7001 356 3 unequivocally unequivocally ADV ejpam-7001 356 4 illustrate illustrate VERB ejpam-7001 356 5 that that SCONJ ejpam-7001 356 6 the the DET ejpam-7001 356 7 crtfw crtfw NOUN ejpam-7001 356 8 distribution distribution NOUN ejpam-7001 356 9 coincides coincide VERB ejpam-7001 356 10 closely closely ADV ejpam-7001 356 11 with with ADP ejpam-7001 356 12 the the DET ejpam-7001 356 13 empirical empirical ADJ ejpam-7001 356 14 data datum NOUN ejpam-7001 356 15 , , PUNCT ejpam-7001 356 16 validating validate VERB ejpam-7001 356 17 its its PRON ejpam-7001 356 18 adaptability adaptability NOUN ejpam-7001 356 19 and and CCONJ ejpam-7001 356 20 suitability suitability NOUN ejpam-7001 356 21 in in ADP ejpam-7001 356 22 estimating estimate VERB ejpam-7001 356 23 survival survival NOUN ejpam-7001 356 24 durations duration NOUN ejpam-7001 356 25 for for ADP ejpam-7001 356 26 head head NOUN ejpam-7001 356 27 and and CCONJ ejpam-7001 356 28 neck neck NOUN ejpam-7001 356 29 cancer cancer NOUN ejpam-7001 356 30 patients patient NOUN ejpam-7001 356 31 . . PUNCT ejpam-7001 357 1 imliyangba imliyangba PROPN ejpam-7001 357 2 et et PROPN ejpam-7001 357 3 al al PROPN ejpam-7001 357 4 . . PUNCT ejpam-7001 357 5 / / SYM ejpam-7001 357 6 eur eur PROPN ejpam-7001 357 7 . . PUNCT ejpam-7001 358 1 j. j. PROPN ejpam-7001 358 2 pure pure PROPN ejpam-7001 358 3 appl appl PROPN ejpam-7001 358 4 . . PROPN ejpam-7001 358 5 math math PROPN ejpam-7001 358 6 , , PUNCT ejpam-7001 358 7 18 18 NUM ejpam-7001 358 8 ( ( PUNCT ejpam-7001 358 9 4 4 NUM ejpam-7001 358 10 ) ) PUNCT ejpam-7001 358 11 ( ( PUNCT ejpam-7001 358 12 2025 2025 NUM ejpam-7001 358 13 ) ) PUNCT ejpam-7001 358 14 , , PUNCT ejpam-7001 358 15 7001 7001 NUM ejpam-7001 358 16 22 22 NUM ejpam-7001 358 17 of of ADP ejpam-7001 358 18 27 27 NUM ejpam-7001 358 19 table table NOUN ejpam-7001 358 20 6 6 NUM ejpam-7001 358 21 : : PUNCT ejpam-7001 358 22 estimates estimate NOUN ejpam-7001 358 23 and and CCONJ ejpam-7001 358 24 ses se NOUN ejpam-7001 358 25 of of ADP ejpam-7001 358 26 parameters parameter NOUN ejpam-7001 358 27 α α X ejpam-7001 358 28 , , PUNCT ejpam-7001 358 29 β β NOUN ejpam-7001 358 30 , , PUNCT ejpam-7001 358 31 λ1 λ1 ADJ ejpam-7001 358 32 , , PUNCT ejpam-7001 358 33 λ2 λ2 PROPN ejpam-7001 358 34 , , PUNCT ejpam-7001 358 35 m m PRON ejpam-7001 358 36 , , PUNCT ejpam-7001 358 37 and and CCONJ ejpam-7001 358 38 k k PROPN ejpam-7001 358 39 for for ADP ejpam-7001 358 40 survival survival NOUN ejpam-7001 358 41 data datum NOUN ejpam-7001 358 42 . . PUNCT ejpam-7001 359 1 distribution distribution NOUN ejpam-7001 359 2 estimated estimate VERB ejpam-7001 359 3 parameter parameter NOUN ejpam-7001 359 4 standard standard NOUN ejpam-7001 359 5 error error NOUN ejpam-7001 359 6 w w NOUN ejpam-7001 359 7 β̂ β̂ NOUN ejpam-7001 359 8 = = PUNCT ejpam-7001 359 9 0.00468 0.00468 NUM ejpam-7001 359 10 0.00075 0.00075 NUM ejpam-7001 359 11 λ̂ λ̂ X ejpam-7001 360 1 = = SYM ejpam-7001 360 2 0.93705 0.93705 NUM ejpam-7001 360 3 0.09950 0.09950 NUM ejpam-7001 360 4 f f NOUN ejpam-7001 360 5 α̂ α̂ NUM ejpam-7001 360 6 = = PUNCT ejpam-7001 360 7 1.01393 1.01393 NUM ejpam-7001 360 8 0.11180 0.11180 NUM ejpam-7001 360 9 β̂ β̂ PUNCT ejpam-7001 361 1 = = SYM ejpam-7001 361 2 76.0134 76.0134 NUM ejpam-7001 361 3 11.9624 11.9624 NUM ejpam-7001 361 4 fw fw NOUN ejpam-7001 361 5 α̂ α̂ NUM ejpam-7001 361 6 = = NOUN ejpam-7001 361 7 2.17257 2.17257 NUM ejpam-7001 361 8 16.5230 16.5230 NUM ejpam-7001 361 9 β̂ β̂ ADP ejpam-7001 361 10 = = SYM ejpam-7001 362 1 9.96635 9.96635 NUM ejpam-7001 362 2 358.498 358.498 NUM ejpam-7001 362 3 λ̂ λ̂ X ejpam-7001 362 4 = = SYM ejpam-7001 362 5 0.55115 0.55115 NUM ejpam-7001 362 6 28.2458 28.2458 NUM ejpam-7001 362 7 k̂ k̂ NOUN ejpam-7001 363 1 = = SYM ejpam-7001 363 2 0.46642 0.46642 NUM ejpam-7001 363 3 3.54731 3.54731 NUM ejpam-7001 363 4 qrtfw qrtfw NOUN ejpam-7001 363 5 α̂ α̂ NUM ejpam-7001 363 6 = = PUNCT ejpam-7001 363 7 2.41281 2.41281 NUM ejpam-7001 363 8 35.9663 35.9663 NUM ejpam-7001 363 9 β̂ β̂ ADP ejpam-7001 363 10 = = SYM ejpam-7001 363 11 2.79247 2.79247 NUM ejpam-7001 363 12 50.8027 50.8027 NUM ejpam-7001 363 13 λ̂ λ̂ X ejpam-7001 363 14 = = SYM ejpam-7001 363 15 0.34095 0.34095 NUM ejpam-7001 363 16 0.36846 0.36846 NUM ejpam-7001 363 17 m̂ m̂ NOUN ejpam-7001 364 1 = = SYM ejpam-7001 364 2 5.48477 5.48477 NUM ejpam-7001 364 3 191.215 191.215 NUM ejpam-7001 364 4 k̂ k̂ NOUN ejpam-7001 364 5 = = SYM ejpam-7001 364 6 0.45558 0.45558 NUM ejpam-7001 364 7 6.79104 6.79104 NUM ejpam-7001 364 8 crtfw crtfw NOUN ejpam-7001 364 9 α̂ α̂ NUM ejpam-7001 364 10 = = SYM ejpam-7001 364 11 3.93798 3.93798 NUM ejpam-7001 364 12 32.6700 32.6700 NUM ejpam-7001 364 13 β̂ β̂ ADP ejpam-7001 364 14 = = SYM ejpam-7001 364 15 2.17735 2.17735 NUM ejpam-7001 364 16 39.0578 39.0578 NUM ejpam-7001 364 17 λ̂1 λ̂1 NOUN ejpam-7001 364 18 = = SYM ejpam-7001 364 19 0.70344 0.70344 NUM ejpam-7001 364 20 0.39757 0.39757 NUM ejpam-7001 364 21 λ̂2 λ̂2 PUNCT ejpam-7001 364 22 = = PUNCT ejpam-7001 365 1 −0.7230 −0.7230 NUM ejpam-7001 365 2 0.80218 0.80218 NUM ejpam-7001 365 3 m̂ m̂ X ejpam-7001 365 4 = = SYM ejpam-7001 365 5 4.44806 4.44806 NUM ejpam-7001 365 6 193.318 193.318 NUM ejpam-7001 365 7 k̂ k̂ NOUN ejpam-7001 365 8 = = SYM ejpam-7001 365 9 0.34204 0.34204 NUM ejpam-7001 365 10 2.83767 2.83767 NUM ejpam-7001 365 11 figure figure NOUN ejpam-7001 365 12 12 12 NUM ejpam-7001 365 13 : : PUNCT ejpam-7001 365 14 fitted fit VERB ejpam-7001 365 15 density density NOUN ejpam-7001 365 16 and and CCONJ ejpam-7001 365 17 distribution distribution NOUN ejpam-7001 365 18 functions function NOUN ejpam-7001 365 19 of of ADP ejpam-7001 365 20 crtfw crtfw NOUN ejpam-7001 365 21 model model NOUN ejpam-7001 365 22 for for ADP ejpam-7001 365 23 survival survival NOUN ejpam-7001 365 24 data data PROPN ejpam-7001 365 25 . . PUNCT ejpam-7001 366 1 imliyangba imliyangba PROPN ejpam-7001 366 2 et et PROPN ejpam-7001 366 3 al al PROPN ejpam-7001 366 4 . . PUNCT ejpam-7001 366 5 / / SYM ejpam-7001 366 6 eur eur PROPN ejpam-7001 366 7 . . PUNCT ejpam-7001 367 1 j. j. PROPN ejpam-7001 367 2 pure pure PROPN ejpam-7001 367 3 appl appl PROPN ejpam-7001 367 4 . . PROPN ejpam-7001 367 5 math math PROPN ejpam-7001 367 6 , , PUNCT ejpam-7001 367 7 18 18 NUM ejpam-7001 367 8 ( ( PUNCT ejpam-7001 367 9 4 4 NUM ejpam-7001 367 10 ) ) PUNCT ejpam-7001 367 11 ( ( PUNCT ejpam-7001 367 12 2025 2025 NUM ejpam-7001 367 13 ) ) PUNCT ejpam-7001 367 14 , , PUNCT ejpam-7001 367 15 7001 7001 NUM ejpam-7001 367 16 23 23 NUM ejpam-7001 367 17 of of ADP ejpam-7001 367 18 27 27 NUM ejpam-7001 367 19 figure figure NOUN ejpam-7001 367 20 13 13 NUM ejpam-7001 367 21 : : PUNCT ejpam-7001 368 1 p p X ejpam-7001 368 2 – – PUNCT ejpam-7001 368 3 p p NOUN ejpam-7001 368 4 plots plot NOUN ejpam-7001 368 5 of of ADP ejpam-7001 368 6 fitted fit VERB ejpam-7001 368 7 distributions distribution NOUN ejpam-7001 368 8 ( ( PUNCT ejpam-7001 368 9 w w NOUN ejpam-7001 368 10 , , PUNCT ejpam-7001 368 11 f f PROPN ejpam-7001 368 12 , , PUNCT ejpam-7001 368 13 fw fw ADJ ejpam-7001 368 14 , , PUNCT ejpam-7001 368 15 qrtfw qrtfw ADJ ejpam-7001 368 16 , , PUNCT ejpam-7001 368 17 crtfw crtfw NOUN ejpam-7001 368 18 ) ) PUNCT ejpam-7001 368 19 for for ADP ejpam-7001 368 20 survival survival NOUN ejpam-7001 368 21 data datum NOUN ejpam-7001 368 22 . . PUNCT ejpam-7001 369 1 9 9 X ejpam-7001 369 2 . . PUNCT ejpam-7001 369 3 conclusions conclusion NOUN ejpam-7001 369 4 this this DET ejpam-7001 369 5 study study NOUN ejpam-7001 369 6 established establish VERB ejpam-7001 369 7 and and CCONJ ejpam-7001 369 8 investigated investigate VERB ejpam-7001 369 9 a a DET ejpam-7001 369 10 novel novel ADJ ejpam-7001 369 11 cubic cubic ADJ ejpam-7001 369 12 rank rank NOUN ejpam-7001 369 13 transmuted transmute VERB ejpam-7001 369 14 fréchet fréchet NOUN ejpam-7001 369 15 – – PUNCT ejpam-7001 369 16 weibull weibull NOUN ejpam-7001 369 17 ( ( PUNCT ejpam-7001 369 18 crtfw crtfw PROPN ejpam-7001 369 19 ) ) PUNCT ejpam-7001 369 20 probability probability NOUN ejpam-7001 369 21 model model NOUN ejpam-7001 369 22 within within ADP ejpam-7001 369 23 the the DET ejpam-7001 369 24 cubic cubic ADJ ejpam-7001 369 25 model model NOUN ejpam-7001 369 26 framework framework NOUN ejpam-7001 369 27 . . PUNCT ejpam-7001 370 1 several several ADJ ejpam-7001 370 2 important important ADJ ejpam-7001 370 3 mathematical mathematical ADJ ejpam-7001 370 4 and and CCONJ ejpam-7001 370 5 statistical statistical ADJ ejpam-7001 370 6 properties property NOUN ejpam-7001 370 7 of of ADP ejpam-7001 370 8 the the DET ejpam-7001 370 9 crtfw crtfw NOUN ejpam-7001 370 10 distribution distribution NOUN ejpam-7001 370 11 were be AUX ejpam-7001 370 12 derived derive VERB ejpam-7001 370 13 and and CCONJ ejpam-7001 370 14 analyzed analyze VERB ejpam-7001 370 15 , , PUNCT ejpam-7001 370 16 including include VERB ejpam-7001 370 17 its its PRON ejpam-7001 370 18 moments moment NOUN ejpam-7001 370 19 , , PUNCT ejpam-7001 370 20 moment moment NOUN ejpam-7001 370 21 generating generate VERB ejpam-7001 370 22 function function NOUN ejpam-7001 370 23 , , PUNCT ejpam-7001 370 24 characteristic characteristic ADJ ejpam-7001 370 25 function function NOUN ejpam-7001 370 26 , , PUNCT ejpam-7001 370 27 quantile quantile ADJ ejpam-7001 370 28 function function NOUN ejpam-7001 370 29 , , PUNCT ejpam-7001 370 30 mode mode NOUN ejpam-7001 370 31 , , PUNCT ejpam-7001 370 32 random random ADJ ejpam-7001 370 33 variate variate NOUN ejpam-7001 370 34 generation generation NOUN ejpam-7001 370 35 , , PUNCT ejpam-7001 370 36 hazard hazard NOUN ejpam-7001 370 37 rate rate NOUN ejpam-7001 370 38 function function NOUN ejpam-7001 370 39 , , PUNCT ejpam-7001 370 40 entropies entropy NOUN ejpam-7001 370 41 , , PUNCT ejpam-7001 370 42 and and CCONJ ejpam-7001 370 43 order order NOUN ejpam-7001 370 44 statistics statistic NOUN ejpam-7001 370 45 . . PUNCT ejpam-7001 371 1 these these DET ejpam-7001 371 2 analyses analysis NOUN ejpam-7001 371 3 provided provide VERB ejpam-7001 371 4 a a DET ejpam-7001 371 5 comprehensive comprehensive ADJ ejpam-7001 371 6 understanding understanding NOUN ejpam-7001 371 7 of of ADP ejpam-7001 371 8 the the DET ejpam-7001 371 9 distribution distribution NOUN ejpam-7001 371 10 ’s ’s PART ejpam-7001 371 11 behavior behavior NOUN ejpam-7001 371 12 and and CCONJ ejpam-7001 371 13 demonstrated demonstrate VERB ejpam-7001 371 14 its its PRON ejpam-7001 371 15 flexibility flexibility NOUN ejpam-7001 371 16 in in ADP ejpam-7001 371 17 modeling model VERB ejpam-7001 371 18 diverse diverse ADJ ejpam-7001 371 19 data datum NOUN ejpam-7001 371 20 patterns pattern NOUN ejpam-7001 371 21 . . PUNCT ejpam-7001 372 1 the the DET ejpam-7001 372 2 model model NOUN ejpam-7001 372 3 effectively effectively ADV ejpam-7001 372 4 handled handle VERB ejpam-7001 372 5 bimodal bimodal NOUN ejpam-7001 372 6 and and CCONJ ejpam-7001 372 7 unimodal unimodal ADJ ejpam-7001 372 8 data datum NOUN ejpam-7001 372 9 structures structure NOUN ejpam-7001 372 10 , , PUNCT ejpam-7001 372 11 as as ADV ejpam-7001 372 12 well well ADV ejpam-7001 372 13 as as ADP ejpam-7001 372 14 symmetrical symmetrical ADJ ejpam-7001 372 15 distributions distribution NOUN ejpam-7001 372 16 with with ADP ejpam-7001 372 17 varying vary VERB ejpam-7001 372 18 degrees degree NOUN ejpam-7001 372 19 of of ADP ejpam-7001 372 20 kurtosis kurtosis NOUN ejpam-7001 372 21 . . PUNCT ejpam-7001 373 1 a a DET ejpam-7001 373 2 thorough thorough ADJ ejpam-7001 373 3 monte monte PROPN ejpam-7001 373 4 carlo carlo PROPN ejpam-7001 373 5 simulation simulation PROPN ejpam-7001 373 6 study study NOUN ejpam-7001 373 7 was be AUX ejpam-7001 373 8 run run VERB ejpam-7001 373 9 to to PART ejpam-7001 373 10 evaluate evaluate VERB ejpam-7001 373 11 the the DET ejpam-7001 373 12 estimators estimator NOUN ejpam-7001 373 13 ’ ’ PART ejpam-7001 373 14 performance performance NOUN ejpam-7001 373 15 and and CCONJ ejpam-7001 373 16 efficiency efficiency NOUN ejpam-7001 373 17 under under ADP ejpam-7001 373 18 different different ADJ ejpam-7001 373 19 circumstances circumstance NOUN ejpam-7001 373 20 , , PUNCT ejpam-7001 373 21 and and CCONJ ejpam-7001 373 22 the the DET ejpam-7001 373 23 maximum maximum ADJ ejpam-7001 373 24 likelihood likelihood NOUN ejpam-7001 373 25 method method NOUN ejpam-7001 373 26 was be AUX ejpam-7001 373 27 used use VERB ejpam-7001 373 28 for for ADP ejpam-7001 373 29 parameter parameter NOUN ejpam-7001 373 30 estimation estimation NOUN ejpam-7001 373 31 . . PUNCT ejpam-7001 374 1 as as SCONJ ejpam-7001 374 2 the the DET ejpam-7001 374 3 sample sample NOUN ejpam-7001 374 4 size size NOUN ejpam-7001 374 5 increased increase VERB ejpam-7001 374 6 , , PUNCT ejpam-7001 374 7 the the DET ejpam-7001 374 8 simulation simulation NOUN ejpam-7001 374 9 results result NOUN ejpam-7001 374 10 showed show VERB ejpam-7001 374 11 that that SCONJ ejpam-7001 374 12 the the DET ejpam-7001 374 13 mles mle NOUN ejpam-7001 374 14 worked work VERB ejpam-7001 374 15 as as SCONJ ejpam-7001 374 16 expected expect VERB ejpam-7001 374 17 , , PUNCT ejpam-7001 374 18 with with ADP ejpam-7001 374 19 bias bias NOUN ejpam-7001 374 20 and and CCONJ ejpam-7001 374 21 mean mean VERB ejpam-7001 374 22 square square ADJ ejpam-7001 374 23 error error NOUN ejpam-7001 374 24 ( ( PUNCT ejpam-7001 374 25 mse mse NOUN ejpam-7001 374 26 ) ) PUNCT ejpam-7001 374 27 decreasing decrease VERB ejpam-7001 374 28 towards towards ADP ejpam-7001 374 29 zero zero NUM ejpam-7001 374 30 , , PUNCT ejpam-7001 374 31 demonstrating demonstrate VERB ejpam-7001 374 32 the the DET ejpam-7001 374 33 estimate estimate NOUN ejpam-7001 374 34 procedure procedure NOUN ejpam-7001 374 35 ’s ’s PART ejpam-7001 374 36 reliability reliability NOUN ejpam-7001 374 37 . . PUNCT ejpam-7001 375 1 we we PRON ejpam-7001 375 2 examined examine VERB ejpam-7001 375 3 two two NUM ejpam-7001 375 4 datasets dataset NOUN ejpam-7001 375 5 pertaining pertain VERB ejpam-7001 375 6 to to ADP ejpam-7001 375 7 sustainability sustainability NOUN ejpam-7001 375 8 in in ADP ejpam-7001 375 9 the the DET ejpam-7001 375 10 real real ADJ ejpam-7001 375 11 world world NOUN ejpam-7001 375 12 to to PART ejpam-7001 375 13 show show VERB ejpam-7001 375 14 how how SCONJ ejpam-7001 375 15 the the DET ejpam-7001 375 16 crtfw crtfw NOUN ejpam-7001 375 17 model model NOUN ejpam-7001 375 18 works work VERB ejpam-7001 375 19 in in ADP ejpam-7001 375 20 practice practice NOUN ejpam-7001 375 21 . . PUNCT ejpam-7001 376 1 in in ADP ejpam-7001 376 2 comparison comparison NOUN ejpam-7001 376 3 to to ADP ejpam-7001 376 4 other other ADJ ejpam-7001 376 5 competing compete VERB ejpam-7001 376 6 lifespan lifespan NOUN ejpam-7001 376 7 and and CCONJ ejpam-7001 376 8 reliability reliability NOUN ejpam-7001 376 9 distributions distribution NOUN ejpam-7001 376 10 , , PUNCT ejpam-7001 376 11 the the DET ejpam-7001 376 12 results result NOUN ejpam-7001 376 13 showed show VERB ejpam-7001 376 14 that that SCONJ ejpam-7001 376 15 the the DET ejpam-7001 376 16 crtfw crtfw NOUN ejpam-7001 376 17 distribution distribution NOUN ejpam-7001 376 18 captured capture VERB ejpam-7001 376 19 the the DET ejpam-7001 376 20 underlying underlie VERB ejpam-7001 376 21 data data NOUN ejpam-7001 376 22 features feature VERB ejpam-7001 376 23 adequately adequately ADV ejpam-7001 376 24 while while SCONJ ejpam-7001 376 25 also also ADV ejpam-7001 376 26 providing provide VERB ejpam-7001 376 27 higher high ADJ ejpam-7001 376 28 flexibility flexibility NOUN ejpam-7001 376 29 and and CCONJ ejpam-7001 376 30 increased increase VERB ejpam-7001 376 31 imliyangba imliyangba PROPN ejpam-7001 376 32 et et PROPN ejpam-7001 376 33 al al PROPN ejpam-7001 376 34 . . PUNCT ejpam-7001 376 35 / / SYM ejpam-7001 376 36 eur eur PROPN ejpam-7001 376 37 . . PUNCT ejpam-7001 377 1 j. j. PROPN ejpam-7001 377 2 pure pure PROPN ejpam-7001 377 3 appl appl PROPN ejpam-7001 377 4 . . PROPN ejpam-7001 377 5 math math PROPN ejpam-7001 377 6 , , PUNCT ejpam-7001 377 7 18 18 NUM ejpam-7001 377 8 ( ( PUNCT ejpam-7001 377 9 4 4 NUM ejpam-7001 377 10 ) ) PUNCT ejpam-7001 377 11 ( ( PUNCT ejpam-7001 377 12 2025 2025 NUM ejpam-7001 377 13 ) ) PUNCT ejpam-7001 377 14 , , PUNCT ejpam-7001 377 15 7001 7001 NUM ejpam-7001 377 16 24 24 NUM ejpam-7001 377 17 of of ADP ejpam-7001 377 18 27 27 NUM ejpam-7001 377 19 goodness goodness NOUN ejpam-7001 377 20 - - PUNCT ejpam-7001 377 21 of of ADP ejpam-7001 377 22 - - PUNCT ejpam-7001 377 23 fit fit NOUN ejpam-7001 377 24 . . PUNCT ejpam-7001 378 1 we we PRON ejpam-7001 378 2 propose propose VERB ejpam-7001 378 3 expanding expand VERB ejpam-7001 378 4 the the DET ejpam-7001 378 5 scope scope NOUN ejpam-7001 378 6 of of ADP ejpam-7001 378 7 the the DET ejpam-7001 378 8 crtfw crtfw NOUN ejpam-7001 378 9 model model NOUN ejpam-7001 378 10 to to PART ejpam-7001 378 11 include include VERB ejpam-7001 378 12 more more ADJ ejpam-7001 378 13 types type NOUN ejpam-7001 378 14 of of ADP ejpam-7001 378 15 environmental environmental ADJ ejpam-7001 378 16 , , PUNCT ejpam-7001 378 17 biological biological ADJ ejpam-7001 378 18 , , PUNCT ejpam-7001 378 19 and and CCONJ ejpam-7001 378 20 engineering engineering NOUN ejpam-7001 378 21 datasets dataset NOUN ejpam-7001 378 22 in in ADP ejpam-7001 378 23 our our PRON ejpam-7001 378 24 future future ADJ ejpam-7001 378 25 studies study NOUN ejpam-7001 378 26 . . PUNCT ejpam-7001 379 1 to to PART ejpam-7001 379 2 further far ADV ejpam-7001 379 3 improve improve VERB ejpam-7001 379 4 parameter parameter NOUN ejpam-7001 379 5 inference inference NOUN ejpam-7001 379 6 , , PUNCT ejpam-7001 379 7 especially especially ADV ejpam-7001 379 8 in in ADP ejpam-7001 379 9 situations situation NOUN ejpam-7001 379 10 with with ADP ejpam-7001 379 11 limited limited ADJ ejpam-7001 379 12 samples sample NOUN ejpam-7001 379 13 or or CCONJ ejpam-7001 379 14 censored censored ADJ ejpam-7001 379 15 observations observation NOUN ejpam-7001 379 16 , , PUNCT ejpam-7001 379 17 it it PRON ejpam-7001 379 18 could could AUX ejpam-7001 379 19 be be AUX ejpam-7001 379 20 worth worth ADJ ejpam-7001 379 21 exploring explore VERB ejpam-7001 379 22 other other ADJ ejpam-7001 379 23 estimating estimate VERB ejpam-7001 379 24 techniques technique NOUN ejpam-7001 379 25 like like ADP ejpam-7001 379 26 bayesian bayesian NOUN ejpam-7001 379 27 or or CCONJ ejpam-7001 379 28 robust robust ADJ ejpam-7001 379 29 methods method NOUN ejpam-7001 379 30 . . PUNCT ejpam-7001 380 1 use use NOUN ejpam-7001 380 2 of of ADP ejpam-7001 380 3 generative generative ADJ ejpam-7001 380 4 - - PUNCT ejpam-7001 380 5 ai ai NOUN ejpam-7001 380 6 tools tool NOUN ejpam-7001 380 7 declaration declaration NOUN ejpam-7001 380 8 the the DET ejpam-7001 380 9 authors author NOUN ejpam-7001 380 10 declare declare VERB ejpam-7001 380 11 they they PRON ejpam-7001 380 12 have have AUX ejpam-7001 380 13 not not PART ejpam-7001 380 14 used use VERB ejpam-7001 380 15 ai ai VERB ejpam-7001 380 16 tools tool NOUN ejpam-7001 380 17 in in ADP ejpam-7001 380 18 the the DET ejpam-7001 380 19 creation creation NOUN ejpam-7001 380 20 of of ADP ejpam-7001 380 21 this this DET ejpam-7001 380 22 article article NOUN ejpam-7001 380 23 . . PUNCT ejpam-7001 381 1 conflict conflict NOUN ejpam-7001 381 2 of of ADP ejpam-7001 381 3 interest interest NOUN ejpam-7001 381 4 all all DET ejpam-7001 381 5 authors author NOUN ejpam-7001 381 6 declare declare VERB ejpam-7001 381 7 no no DET ejpam-7001 381 8 conflicts conflict NOUN ejpam-7001 381 9 of of ADP ejpam-7001 381 10 interest interest NOUN ejpam-7001 381 11 in in ADP ejpam-7001 381 12 this this DET ejpam-7001 381 13 paper paper NOUN ejpam-7001 381 14 . . PUNCT ejpam-7001 382 1 data datum NOUN ejpam-7001 382 2 availability availability NOUN ejpam-7001 382 3 the the DET ejpam-7001 382 4 datasets dataset NOUN ejpam-7001 382 5 used use VERB ejpam-7001 382 6 and and CCONJ ejpam-7001 382 7 analyzed analyze VERB ejpam-7001 382 8 during during ADP ejpam-7001 382 9 the the DET ejpam-7001 382 10 current current ADJ ejpam-7001 382 11 study study NOUN ejpam-7001 382 12 are be AUX ejpam-7001 382 13 included include VERB ejpam-7001 382 14 within within ADP ejpam-7001 382 15 this this DET ejpam-7001 382 16 published publish VERB ejpam-7001 382 17 article article NOUN ejpam-7001 382 18 . . PUNCT ejpam-7001 383 1 appendix appendix VERB ejpam-7001 383 2 the the DET ejpam-7001 383 3 derivation derivation NOUN ejpam-7001 383 4 of of ADP ejpam-7001 383 5 the the DET ejpam-7001 383 6 coefficients coefficient NOUN ejpam-7001 383 7 of of ADP ejpam-7001 383 8 skewness skewness NOUN ejpam-7001 383 9 , , PUNCT ejpam-7001 383 10 kurtosis kurtosis NOUN ejpam-7001 383 11 , , PUNCT ejpam-7001 383 12 and and CCONJ ejpam-7001 383 13 variation variation NOUN ejpam-7001 383 14 can can AUX ejpam-7001 383 15 be be AUX ejpam-7001 383 16 obtained obtain VERB ejpam-7001 383 17 by by ADP ejpam-7001 383 18 the the DET ejpam-7001 383 19 following following NOUN ejpam-7001 383 20 : : PUNCT ejpam-7001 383 21 for for ADP ejpam-7001 383 22 convenience convenience NOUN ejpam-7001 383 23 , , PUNCT ejpam-7001 383 24 let let VERB ejpam-7001 383 25 µ′ µ′ NOUN ejpam-7001 383 26 1 1 NUM ejpam-7001 383 27 = = SYM ejpam-7001 383 28 µ µ X ejpam-7001 383 29 = = PUNCT ejpam-7001 383 30 mβ1 mβ1 PROPN ejpam-7001 383 31 / / SYM ejpam-7001 383 32 k k PROPN ejpam-7001 383 33 61/(αk 61/(αk PROPN ejpam-7001 383 34 ) ) PUNCT ejpam-7001 383 35 a a PRON ejpam-7001 383 36 , , PUNCT ejpam-7001 383 37 σ2 σ2 NOUN ejpam-7001 383 38 = = SYM ejpam-7001 383 39 µ2 µ2 PROPN ejpam-7001 383 40 = = PUNCT ejpam-7001 383 41 m2β2 m2β2 PROPN ejpam-7001 383 42 / / SYM ejpam-7001 383 43 k k NOUN ejpam-7001 383 44 62/(αk 62/(αk NOUN ejpam-7001 383 45 ) ) PUNCT ejpam-7001 383 46 ( ( PUNCT ejpam-7001 383 47 b− b− PROPN ejpam-7001 383 48 a2 a2 PROPN ejpam-7001 383 49 ) ) PUNCT ejpam-7001 383 50 , , PUNCT ejpam-7001 383 51 µ3 µ3 NOUN ejpam-7001 383 52 = = SYM ejpam-7001 383 53 m3β3 m3β3 PROPN ejpam-7001 383 54 / / SYM ejpam-7001 383 55 k k NOUN ejpam-7001 383 56 63/(αk 63/(αk NUM ejpam-7001 383 57 ) ) PUNCT ejpam-7001 383 58 ( ( PUNCT ejpam-7001 383 59 c− c− X ejpam-7001 383 60 3ab+ 3ab+ PROPN ejpam-7001 383 61 2a3 2a3 NUM ejpam-7001 383 62 ) ) PUNCT ejpam-7001 383 63 , , PUNCT ejpam-7001 383 64 µ4 µ4 PROPN ejpam-7001 383 65 = = SYM ejpam-7001 383 66 m4β4 m4β4 PROPN ejpam-7001 383 67 / / SYM ejpam-7001 383 68 k k NOUN ejpam-7001 383 69 64/(αk 64/(αk NUM ejpam-7001 383 70 ) ) PUNCT ejpam-7001 383 71 ( ( PUNCT ejpam-7001 383 72 d− d− PROPN ejpam-7001 383 73 4ac+ 4ac+ NUM ejpam-7001 383 74 6a2b+ 6a2b+ PROPN ejpam-7001 383 75 3a4 3a4 NUM ejpam-7001 383 76 ) ) PUNCT ejpam-7001 383 77 , , PUNCT ejpam-7001 383 78 where where SCONJ ejpam-7001 383 79 a a DET ejpam-7001 383 80 = = X ejpam-7001 383 81 γ γ X ejpam-7001 383 82 ( ( PUNCT ejpam-7001 383 83 1− 1− NUM ejpam-7001 383 84 1 1 NUM ejpam-7001 383 85 αk αk NOUN ejpam-7001 383 86 ) ) PUNCT ejpam-7001 383 87 [ [ PUNCT ejpam-7001 383 88 61/(αk)λ1 61/(αk)λ1 NUM ejpam-7001 383 89 + + SYM ejpam-7001 383 90 31/(αk)(λ2 31/(αk)(λ2 NUM ejpam-7001 383 91 − − NOUN ejpam-7001 383 92 λ1 λ1 PROPN ejpam-7001 383 93 ) ) PUNCT ejpam-7001 383 94 + + NUM ejpam-7001 383 95 61/(αk)(1− 61/(αk)(1− NUM ejpam-7001 383 96 λ2 λ2 NOUN ejpam-7001 383 97 ) ) PUNCT ejpam-7001 383 98 ] ] PUNCT ejpam-7001 383 99 , , PUNCT ejpam-7001 383 100 b b X ejpam-7001 383 101 = = SYM ejpam-7001 383 102 γ γ X ejpam-7001 383 103 ( ( PUNCT ejpam-7001 383 104 1− 1− NUM ejpam-7001 383 105 2 2 NUM ejpam-7001 383 106 αk αk NOUN ejpam-7001 383 107 ) ) PUNCT ejpam-7001 383 108 [ [ PUNCT ejpam-7001 384 1 62/(αk)λ1 62/(αk)λ1 NUM ejpam-7001 384 2 + + CCONJ ejpam-7001 384 3 32/(αk)(λ2 32/(αk)(λ2 NUM ejpam-7001 384 4 − − NOUN ejpam-7001 384 5 λ1 λ1 NUM ejpam-7001 384 6 ) ) PUNCT ejpam-7001 384 7 + + PROPN ejpam-7001 384 8 62/(αk)(1− 62/(αk)(1− NUM ejpam-7001 384 9 λ2 λ2 NOUN ejpam-7001 384 10 ) ) PUNCT ejpam-7001 384 11 ] ] PUNCT ejpam-7001 384 12 , , PUNCT ejpam-7001 384 13 c c X ejpam-7001 384 14 = = SYM ejpam-7001 384 15 γ γ X ejpam-7001 384 16 ( ( PUNCT ejpam-7001 384 17 1− 1− NUM ejpam-7001 384 18 3 3 NUM ejpam-7001 384 19 αk αk NOUN ejpam-7001 384 20 ) ) PUNCT ejpam-7001 384 21 [ [ PUNCT ejpam-7001 384 22 63/(αk)λ1 63/(αk)λ1 NUM ejpam-7001 384 23 + + SYM ejpam-7001 384 24 33/(αk)(λ2 33/(αk)(λ2 NUM ejpam-7001 384 25 − − NOUN ejpam-7001 384 26 λ1 λ1 ADJ ejpam-7001 384 27 ) ) PUNCT ejpam-7001 384 28 + + CCONJ ejpam-7001 384 29 63/(αk)(1− 63/(αk)(1− NUM ejpam-7001 384 30 λ2 λ2 NOUN ejpam-7001 384 31 ) ) PUNCT ejpam-7001 384 32 ] ] PUNCT ejpam-7001 384 33 , , PUNCT ejpam-7001 384 34 d d X ejpam-7001 384 35 = = SYM ejpam-7001 384 36 γ γ X ejpam-7001 384 37 ( ( PUNCT ejpam-7001 384 38 1− 1− NUM ejpam-7001 384 39 4 4 NUM ejpam-7001 384 40 αk αk NOUN ejpam-7001 384 41 ) ) PUNCT ejpam-7001 384 42 [ [ PUNCT ejpam-7001 385 1 64/(αk)λ1 64/(αk)λ1 NUM ejpam-7001 385 2 + + SYM ejpam-7001 385 3 34/(αk)(λ2 34/(αk)(λ2 NUM ejpam-7001 385 4 − − NOUN ejpam-7001 385 5 λ1 λ1 PROPN ejpam-7001 385 6 ) ) PUNCT ejpam-7001 385 7 + + CCONJ ejpam-7001 385 8 64/(αk)(1− 64/(αk)(1− NUM ejpam-7001 385 9 λ2 λ2 NOUN ejpam-7001 385 10 ) ) PUNCT ejpam-7001 385 11 ] ] PUNCT ejpam-7001 385 12 . . PUNCT ejpam-7001 386 1 imliyangba imliyangba PROPN ejpam-7001 386 2 et et PROPN ejpam-7001 386 3 al al PROPN ejpam-7001 386 4 . . PUNCT ejpam-7001 386 5 / / SYM ejpam-7001 386 6 eur eur PROPN ejpam-7001 386 7 . . PUNCT ejpam-7001 387 1 j. j. PROPN ejpam-7001 387 2 pure pure PROPN ejpam-7001 387 3 appl appl PROPN ejpam-7001 387 4 . . PROPN ejpam-7001 387 5 math math PROPN ejpam-7001 387 6 , , PUNCT ejpam-7001 387 7 18 18 NUM ejpam-7001 387 8 ( ( PUNCT ejpam-7001 387 9 4 4 NUM ejpam-7001 387 10 ) ) PUNCT ejpam-7001 387 11 ( ( PUNCT ejpam-7001 387 12 2025 2025 NUM ejpam-7001 387 13 ) ) PUNCT ejpam-7001 387 14 , , PUNCT ejpam-7001 387 15 7001 7001 NUM ejpam-7001 387 16 25 25 NUM ejpam-7001 387 17 of of ADP ejpam-7001 387 18 27 27 NUM ejpam-7001 387 19 references reference NOUN ejpam-7001 387 20 [ [ X ejpam-7001 387 21 1 1 NUM ejpam-7001 387 22 ] ] PUNCT ejpam-7001 387 23 innocent innocent ADJ ejpam-7001 387 24 boyle boyle NOUN ejpam-7001 387 25 eraikhuemen eraikhuemen PROPN ejpam-7001 387 26 , , PUNCT ejpam-7001 387 27 adana’a adana’a NOUN ejpam-7001 387 28 felix felix PROPN ejpam-7001 387 29 chama chama PROPN ejpam-7001 387 30 , , PUNCT ejpam-7001 387 31 abraham abraham PROPN ejpam-7001 387 32 iorkaa iorkaa PROPN ejpam-7001 387 33 asongo asongo PROPN ejpam-7001 387 34 , , PUNCT ejpam-7001 387 35 bassa bassa PROPN ejpam-7001 387 36 shiwaye shiwaye VERB ejpam-7001 387 37 yakura yakura NOUN ejpam-7001 387 38 , , PUNCT ejpam-7001 387 39 and and CCONJ ejpam-7001 387 40 abdul abdul PROPN ejpam-7001 387 41 haruna haruna PROPN ejpam-7001 387 42 bala bala PROPN ejpam-7001 387 43 . . PUNCT ejpam-7001 388 1 properties property NOUN ejpam-7001 388 2 and and CCONJ ejpam-7001 388 3 applications application NOUN ejpam-7001 388 4 of of ADP ejpam-7001 388 5 a a DET ejpam-7001 388 6 transmuted transmuted ADJ ejpam-7001 388 7 power power NOUN ejpam-7001 388 8 gompertz gompertz NOUN ejpam-7001 388 9 distribution distribution NOUN ejpam-7001 388 10 . . PUNCT ejpam-7001 389 1 asian asian ADJ ejpam-7001 389 2 journal journal NOUN ejpam-7001 389 3 of of ADP ejpam-7001 389 4 probability probability NOUN ejpam-7001 389 5 and and CCONJ ejpam-7001 389 6 statistics statistic NOUN ejpam-7001 389 7 , , PUNCT ejpam-7001 389 8 7(1):41–58 7(1):41–58 NUM ejpam-7001 389 9 , , PUNCT ejpam-7001 389 10 2020 2020 NUM ejpam-7001 389 11 . . PUNCT ejpam-7001 390 1 [ [ X ejpam-7001 390 2 2 2 NUM ejpam-7001 390 3 ] ] PUNCT ejpam-7001 390 4 william william PROPN ejpam-7001 390 5 t t PROPN ejpam-7001 390 6 shaw shaw PROPN ejpam-7001 390 7 and and CCONJ ejpam-7001 390 8 ian ian PROPN ejpam-7001 390 9 rc rc PROPN ejpam-7001 390 10 buckley buckley NOUN ejpam-7001 390 11 . . PUNCT ejpam-7001 391 1 the the DET ejpam-7001 391 2 alchemy alchemy NOUN ejpam-7001 391 3 of of ADP ejpam-7001 391 4 probability probability NOUN ejpam-7001 391 5 distributions distribution NOUN ejpam-7001 391 6 : : PUNCT ejpam-7001 391 7 beyond beyond ADP ejpam-7001 391 8 gram gram NOUN ejpam-7001 391 9 - - PUNCT ejpam-7001 391 10 charlier charlier NOUN ejpam-7001 391 11 expansions expansion NOUN ejpam-7001 391 12 , , PUNCT ejpam-7001 391 13 and and CCONJ ejpam-7001 391 14 a a DET ejpam-7001 391 15 skew skew ADJ ejpam-7001 391 16 - - PUNCT ejpam-7001 391 17 kurtotic kurtotic ADJ ejpam-7001 391 18 - - PUNCT ejpam-7001 391 19 normal normal ADJ ejpam-7001 391 20 distribution distribution NOUN ejpam-7001 391 21 from from ADP ejpam-7001 391 22 a a DET ejpam-7001 391 23 rank rank NOUN ejpam-7001 391 24 transmutation transmutation NOUN ejpam-7001 391 25 map map NOUN ejpam-7001 391 26 . . PUNCT ejpam-7001 392 1 arxiv arxiv PROPN ejpam-7001 392 2 preprint preprint PROPN ejpam-7001 392 3 arxiv:0901.0434 arxiv:0901.0434 NOUN ejpam-7001 392 4 , , PUNCT ejpam-7001 392 5 2009 2009 NUM ejpam-7001 392 6 . . PUNCT ejpam-7001 393 1 [ [ X ejpam-7001 393 2 3 3 X ejpam-7001 393 3 ] ] X ejpam-7001 393 4 gokarna gokarna NOUN ejpam-7001 393 5 r r NOUN ejpam-7001 393 6 aryal aryal NOUN ejpam-7001 393 7 and and CCONJ ejpam-7001 393 8 chris chris PROPN ejpam-7001 393 9 p p PROPN ejpam-7001 393 10 tsokos tsokos PROPN ejpam-7001 393 11 . . PUNCT ejpam-7001 394 1 transmuted transmute VERB ejpam-7001 394 2 weibull weibull NOUN ejpam-7001 394 3 distribution distribution NOUN ejpam-7001 394 4 : : PUNCT ejpam-7001 394 5 a a DET ejpam-7001 394 6 generalization generalization NOUN ejpam-7001 394 7 of of ADP ejpam-7001 394 8 theweibull theweibull NOUN ejpam-7001 394 9 probability probability NOUN ejpam-7001 394 10 distribution distribution NOUN ejpam-7001 394 11 . . PUNCT ejpam-7001 395 1 european european ADJ ejpam-7001 395 2 journal journal PROPN ejpam-7001 395 3 of of ADP ejpam-7001 395 4 pure pure ADJ ejpam-7001 395 5 and and CCONJ ejpam-7001 395 6 applied applied ADJ ejpam-7001 395 7 mathematics mathematic NOUN ejpam-7001 395 8 , , PUNCT ejpam-7001 395 9 4(2):89–102 4(2):89–102 NUM ejpam-7001 395 10 , , PUNCT ejpam-7001 395 11 2011 2011 NUM ejpam-7001 395 12 . . PUNCT ejpam-7001 396 1 [ [ X ejpam-7001 396 2 4 4 X ejpam-7001 396 3 ] ] PUNCT ejpam-7001 396 4 ivana ivana PROPN ejpam-7001 396 5 poboč́ıková poboč́ıková PROPN ejpam-7001 396 6 , , PUNCT ejpam-7001 396 7 zuzana zuzana PROPN ejpam-7001 396 8 sedliačková sedliačková PROPN ejpam-7001 396 9 , , PUNCT ejpam-7001 396 10 and and CCONJ ejpam-7001 396 11 mária mária VERB ejpam-7001 396 12 michalková. michalková. PROPN ejpam-7001 396 13 transmuted transmute VERB ejpam-7001 396 14 weibull weibull NOUN ejpam-7001 396 15 distribution distribution NOUN ejpam-7001 396 16 and and CCONJ ejpam-7001 396 17 its its PRON ejpam-7001 396 18 applications application NOUN ejpam-7001 396 19 . . PUNCT ejpam-7001 397 1 in in ADP ejpam-7001 397 2 matec matec ADJ ejpam-7001 397 3 web web NOUN ejpam-7001 397 4 of of ADP ejpam-7001 397 5 conferences conference NOUN ejpam-7001 397 6 , , PUNCT ejpam-7001 397 7 volume volume NOUN ejpam-7001 397 8 157 157 NUM ejpam-7001 397 9 , , PUNCT ejpam-7001 397 10 page page NOUN ejpam-7001 397 11 08007 08007 NUM ejpam-7001 397 12 . . PUNCT ejpam-7001 398 1 edp edp PROPN ejpam-7001 398 2 sciences sciences PROPN ejpam-7001 398 3 , , PUNCT ejpam-7001 398 4 2018 2018 NUM ejpam-7001 398 5 . . PUNCT ejpam-7001 399 1 [ [ X ejpam-7001 399 2 5 5 NUM ejpam-7001 399 3 ] ] X ejpam-7001 399 4 dct dct PROPN ejpam-7001 399 5 granzotto granzotto PROPN ejpam-7001 399 6 , , PUNCT ejpam-7001 399 7 francisco francisco PROPN ejpam-7001 399 8 louzada louzada PROPN ejpam-7001 399 9 , , PUNCT ejpam-7001 399 10 and and CCONJ ejpam-7001 399 11 n n PRON ejpam-7001 399 12 balakrishnan balakrishnan PROPN ejpam-7001 399 13 . . PUNCT ejpam-7001 400 1 cubic cubic ADJ ejpam-7001 400 2 rank rank PROPN ejpam-7001 400 3 transmuted transmute VERB ejpam-7001 400 4 distributions distribution NOUN ejpam-7001 400 5 : : PUNCT ejpam-7001 400 6 inferential inferential ADJ ejpam-7001 400 7 issues issue NOUN ejpam-7001 400 8 and and CCONJ ejpam-7001 400 9 applications application NOUN ejpam-7001 400 10 . . PUNCT ejpam-7001 401 1 journal journal NOUN ejpam-7001 401 2 of of ADP ejpam-7001 401 3 statistical statistical ADJ ejpam-7001 401 4 computation computation NOUN ejpam-7001 401 5 and and CCONJ ejpam-7001 401 6 simulation simulation NOUN ejpam-7001 401 7 , , PUNCT ejpam-7001 401 8 87(14):2760–2778 87(14):2760–2778 PROPN ejpam-7001 401 9 , , PUNCT ejpam-7001 401 10 2017 2017 NUM ejpam-7001 401 11 . . PUNCT ejpam-7001 402 1 [ [ X ejpam-7001 402 2 6 6 NUM ejpam-7001 402 3 ] ] PUNCT ejpam-7001 402 4 md md PROPN ejpam-7001 402 5 mahabubur mahabubur PROPN ejpam-7001 402 6 rahman rahman PROPN ejpam-7001 402 7 , , PUNCT ejpam-7001 402 8 bander bander PROPN ejpam-7001 402 9 al al PROPN ejpam-7001 402 10 - - PUNCT ejpam-7001 402 11 zahrani zahrani PROPN ejpam-7001 402 12 , , PUNCT ejpam-7001 402 13 and and CCONJ ejpam-7001 402 14 muhammad muhammad PROPN ejpam-7001 402 15 qaiser qaiser PROPN ejpam-7001 402 16 shahbaz shahbaz PROPN ejpam-7001 402 17 . . PUNCT ejpam-7001 403 1 a a DET ejpam-7001 403 2 general general ADJ ejpam-7001 403 3 transmuted transmuted ADJ ejpam-7001 403 4 family family NOUN ejpam-7001 403 5 of of ADP ejpam-7001 403 6 distributions distribution NOUN ejpam-7001 403 7 . . PUNCT ejpam-7001 404 1 pakistan pakistan PROPN ejpam-7001 404 2 journal journal PROPN ejpam-7001 404 3 of of ADP ejpam-7001 404 4 statistics statistic NOUN ejpam-7001 404 5 and and CCONJ ejpam-7001 404 6 operation operation NOUN ejpam-7001 404 7 research research NOUN ejpam-7001 404 8 , , PUNCT ejpam-7001 404 9 pages page NOUN ejpam-7001 404 10 451–469 451–469 NUM ejpam-7001 404 11 , , PUNCT ejpam-7001 404 12 2018 2018 NUM ejpam-7001 404 13 . . PUNCT ejpam-7001 405 1 [ [ X ejpam-7001 405 2 7 7 X ejpam-7001 405 3 ] ] PUNCT ejpam-7001 405 4 n n PRON ejpam-7001 405 5 celik celik VERB ejpam-7001 405 6 . . PUNCT ejpam-7001 406 1 some some DET ejpam-7001 406 2 cubic cubic ADJ ejpam-7001 406 3 rank rank NOUN ejpam-7001 406 4 transmuted transmute VERB ejpam-7001 406 5 distributions distribution NOUN ejpam-7001 406 6 . . PUNCT ejpam-7001 407 1 journal journal NOUN ejpam-7001 407 2 of of ADP ejpam-7001 407 3 applied apply VERB ejpam-7001 407 4 mathematics mathematic NOUN ejpam-7001 407 5 , , PUNCT ejpam-7001 407 6 statistics statistic NOUN ejpam-7001 407 7 and and CCONJ ejpam-7001 407 8 informatics informatic NOUN ejpam-7001 407 9 , , PUNCT ejpam-7001 407 10 14(2):27–43 14(2):27–43 NUM ejpam-7001 407 11 , , PUNCT ejpam-7001 407 12 2018 2018 NUM ejpam-7001 407 13 . . PUNCT ejpam-7001 408 1 [ [ X ejpam-7001 408 2 8 8 X ejpam-7001 408 3 ] ] X ejpam-7001 408 4 mdmahabubur mdmahabubur PROPN ejpam-7001 408 5 rahman rahman PROPN ejpam-7001 408 6 , , PUNCT ejpam-7001 408 7 bander bander PROPN ejpam-7001 408 8 al al PROPN ejpam-7001 408 9 - - PUNCT ejpam-7001 408 10 zahrani zahrani PROPN ejpam-7001 408 11 , , PUNCT ejpam-7001 408 12 and and CCONJ ejpam-7001 408 13 muhammad muhammad PROPN ejpam-7001 408 14 qaiser qaiser PROPN ejpam-7001 408 15 shahbaz shahbaz PROPN ejpam-7001 408 16 . . PUNCT ejpam-7001 408 17 cubic cubic PROPN ejpam-7001 408 18 transmuted transmute VERB ejpam-7001 408 19 weibull weibull NOUN ejpam-7001 408 20 distribution distribution NOUN ejpam-7001 408 21 : : PUNCT ejpam-7001 408 22 properties property NOUN ejpam-7001 408 23 and and CCONJ ejpam-7001 408 24 applications application NOUN ejpam-7001 408 25 . . PUNCT ejpam-7001 408 26 annals annal NOUN ejpam-7001 408 27 of of ADP ejpam-7001 408 28 data data NOUN ejpam-7001 408 29 science science NOUN ejpam-7001 408 30 , , PUNCT ejpam-7001 408 31 6(1):83–102 6(1):83–102 NUM ejpam-7001 408 32 , , PUNCT ejpam-7001 408 33 2019 2019 NUM ejpam-7001 408 34 . . PUNCT ejpam-7001 409 1 [ [ X ejpam-7001 409 2 9 9 NUM ejpam-7001 409 3 ] ] SYM ejpam-7001 409 4 sumaia sumaia PROPN ejpam-7001 409 5 akter akter PROPN ejpam-7001 409 6 , , PUNCT ejpam-7001 409 7 md md PROPN ejpam-7001 409 8 awwal awwal PROPN ejpam-7001 409 9 islam islam PROPN ejpam-7001 409 10 khan khan PROPN ejpam-7001 409 11 , , PUNCT ejpam-7001 409 12 md md PROPN ejpam-7001 409 13 shohel shohel PROPN ejpam-7001 409 14 rana rana PROPN ejpam-7001 409 15 , , PUNCT ejpam-7001 409 16 and and CCONJ ejpam-7001 409 17 md md PROPN ejpam-7001 409 18 mahabubur mahabubur PROPN ejpam-7001 409 19 rahman rahman PROPN ejpam-7001 409 20 . . PUNCT ejpam-7001 410 1 cubic cubic ADJ ejpam-7001 410 2 transmuted transmute VERB ejpam-7001 410 3 burr burr NOUN ejpam-7001 410 4 - - PUNCT ejpam-7001 410 5 xii xii NOUN ejpam-7001 410 6 distribution distribution NOUN ejpam-7001 410 7 with with ADP ejpam-7001 410 8 properties property NOUN ejpam-7001 410 9 and and CCONJ ejpam-7001 410 10 applications application NOUN ejpam-7001 410 11 . . PUNCT ejpam-7001 411 1 journal journal PROPN ejpam-7001 411 2 of of ADP ejpam-7001 411 3 statistics statistic NOUN ejpam-7001 411 4 applications application NOUN ejpam-7001 411 5 and and CCONJ ejpam-7001 411 6 probability probability NOUN ejpam-7001 411 7 letters letter NOUN ejpam-7001 411 8 , , PUNCT ejpam-7001 411 9 1:23–32 1:23–32 NUM ejpam-7001 411 10 , , PUNCT ejpam-7001 411 11 2021 2021 NUM ejpam-7001 411 12 . . PUNCT ejpam-7001 412 1 [ [ X ejpam-7001 412 2 10 10 NUM ejpam-7001 412 3 ] ] X ejpam-7001 412 4 ma ma PROPN ejpam-7001 412 5 ali ali PROPN ejpam-7001 412 6 and and CCONJ ejpam-7001 412 7 haseeb haseeb PROPN ejpam-7001 412 8 athar athar PROPN ejpam-7001 412 9 . . PUNCT ejpam-7001 413 1 generalized generalized ADJ ejpam-7001 413 2 rank rank NOUN ejpam-7001 413 3 mapped map VERB ejpam-7001 413 4 transmuted transmute VERB ejpam-7001 413 5 distribution distribution NOUN ejpam-7001 413 6 for for ADP ejpam-7001 413 7 generating generate VERB ejpam-7001 413 8 families family NOUN ejpam-7001 413 9 of of ADP ejpam-7001 413 10 continuous continuous ADJ ejpam-7001 413 11 distributions distribution NOUN ejpam-7001 413 12 . . PUNCT ejpam-7001 414 1 journal journal NOUN ejpam-7001 414 2 of of ADP ejpam-7001 414 3 statistical statistical ADJ ejpam-7001 414 4 theory theory NOUN ejpam-7001 414 5 and and CCONJ ejpam-7001 414 6 applications application NOUN ejpam-7001 414 7 , , PUNCT ejpam-7001 414 8 20(1):132–148 20(1):132–148 NOUN ejpam-7001 414 9 , , PUNCT ejpam-7001 414 10 2021 2021 NUM ejpam-7001 414 11 . . PUNCT ejpam-7001 415 1 [ [ X ejpam-7001 415 2 11 11 NUM ejpam-7001 415 3 ] ] X ejpam-7001 415 4 imliyangba imliyangba PROPN ejpam-7001 415 5 , , PUNCT ejpam-7001 415 6 bhanita bhanita NOUN ejpam-7001 415 7 das das PROPN ejpam-7001 415 8 , , PUNCT ejpam-7001 415 9 and and CCONJ ejpam-7001 415 10 seema seema PROPN ejpam-7001 415 11 chettri chettri PROPN ejpam-7001 415 12 . . PUNCT ejpam-7001 416 1 generalized generalized ADJ ejpam-7001 416 2 rank rank NOUN ejpam-7001 416 3 mapped map VERB ejpam-7001 416 4 transmuted transmute VERB ejpam-7001 416 5 distributions distribution NOUN ejpam-7001 416 6 with with ADP ejpam-7001 416 7 properties property NOUN ejpam-7001 416 8 and and CCONJ ejpam-7001 416 9 application application NOUN ejpam-7001 416 10 : : PUNCT ejpam-7001 416 11 a a DET ejpam-7001 416 12 review review NOUN ejpam-7001 416 13 . . PUNCT ejpam-7001 417 1 asian asian ADJ ejpam-7001 417 2 journal journal PROPN ejpam-7001 417 3 of of ADP ejpam-7001 417 4 probability probability NOUN ejpam-7001 417 5 and and CCONJ ejpam-7001 417 6 statistics statistic NOUN ejpam-7001 417 7 , , PUNCT ejpam-7001 417 8 13(3):44–61 13(3):44–61 NUM ejpam-7001 417 9 , , PUNCT ejpam-7001 417 10 2021 2021 NUM ejpam-7001 417 11 . . PUNCT ejpam-7001 418 1 [ [ X ejpam-7001 418 2 12 12 NUM ejpam-7001 418 3 ] ] X ejpam-7001 418 4 wweihull wweihull PROPN ejpam-7001 418 5 . . PUNCT ejpam-7001 419 1 a a DET ejpam-7001 419 2 statistical statistical ADJ ejpam-7001 419 3 distribution distribution NOUN ejpam-7001 419 4 function function NOUN ejpam-7001 419 5 of of ADP ejpam-7001 419 6 wide wide ADJ ejpam-7001 419 7 applicability applicability NOUN ejpam-7001 419 8 . . PUNCT ejpam-7001 420 1 journal journal PROPN ejpam-7001 420 2 of of ADP ejpam-7001 420 3 applied apply VERB ejpam-7001 420 4 mechanics mechanic NOUN ejpam-7001 420 5 , , PUNCT ejpam-7001 420 6 18:290–293 18:290–293 NUM ejpam-7001 420 7 , , PUNCT ejpam-7001 420 8 1951 1951 NUM ejpam-7001 420 9 . . PUNCT ejpam-7001 421 1 [ [ X ejpam-7001 421 2 13 13 NUM ejpam-7001 421 3 ] ] PUNCT ejpam-7001 421 4 ahmed ahmed PROPN ejpam-7001 421 5 z z PROPN ejpam-7001 421 6 afify afify NOUN ejpam-7001 421 7 , , PUNCT ejpam-7001 421 8 haitham haitham PROPN ejpam-7001 421 9 m m PROPN ejpam-7001 421 10 yousof yousof NOUN ejpam-7001 421 11 , , PUNCT ejpam-7001 421 12 gg gg NOUN ejpam-7001 421 13 hamedani hamedani NOUN ejpam-7001 421 14 , , PUNCT ejpam-7001 421 15 and and CCONJ ejpam-7001 421 16 gokarna gokarna NOUN ejpam-7001 421 17 r r NOUN ejpam-7001 421 18 aryal aryal NOUN ejpam-7001 421 19 . . PUNCT ejpam-7001 422 1 the the DET ejpam-7001 422 2 exponentiated exponentiated ADJ ejpam-7001 422 3 weibull weibull PROPN ejpam-7001 422 4 - - PUNCT ejpam-7001 422 5 pareto pareto VERB ejpam-7001 422 6 distribution distribution NOUN ejpam-7001 422 7 with with ADP ejpam-7001 422 8 application application NOUN ejpam-7001 422 9 . . PUNCT ejpam-7001 423 1 journal journal NOUN ejpam-7001 423 2 of of ADP ejpam-7001 423 3 statistical statistical ADJ ejpam-7001 423 4 theory theory NOUN ejpam-7001 423 5 and and CCONJ ejpam-7001 423 6 applications application NOUN ejpam-7001 423 7 , , PUNCT ejpam-7001 423 8 15(4):326–344 15(4):326–344 PROPN ejpam-7001 423 9 , , PUNCT ejpam-7001 423 10 2016 2016 NUM ejpam-7001 423 11 . . PUNCT ejpam-7001 424 1 [ [ X ejpam-7001 424 2 14 14 NUM ejpam-7001 424 3 ] ] X ejpam-7001 424 4 hamid hamid PROPN ejpam-7001 424 5 bidram bidram PROPN ejpam-7001 424 6 , , PUNCT ejpam-7001 424 7 mohammad mohammad PROPN ejpam-7001 424 8 hossein hossein PROPN ejpam-7001 424 9 alamatsaz alamatsaz PROPN ejpam-7001 424 10 , , PUNCT ejpam-7001 424 11 and and CCONJ ejpam-7001 424 12 vahid vahid PROPN ejpam-7001 424 13 nekoukhou nekoukhou PROPN ejpam-7001 424 14 . . PUNCT ejpam-7001 425 1 on on ADP ejpam-7001 425 2 an an DET ejpam-7001 425 3 extension extension NOUN ejpam-7001 425 4 of of ADP ejpam-7001 425 5 the the DET ejpam-7001 425 6 exponentiated exponentiated ADJ ejpam-7001 425 7 weibull weibull NOUN ejpam-7001 425 8 distribution distribution NOUN ejpam-7001 425 9 . . PUNCT ejpam-7001 426 1 communications communication NOUN ejpam-7001 426 2 in in ADP ejpam-7001 426 3 statisticssimulation statisticssimulation NOUN ejpam-7001 426 4 and and CCONJ ejpam-7001 426 5 computation computation NOUN ejpam-7001 426 6 , , PUNCT ejpam-7001 426 7 44(6):1389–1404 44(6):1389–1404 NOUN ejpam-7001 426 8 , , PUNCT ejpam-7001 426 9 2015 2015 NUM ejpam-7001 426 10 . . PUNCT ejpam-7001 427 1 imliyangba imliyangba PROPN ejpam-7001 427 2 et et PROPN ejpam-7001 427 3 al al PROPN ejpam-7001 427 4 . . PUNCT ejpam-7001 427 5 / / SYM ejpam-7001 427 6 eur eur PROPN ejpam-7001 427 7 . . PUNCT ejpam-7001 428 1 j. j. PROPN ejpam-7001 428 2 pure pure PROPN ejpam-7001 428 3 appl appl PROPN ejpam-7001 428 4 . . PROPN ejpam-7001 428 5 math math PROPN ejpam-7001 428 6 , , PUNCT ejpam-7001 428 7 18 18 NUM ejpam-7001 428 8 ( ( PUNCT ejpam-7001 428 9 4 4 NUM ejpam-7001 428 10 ) ) PUNCT ejpam-7001 428 11 ( ( PUNCT ejpam-7001 428 12 2025 2025 NUM ejpam-7001 428 13 ) ) PUNCT ejpam-7001 428 14 , , PUNCT ejpam-7001 428 15 7001 7001 NUM ejpam-7001 428 16 26 26 NUM ejpam-7001 428 17 of of ADP ejpam-7001 428 18 27 27 NUM ejpam-7001 428 19 [ [ SYM ejpam-7001 428 20 15 15 NUM ejpam-7001 428 21 ] ] PUNCT ejpam-7001 428 22 beih beih NOUN ejpam-7001 428 23 s s PART ejpam-7001 428 24 el el PROPN ejpam-7001 428 25 - - PUNCT ejpam-7001 428 26 desouky desouky PROPN ejpam-7001 428 27 , , PUNCT ejpam-7001 428 28 abdelfattah abdelfattah PROPN ejpam-7001 428 29 mustafa mustafa PROPN ejpam-7001 428 30 , , PUNCT ejpam-7001 428 31 and and CCONJ ejpam-7001 428 32 shamsan shamsan PROPN ejpam-7001 428 33 al al PROPN ejpam-7001 428 34 - - PUNCT ejpam-7001 428 35 garash garash NOUN ejpam-7001 428 36 . . PUNCT ejpam-7001 429 1 the the DET ejpam-7001 429 2 exponential exponential ADJ ejpam-7001 429 3 flexible flexible ADJ ejpam-7001 429 4 weibull weibull NOUN ejpam-7001 429 5 extension extension NOUN ejpam-7001 429 6 distribution distribution NOUN ejpam-7001 429 7 . . PUNCT ejpam-7001 430 1 arxiv arxiv PROPN ejpam-7001 430 2 preprint preprint PROPN ejpam-7001 430 3 arxiv:1605.08152 arxiv:1605.08152 PROPN ejpam-7001 430 4 , , PUNCT ejpam-7001 430 5 2016 2016 NUM ejpam-7001 430 6 . . PUNCT ejpam-7001 431 1 [ [ X ejpam-7001 431 2 16 16 NUM ejpam-7001 431 3 ] ] X ejpam-7001 431 4 gauss gauss PROPN ejpam-7001 431 5 m m PROPN ejpam-7001 431 6 cordeiro cordeiro PROPN ejpam-7001 431 7 , , PUNCT ejpam-7001 431 8 abdus abdus PRON ejpam-7001 431 9 saboor saboor PROPN ejpam-7001 431 10 , , PUNCT ejpam-7001 431 11 muhammad muhammad PROPN ejpam-7001 431 12 nauman nauman PROPN ejpam-7001 431 13 khan khan PROPN ejpam-7001 431 14 , , PUNCT ejpam-7001 431 15 serge serge PROPN ejpam-7001 431 16 b b X ejpam-7001 431 17 provost provost NOUN ejpam-7001 431 18 , , PUNCT ejpam-7001 431 19 and and CCONJ ejpam-7001 431 20 edwin edwin PROPN ejpam-7001 431 21 mm mm PROPN ejpam-7001 431 22 ortega ortega PROPN ejpam-7001 431 23 . . PUNCT ejpam-7001 432 1 the the DET ejpam-7001 432 2 transmuted transmuted ADJ ejpam-7001 432 3 generalized generalized ADJ ejpam-7001 432 4 modified modify VERB ejpam-7001 432 5 weibull weibull NOUN ejpam-7001 432 6 distribution distribution NOUN ejpam-7001 432 7 . . PUNCT ejpam-7001 433 1 filomat filomat NOUN ejpam-7001 433 2 , , PUNCT ejpam-7001 433 3 31(5):1395–1412 31(5):1395–1412 NUM ejpam-7001 433 4 , , PUNCT ejpam-7001 433 5 2017 2017 NUM ejpam-7001 433 6 . . PUNCT ejpam-7001 434 1 [ [ X ejpam-7001 434 2 17 17 NUM ejpam-7001 434 3 ] ] X ejpam-7001 434 4 gauss gauss PROPN ejpam-7001 434 5 m m PROPN ejpam-7001 434 6 cordeiro cordeiro PROPN ejpam-7001 434 7 , , PUNCT ejpam-7001 434 8 ahmed ahmed PROPN ejpam-7001 434 9 z z PROPN ejpam-7001 434 10 afify afify NOUN ejpam-7001 434 11 , , PUNCT ejpam-7001 434 12 haitham haitham PROPN ejpam-7001 434 13 m m PROPN ejpam-7001 434 14 yousof yousof NOUN ejpam-7001 434 15 , , PUNCT ejpam-7001 434 16 selen selen NOUN ejpam-7001 434 17 cakmakyapan cakmakyapan PROPN ejpam-7001 434 18 , , PUNCT ejpam-7001 434 19 and and CCONJ ejpam-7001 434 20 gamze gamze NOUN ejpam-7001 434 21 ozel ozel NOUN ejpam-7001 434 22 . . PUNCT ejpam-7001 435 1 the the DET ejpam-7001 435 2 lindley lindley ADJ ejpam-7001 435 3 weibull weibull NOUN ejpam-7001 435 4 distribution distribution NOUN ejpam-7001 435 5 : : PUNCT ejpam-7001 435 6 properties property NOUN ejpam-7001 435 7 and and CCONJ ejpam-7001 435 8 applications application NOUN ejpam-7001 435 9 . . PUNCT ejpam-7001 436 1 anais anais PROPN ejpam-7001 436 2 da da PROPN ejpam-7001 436 3 academia academia PROPN ejpam-7001 436 4 brasileira brasileira PROPN ejpam-7001 436 5 de de PROPN ejpam-7001 436 6 ciências ciências PROPN ejpam-7001 436 7 , , PUNCT ejpam-7001 436 8 90:2579–2598 90:2579–2598 NUM ejpam-7001 436 9 , , PUNCT ejpam-7001 436 10 2018 2018 NUM ejpam-7001 436 11 . . PUNCT ejpam-7001 437 1 [ [ X ejpam-7001 437 2 18 18 NUM ejpam-7001 437 3 ] ] PUNCT ejpam-7001 437 4 said say VERB ejpam-7001 437 5 alkarni alkarni PROPN ejpam-7001 437 6 , , PUNCT ejpam-7001 437 7 ahmed ahmed PROPN ejpam-7001 437 8 z z PROPN ejpam-7001 437 9 afify afify NOUN ejpam-7001 437 10 , , PUNCT ejpam-7001 437 11 ibrahim ibrahim PROPN ejpam-7001 437 12 elbatal elbatal PROPN ejpam-7001 437 13 , , PUNCT ejpam-7001 437 14 and and CCONJ ejpam-7001 437 15 mohammed mohammed PROPN ejpam-7001 437 16 elgarhy elgarhy PROPN ejpam-7001 437 17 . . PUNCT ejpam-7001 438 1 the the DET ejpam-7001 438 2 extended extended ADJ ejpam-7001 438 3 inverse inverse NOUN ejpam-7001 438 4 weibull weibull NOUN ejpam-7001 438 5 distribution distribution NOUN ejpam-7001 438 6 : : PUNCT ejpam-7001 438 7 properties property NOUN ejpam-7001 438 8 and and CCONJ ejpam-7001 438 9 applications application NOUN ejpam-7001 438 10 . . PUNCT ejpam-7001 439 1 complexity complexity NOUN ejpam-7001 439 2 , , PUNCT ejpam-7001 439 3 2020(1):3297693 2020(1):3297693 NUM ejpam-7001 439 4 , , PUNCT ejpam-7001 439 5 2020 2020 NUM ejpam-7001 439 6 . . PUNCT ejpam-7001 440 1 [ [ X ejpam-7001 440 2 19 19 NUM ejpam-7001 440 3 ] ] X ejpam-7001 440 4 hisham hisham PROPN ejpam-7001 440 5 m m PROPN ejpam-7001 440 6 almongy almongy PROPN ejpam-7001 440 7 , , PUNCT ejpam-7001 440 8 fatma fatma PROPN ejpam-7001 440 9 y y PROPN ejpam-7001 440 10 alshenawy alshenawy PROPN ejpam-7001 440 11 , , PUNCT ejpam-7001 440 12 ehab ehab PROPN ejpam-7001 440 13 m m VERB ejpam-7001 440 14 almetwally almetwally ADV ejpam-7001 440 15 , , PUNCT ejpam-7001 440 16 and and CCONJ ejpam-7001 440 17 doaa doaa VERB ejpam-7001 440 18 a a DET ejpam-7001 440 19 abdo abdo NOUN ejpam-7001 440 20 . . PUNCT ejpam-7001 441 1 applying apply VERB ejpam-7001 441 2 transformer transformer NOUN ejpam-7001 441 3 insulation insulation NOUN ejpam-7001 441 4 using use VERB ejpam-7001 441 5 weibull weibull NOUN ejpam-7001 441 6 extended extend VERB ejpam-7001 441 7 distribution distribution NOUN ejpam-7001 441 8 based base VERB ejpam-7001 441 9 on on ADP ejpam-7001 441 10 progressive progressive ADJ ejpam-7001 441 11 censoring censor VERB ejpam-7001 441 12 scheme scheme NOUN ejpam-7001 441 13 . . PUNCT ejpam-7001 442 1 axioms axiom NOUN ejpam-7001 442 2 , , PUNCT ejpam-7001 442 3 10(2):100 10(2):100 NUM ejpam-7001 442 4 , , PUNCT ejpam-7001 442 5 2021 2021 NUM ejpam-7001 442 6 . . PUNCT ejpam-7001 443 1 [ [ X ejpam-7001 443 2 20 20 NUM ejpam-7001 443 3 ] ] PUNCT ejpam-7001 443 4 sajid sajid PROPN ejpam-7001 443 5 mehboob mehboob PROPN ejpam-7001 443 6 zaidi zaidi PROPN ejpam-7001 443 7 , , PUNCT ejpam-7001 443 8 mma mma PROPN ejpam-7001 443 9 sobhi sobhi PROPN ejpam-7001 443 10 , , PUNCT ejpam-7001 443 11 m m PROPN ejpam-7001 443 12 el el PROPN ejpam-7001 443 13 - - PUNCT ejpam-7001 443 14 morshedy morshedy PROPN ejpam-7001 443 15 , , PUNCT ejpam-7001 443 16 and and CCONJ ejpam-7001 443 17 ahmed ahmed PROPN ejpam-7001 443 18 z z PROPN ejpam-7001 443 19 afify afify NOUN ejpam-7001 443 20 . . PUNCT ejpam-7001 444 1 a a DET ejpam-7001 444 2 new new ADJ ejpam-7001 444 3 generalized generalized ADJ ejpam-7001 444 4 family family NOUN ejpam-7001 444 5 of of ADP ejpam-7001 444 6 distributions distribution NOUN ejpam-7001 444 7 : : PUNCT ejpam-7001 444 8 properties property NOUN ejpam-7001 444 9 and and CCONJ ejpam-7001 444 10 applications application NOUN ejpam-7001 444 11 . . PUNCT ejpam-7001 445 1 aims aim VERB ejpam-7001 445 2 math math NOUN ejpam-7001 445 3 , , PUNCT ejpam-7001 445 4 6(1):456 6(1):456 NUM ejpam-7001 445 5 – – PUNCT ejpam-7001 445 6 476 476 NUM ejpam-7001 445 7 , , PUNCT ejpam-7001 445 8 2021 2021 NUM ejpam-7001 445 9 . . PUNCT ejpam-7001 446 1 [ [ X ejpam-7001 446 2 21 21 NUM ejpam-7001 446 3 ] ] X ejpam-7001 446 4 naif naif ADJ ejpam-7001 446 5 alotaibi alotaibi NOUN ejpam-7001 446 6 , , PUNCT ejpam-7001 446 7 ibrahim ibrahim PROPN ejpam-7001 446 8 elbatal elbatal PROPN ejpam-7001 446 9 , , PUNCT ejpam-7001 446 10 ehab ehab PROPN ejpam-7001 446 11 m m VERB ejpam-7001 446 12 almetwally almetwally ADV ejpam-7001 446 13 , , PUNCT ejpam-7001 446 14 salem salem VERB ejpam-7001 446 15 a a DET ejpam-7001 446 16 alyami alyami NOUN ejpam-7001 446 17 , , PUNCT ejpam-7001 446 18 as as ADP ejpam-7001 446 19 almoisheer almoisheer NOUN ejpam-7001 446 20 , , PUNCT ejpam-7001 446 21 and and CCONJ ejpam-7001 446 22 mohammed mohammed PROPN ejpam-7001 446 23 elgarhy elgarhy PROPN ejpam-7001 446 24 . . PUNCT ejpam-7001 447 1 bivariate bivariate ADJ ejpam-7001 447 2 step step NOUN ejpam-7001 447 3 - - PUNCT ejpam-7001 447 4 stress stress NOUN ejpam-7001 447 5 accelerated accelerate VERB ejpam-7001 447 6 life life NOUN ejpam-7001 447 7 tests test NOUN ejpam-7001 447 8 for for ADP ejpam-7001 447 9 the the DET ejpam-7001 447 10 kavya kavya PROPN ejpam-7001 447 11 – – PUNCT ejpam-7001 447 12 manoharan manoharan NOUN ejpam-7001 447 13 exponentiated exponentiate VERB ejpam-7001 447 14 weibull weibull PROPN ejpam-7001 447 15 model model PROPN ejpam-7001 447 16 under under ADP ejpam-7001 447 17 progressive progressive ADJ ejpam-7001 447 18 censoring censor VERB ejpam-7001 447 19 with with ADP ejpam-7001 447 20 applications application NOUN ejpam-7001 447 21 . . PUNCT ejpam-7001 448 1 symmetry symmetry NOUN ejpam-7001 448 2 , , PUNCT ejpam-7001 448 3 14(9):1791 14(9):1791 NUM ejpam-7001 448 4 , , PUNCT ejpam-7001 448 5 2022 2022 NUM ejpam-7001 448 6 . . PUNCT ejpam-7001 449 1 [ [ X ejpam-7001 449 2 22 22 NUM ejpam-7001 449 3 ] ] X ejpam-7001 449 4 farwa farwa NOUN ejpam-7001 449 5 willayat willayat PROPN ejpam-7001 449 6 , , PUNCT ejpam-7001 449 7 naz naz PROPN ejpam-7001 449 8 saud saud PROPN ejpam-7001 449 9 , , PUNCT ejpam-7001 449 10 muhammad muhammad PROPN ejpam-7001 449 11 ijaz ijaz PROPN ejpam-7001 449 12 , , PUNCT ejpam-7001 449 13 anita anita PROPN ejpam-7001 449 14 silvianita silvianita PROPN ejpam-7001 449 15 , , PUNCT ejpam-7001 449 16 and and CCONJ ejpam-7001 449 17 mahmoud mahmoud PROPN ejpam-7001 449 18 elmorshedy elmorshedy PROPN ejpam-7001 449 19 . . PUNCT ejpam-7001 450 1 marshall marshall PROPN ejpam-7001 450 2 – – PUNCT ejpam-7001 450 3 olkin olkin NOUN ejpam-7001 450 4 extended extend VERB ejpam-7001 450 5 gumbel gumbel NOUN ejpam-7001 450 6 type type NOUN ejpam-7001 450 7 - - PUNCT ejpam-7001 450 8 ii ii NOUN ejpam-7001 450 9 distribution distribution NOUN ejpam-7001 450 10 : : PUNCT ejpam-7001 450 11 properties property NOUN ejpam-7001 450 12 and and CCONJ ejpam-7001 450 13 applications application NOUN ejpam-7001 450 14 . . PUNCT ejpam-7001 451 1 complexity complexity NOUN ejpam-7001 451 2 , , PUNCT ejpam-7001 451 3 2022(1):2219570 2022(1):2219570 NOUN ejpam-7001 451 4 , , PUNCT ejpam-7001 451 5 2022 2022 NUM ejpam-7001 451 6 . . PUNCT ejpam-7001 452 1 [ [ X ejpam-7001 452 2 23 23 NUM ejpam-7001 452 3 ] ] PUNCT ejpam-7001 452 4 sidahmed sidahme VERB ejpam-7001 452 5 benchiha benchiha PROPN ejpam-7001 452 6 , , PUNCT ejpam-7001 452 7 laxmi laxmi PROPN ejpam-7001 452 8 prasad prasad PROPN ejpam-7001 452 9 sapkota sapkota NOUN ejpam-7001 452 10 , , PUNCT ejpam-7001 452 11 aned ane VERB ejpam-7001 452 12 al al PROPN ejpam-7001 452 13 mutairi mutairi PROPN ejpam-7001 452 14 , , PUNCT ejpam-7001 452 15 vijay vijay PROPN ejpam-7001 452 16 kumar kumar PROPN ejpam-7001 452 17 , , PUNCT ejpam-7001 452 18 rana rana PROPN ejpam-7001 452 19 h h PROPN ejpam-7001 452 20 khashab khashab PROPN ejpam-7001 452 21 , , PUNCT ejpam-7001 452 22 ahmed ahmed PROPN ejpam-7001 452 23 m m PROPN ejpam-7001 452 24 gemeay gemeay ADJ ejpam-7001 452 25 , , PUNCT ejpam-7001 452 26 mohammed mohammed PROPN ejpam-7001 452 27 elgarhy elgarhy PROPN ejpam-7001 452 28 , , PUNCT ejpam-7001 452 29 and and CCONJ ejpam-7001 452 30 said say VERB ejpam-7001 452 31 g g PROPN ejpam-7001 452 32 nassr nassr PROPN ejpam-7001 452 33 . . PUNCT ejpam-7001 453 1 a a DET ejpam-7001 453 2 new new ADJ ejpam-7001 453 3 sine sine ADJ ejpam-7001 453 4 family family NOUN ejpam-7001 453 5 of of ADP ejpam-7001 453 6 generalized generalized ADJ ejpam-7001 453 7 distributions distribution NOUN ejpam-7001 453 8 : : PUNCT ejpam-7001 453 9 statistical statistical ADJ ejpam-7001 453 10 inference inference NOUN ejpam-7001 453 11 with with ADP ejpam-7001 453 12 applications application NOUN ejpam-7001 453 13 . . PUNCT ejpam-7001 454 1 mathematical mathematical ADJ ejpam-7001 454 2 and and CCONJ ejpam-7001 454 3 computational computational ADJ ejpam-7001 454 4 applications application NOUN ejpam-7001 454 5 , , PUNCT ejpam-7001 454 6 28(4):83 28(4):83 NUM ejpam-7001 454 7 , , PUNCT ejpam-7001 454 8 2023 2023 NUM ejpam-7001 454 9 . . PUNCT ejpam-7001 455 1 [ [ X ejpam-7001 455 2 24 24 NUM ejpam-7001 455 3 ] ] X ejpam-7001 455 4 m m VERB ejpam-7001 455 5 frechet frechet PROPN ejpam-7001 455 6 . . PUNCT ejpam-7001 456 1 on on ADP ejpam-7001 456 2 the the DET ejpam-7001 456 3 law law NOUN ejpam-7001 456 4 of of ADP ejpam-7001 456 5 probability probability NOUN ejpam-7001 456 6 of of ADP ejpam-7001 456 7 the the DET ejpam-7001 456 8 maximum maximum ADJ ejpam-7001 456 9 deviation deviation NOUN ejpam-7001 456 10 , , PUNCT ejpam-7001 456 11 annals annal NOUN ejpam-7001 456 12 of of ADP ejpam-7001 456 13 the the DET ejpam-7001 456 14 polish polish ADJ ejpam-7001 456 15 mathematical mathematical ADJ ejpam-7001 456 16 society society NOUN ejpam-7001 456 17 . . PUNCT ejpam-7001 457 1 cracovie cracovie NOUN ejpam-7001 457 2 , , PUNCT ejpam-7001 457 3 6:93–116 6:93–116 NUM ejpam-7001 457 4 , , PUNCT ejpam-7001 457 5 1927 1927 NUM ejpam-7001 457 6 . . PUNCT ejpam-7001 458 1 [ [ X ejpam-7001 458 2 25 25 NUM ejpam-7001 458 3 ] ] X ejpam-7001 458 4 ronaldo ronaldo NOUN ejpam-7001 458 5 v v ADP ejpam-7001 458 6 da da PROPN ejpam-7001 458 7 silva silva PROPN ejpam-7001 458 8 , , PUNCT ejpam-7001 458 9 thiago thiago VERB ejpam-7001 458 10 an an DET ejpam-7001 458 11 de de X ejpam-7001 458 12 andrade andrade PROPN ejpam-7001 458 13 , , PUNCT ejpam-7001 458 14 diego diego PROPN ejpam-7001 458 15 bm bm PROPN ejpam-7001 458 16 maciel maciel PROPN ejpam-7001 458 17 , , PUNCT ejpam-7001 458 18 renilma renilma PROPN ejpam-7001 458 19 ps ps PROPN ejpam-7001 458 20 campos campos PROPN ejpam-7001 458 21 , , PUNCT ejpam-7001 458 22 and and CCONJ ejpam-7001 458 23 gauss gauss PROPN ejpam-7001 458 24 m m VERB ejpam-7001 458 25 cordeiro cordeiro PROPN ejpam-7001 458 26 . . PUNCT ejpam-7001 459 1 a a DET ejpam-7001 459 2 new new ADJ ejpam-7001 459 3 lifetime lifetime NOUN ejpam-7001 459 4 model model NOUN ejpam-7001 459 5 : : PUNCT ejpam-7001 459 6 the the DET ejpam-7001 459 7 gamma gamma NOUN ejpam-7001 459 8 extended extend VERB ejpam-7001 459 9 fréchet fréchet NOUN ejpam-7001 459 10 distribution distribution NOUN ejpam-7001 459 11 . . PUNCT ejpam-7001 460 1 journal journal NOUN ejpam-7001 460 2 of of ADP ejpam-7001 460 3 statistical statistical ADJ ejpam-7001 460 4 theory theory NOUN ejpam-7001 460 5 and and CCONJ ejpam-7001 460 6 applications application NOUN ejpam-7001 460 7 , , PUNCT ejpam-7001 460 8 12(1):39–54 12(1):39–54 NUM ejpam-7001 460 9 , , PUNCT ejpam-7001 460 10 2013 2013 NUM ejpam-7001 460 11 . . PUNCT ejpam-7001 461 1 [ [ X ejpam-7001 461 2 26 26 NUM ejpam-7001 461 3 ] ] SYM ejpam-7001 461 4 s s PART ejpam-7001 461 5 nadarajah nadarajah NOUN ejpam-7001 461 6 and and CCONJ ejpam-7001 461 7 ak ak PROPN ejpam-7001 461 8 gupta gupta PROPN ejpam-7001 461 9 . . PUNCT ejpam-7001 462 1 the the DET ejpam-7001 462 2 beta beta ADJ ejpam-7001 462 3 fréchet fréchet NOUN ejpam-7001 462 4 distribution distribution NOUN ejpam-7001 462 5 . . PUNCT ejpam-7001 463 1 far far PROPN ejpam-7001 463 2 east east PROPN ejpam-7001 463 3 journal journal PROPN ejpam-7001 463 4 of of ADP ejpam-7001 463 5 theoretical theoretical ADJ ejpam-7001 463 6 statistics statistic NOUN ejpam-7001 463 7 , , PUNCT ejpam-7001 463 8 14(1):15–24 14(1):15–24 NUM ejpam-7001 463 9 , , PUNCT ejpam-7001 463 10 2004 2004 NUM ejpam-7001 463 11 . . PUNCT ejpam-7001 464 1 [ [ X ejpam-7001 464 2 27 27 NUM ejpam-7001 464 3 ] ] X ejpam-7001 464 4 mr mr PROPN ejpam-7001 464 5 mahmoud mahmoud PROPN ejpam-7001 464 6 and and CCONJ ejpam-7001 464 7 rm rm PROPN ejpam-7001 464 8 mandouh mandouh NOUN ejpam-7001 464 9 . . PUNCT ejpam-7001 465 1 on on ADP ejpam-7001 465 2 the the DET ejpam-7001 465 3 transmuted transmuted ADJ ejpam-7001 465 4 fréchet fréchet NOUN ejpam-7001 465 5 distribution distribution NOUN ejpam-7001 465 6 . . PUNCT ejpam-7001 466 1 journal journal NOUN ejpam-7001 466 2 of of ADP ejpam-7001 466 3 applied apply VERB ejpam-7001 466 4 sciences science NOUN ejpam-7001 466 5 research research NOUN ejpam-7001 466 6 , , PUNCT ejpam-7001 466 7 9(10):5553–5561 9(10):5553–5561 NUM ejpam-7001 466 8 , , PUNCT ejpam-7001 466 9 2013 2013 NUM ejpam-7001 466 10 . . PUNCT ejpam-7001 467 1 [ [ X ejpam-7001 467 2 28 28 NUM ejpam-7001 467 3 ] ] PUNCT ejpam-7001 467 4 am be AUX ejpam-7001 467 5 abd abd PROPN ejpam-7001 467 6 - - PUNCT ejpam-7001 467 7 elfattah elfattah PROPN ejpam-7001 467 8 , , PUNCT ejpam-7001 467 9 sm sm PROPN ejpam-7001 467 10 assar assar PROPN ejpam-7001 467 11 , , PUNCT ejpam-7001 467 12 and and CCONJ ejpam-7001 467 13 hi hi INTJ ejpam-7001 467 14 abd abd NOUN ejpam-7001 467 15 - - PUNCT ejpam-7001 467 16 elghaffar elghaffar PROPN ejpam-7001 467 17 . . PUNCT ejpam-7001 468 1 exponentiated exponentiated PROPN ejpam-7001 468 2 generalized generalize VERB ejpam-7001 468 3 frechet frechet ADJ ejpam-7001 468 4 distribution distribution NOUN ejpam-7001 468 5 . . PUNCT ejpam-7001 469 1 international international ADJ ejpam-7001 469 2 journal journal PROPN ejpam-7001 469 3 of of ADP ejpam-7001 469 4 mathematical mathematical ADJ ejpam-7001 469 5 analysis analysis NOUN ejpam-7001 469 6 and and CCONJ ejpam-7001 469 7 applications application NOUN ejpam-7001 469 8 , , PUNCT ejpam-7001 469 9 3(5):39–48 3(5):39–48 NUM ejpam-7001 469 10 , , PUNCT ejpam-7001 469 11 2016 2016 NUM ejpam-7001 469 12 . . PUNCT ejpam-7001 470 1 [ [ X ejpam-7001 470 2 29 29 NUM ejpam-7001 470 3 ] ] X ejpam-7001 470 4 majdah majdah PROPN ejpam-7001 470 5 m m PROPN ejpam-7001 470 6 badr badr PROPN ejpam-7001 470 7 . . PUNCT ejpam-7001 471 1 beta beta ADJ ejpam-7001 471 2 generalized generalize VERB ejpam-7001 471 3 exponentiated exponentiate VERB ejpam-7001 471 4 frechet frechet NOUN ejpam-7001 471 5 distribution distribution NOUN ejpam-7001 471 6 with with ADP ejpam-7001 471 7 applications application NOUN ejpam-7001 471 8 . . PUNCT ejpam-7001 472 1 open open ADJ ejpam-7001 472 2 physics physics PROPN ejpam-7001 472 3 , , PUNCT ejpam-7001 472 4 17(1):687–697 17(1):687–697 PROPN ejpam-7001 472 5 , , PUNCT ejpam-7001 472 6 2019 2019 NUM ejpam-7001 472 7 . . PUNCT ejpam-7001 473 1 [ [ X ejpam-7001 473 2 30 30 NUM ejpam-7001 473 3 ] ] X ejpam-7001 473 4 huda huda PROPN ejpam-7001 473 5 m m PROPN ejpam-7001 473 6 alshanbari alshanbari PROPN ejpam-7001 473 7 , , PUNCT ejpam-7001 473 8 ahmed ahmed PROPN ejpam-7001 473 9 m m PROPN ejpam-7001 473 10 gemeay gemeay ADJ ejpam-7001 473 11 , , PUNCT ejpam-7001 473 12 abd abd PROPN ejpam-7001 473 13 al al PROPN ejpam-7001 473 14 - - PROPN ejpam-7001 473 15 aziz aziz PROPN ejpam-7001 473 16 hosni hosni PROPN ejpam-7001 473 17 el el PROPN ejpam-7001 473 18 - - PUNCT ejpam-7001 473 19 bagoury bagoury PROPN ejpam-7001 473 20 , , PUNCT ejpam-7001 473 21 saima saima PROPN ejpam-7001 473 22 khan khan PROPN ejpam-7001 473 23 imliyangba imliyangba PROPN ejpam-7001 473 24 et et PROPN ejpam-7001 473 25 al al PROPN ejpam-7001 473 26 . . PUNCT ejpam-7001 473 27 / / SYM ejpam-7001 473 28 eur eur PROPN ejpam-7001 473 29 . . PUNCT ejpam-7001 474 1 j. j. PROPN ejpam-7001 474 2 pure pure PROPN ejpam-7001 474 3 appl appl PROPN ejpam-7001 474 4 . . PROPN ejpam-7001 474 5 math math PROPN ejpam-7001 474 6 , , PUNCT ejpam-7001 474 7 18 18 NUM ejpam-7001 474 8 ( ( PUNCT ejpam-7001 474 9 4 4 NUM ejpam-7001 474 10 ) ) PUNCT ejpam-7001 474 11 ( ( PUNCT ejpam-7001 474 12 2025 2025 NUM ejpam-7001 474 13 ) ) PUNCT ejpam-7001 474 14 , , PUNCT ejpam-7001 474 15 7001 7001 NUM ejpam-7001 474 16 27 27 NUM ejpam-7001 474 17 of of ADP ejpam-7001 474 18 27 27 NUM ejpam-7001 474 19 khosa khosa NOUN ejpam-7001 474 20 , , PUNCT ejpam-7001 474 21 eh eh INTJ ejpam-7001 474 22 hafez hafez PROPN ejpam-7001 474 23 , , PUNCT ejpam-7001 474 24 and and CCONJ ejpam-7001 474 25 abdisalam abdisalam PROPN ejpam-7001 474 26 hassan hassan PROPN ejpam-7001 474 27 muse muse PROPN ejpam-7001 474 28 . . PUNCT ejpam-7001 475 1 a a DET ejpam-7001 475 2 novel novel ADJ ejpam-7001 475 3 extension extension NOUN ejpam-7001 475 4 of of ADP ejpam-7001 475 5 fréchet fréchet ADJ ejpam-7001 475 6 distribution distribution NOUN ejpam-7001 475 7 : : PUNCT ejpam-7001 475 8 application application NOUN ejpam-7001 475 9 on on ADP ejpam-7001 475 10 real real ADJ ejpam-7001 475 11 data datum NOUN ejpam-7001 475 12 and and CCONJ ejpam-7001 475 13 simulation simulation NOUN ejpam-7001 475 14 . . PUNCT ejpam-7001 476 1 alexandria alexandria PROPN ejpam-7001 476 2 engineering engineering PROPN ejpam-7001 476 3 journal journal PROPN ejpam-7001 476 4 , , PUNCT ejpam-7001 476 5 61(10):7917–7938 61(10):7917–7938 NUM ejpam-7001 476 6 , , PUNCT ejpam-7001 476 7 2022 2022 NUM ejpam-7001 476 8 . . PUNCT ejpam-7001 477 1 [ [ X ejpam-7001 477 2 31 31 NUM ejpam-7001 477 3 ] ] X ejpam-7001 477 4 abd abd PROPN ejpam-7001 477 5 - - PUNCT ejpam-7001 477 6 elmonem elmonem PROPN ejpam-7001 477 7 am am PROPN ejpam-7001 477 8 teamah teamah NOUN ejpam-7001 477 9 , , PUNCT ejpam-7001 477 10 ahmed ahme VERB ejpam-7001 477 11 a a DET ejpam-7001 477 12 elbanna elbanna ADJ ejpam-7001 477 13 , , PUNCT ejpam-7001 477 14 and and CCONJ ejpam-7001 477 15 ahmed ahmed PROPN ejpam-7001 477 16 m m PROPN ejpam-7001 477 17 gemeay gemeay PROPN ejpam-7001 477 18 . . PUNCT ejpam-7001 478 1 fréchetweibull fréchetweibull NOUN ejpam-7001 478 2 distribution distribution NOUN ejpam-7001 478 3 with with ADP ejpam-7001 478 4 applications application NOUN ejpam-7001 478 5 to to ADP ejpam-7001 478 6 earthquakes earthquake NOUN ejpam-7001 478 7 data datum NOUN ejpam-7001 478 8 sets set NOUN ejpam-7001 478 9 . . PUNCT ejpam-7001 479 1 pakistan pakistan PROPN ejpam-7001 479 2 journal journal PROPN ejpam-7001 479 3 of of ADP ejpam-7001 479 4 statistics statistic NOUN ejpam-7001 479 5 , , PUNCT ejpam-7001 479 6 36(2 36(2 NUM ejpam-7001 479 7 ) ) PUNCT ejpam-7001 479 8 , , PUNCT ejpam-7001 479 9 2020 2020 NUM ejpam-7001 479 10 . . PUNCT ejpam-7001 480 1 [ [ X ejpam-7001 480 2 32 32 NUM ejpam-7001 480 3 ] ] SYM ejpam-7001 480 4 deepshikha deepshikha NOUN ejpam-7001 480 5 deka deka NOUN ejpam-7001 480 6 , , PUNCT ejpam-7001 480 7 bhanita bhanita NOUN ejpam-7001 480 8 das das PROPN ejpam-7001 480 9 , , PUNCT ejpam-7001 480 10 bhupen bhupen VERB ejpam-7001 480 11 k k PROPN ejpam-7001 480 12 baruah baruah NOUN ejpam-7001 480 13 , , PUNCT ejpam-7001 480 14 and and CCONJ ejpam-7001 480 15 bhupen bhupen ADJ ejpam-7001 480 16 baruah baruah NOUN ejpam-7001 480 17 . . PUNCT ejpam-7001 481 1 some some DET ejpam-7001 481 2 properties property NOUN ejpam-7001 481 3 on on ADP ejpam-7001 481 4 fréchet fréchet NOUN ejpam-7001 481 5 - - PUNCT ejpam-7001 481 6 weibull weibull NOUN ejpam-7001 481 7 distribution distribution NOUN ejpam-7001 481 8 with with ADP ejpam-7001 481 9 application application NOUN ejpam-7001 481 10 to to ADP ejpam-7001 481 11 real real ADJ ejpam-7001 481 12 life life NOUN ejpam-7001 481 13 data datum NOUN ejpam-7001 481 14 . . PUNCT ejpam-7001 482 1 mathematics mathematic NOUN ejpam-7001 482 2 and and CCONJ ejpam-7001 482 3 statistics statistic NOUN ejpam-7001 482 4 , , PUNCT ejpam-7001 482 5 9(1):8–15 9(1):8–15 NUM ejpam-7001 482 6 , , PUNCT ejpam-7001 482 7 2021 2021 NUM ejpam-7001 482 8 . . PUNCT ejpam-7001 483 1 [ [ X ejpam-7001 483 2 33 33 NUM ejpam-7001 483 3 ] ] X ejpam-7001 483 4 hadeel hadeel PROPN ejpam-7001 483 5 s s X ejpam-7001 483 6 klakattawi klakattawi PROPN ejpam-7001 483 7 , , PUNCT ejpam-7001 483 8 aisha aisha PROPN ejpam-7001 483 9 a a DET ejpam-7001 483 10 khormi khormi NOUN ejpam-7001 483 11 , , PUNCT ejpam-7001 483 12 and and CCONJ ejpam-7001 483 13 lamya lamya ADV ejpam-7001 483 14 a a DET ejpam-7001 483 15 baharith baharith NOUN ejpam-7001 483 16 . . PUNCT ejpam-7001 484 1 the the DET ejpam-7001 484 2 new new ADJ ejpam-7001 484 3 generalized generalize VERB ejpam-7001 484 4 exponentiated exponentiate VERB ejpam-7001 484 5 fréchet fréchet PROPN ejpam-7001 484 6 – – PUNCT ejpam-7001 484 7 weibull weibull NOUN ejpam-7001 484 8 distribution distribution NOUN ejpam-7001 484 9 : : PUNCT ejpam-7001 484 10 properties property NOUN ejpam-7001 484 11 , , PUNCT ejpam-7001 484 12 applications application NOUN ejpam-7001 484 13 , , PUNCT ejpam-7001 484 14 and and CCONJ ejpam-7001 484 15 regression regression NOUN ejpam-7001 484 16 model model NOUN ejpam-7001 484 17 . . PUNCT ejpam-7001 485 1 complexity complexity NOUN ejpam-7001 485 2 , , PUNCT ejpam-7001 485 3 2023(1):2196572 2023(1):2196572 NOUN ejpam-7001 485 4 , , PUNCT ejpam-7001 485 5 2023 2023 NUM ejpam-7001 485 6 . . PUNCT ejpam-7001 486 1 [ [ X ejpam-7001 486 2 34 34 NUM ejpam-7001 486 3 ] ] SYM ejpam-7001 486 4 caner caner NOUN ejpam-7001 486 5 tanış. tanış. ADV ejpam-7001 486 6 cubic cubic ADJ ejpam-7001 486 7 ranked rank VERB ejpam-7001 486 8 record record NOUN ejpam-7001 486 9 based base VERB ejpam-7001 486 10 transmuted transmuted ADJ ejpam-7001 486 11 family family NOUN ejpam-7001 486 12 of of ADP ejpam-7001 486 13 distributions distribution NOUN ejpam-7001 486 14 : : PUNCT ejpam-7001 486 15 applications application NOUN ejpam-7001 486 16 and and CCONJ ejpam-7001 486 17 properties property NOUN ejpam-7001 486 18 . . PUNCT ejpam-7001 487 1 communications communication NOUN ejpam-7001 487 2 in in ADP ejpam-7001 487 3 statistics statistic NOUN ejpam-7001 487 4 - - PUNCT ejpam-7001 487 5 theory theory NOUN ejpam-7001 487 6 and and CCONJ ejpam-7001 487 7 methods method NOUN ejpam-7001 487 8 , , PUNCT ejpam-7001 487 9 pages page NOUN ejpam-7001 487 10 1–21 1–21 PROPN ejpam-7001 487 11 , , PUNCT ejpam-7001 487 12 2025 2025 NUM ejpam-7001 487 13 . . PUNCT ejpam-7001 488 1 [ [ X ejpam-7001 488 2 35 35 NUM ejpam-7001 488 3 ] ] X ejpam-7001 488 4 ce ce PROPN ejpam-7001 488 5 shannon shannon PROPN ejpam-7001 488 6 . . PUNCT ejpam-7001 489 1 a a DET ejpam-7001 489 2 mathematical mathematical ADJ ejpam-7001 489 3 theory theory NOUN ejpam-7001 489 4 of of ADP ejpam-7001 489 5 communication communication NOUN ejpam-7001 489 6 . . PUNCT ejpam-7001 490 1 the the DET ejpam-7001 490 2 bell bell PROPN ejpam-7001 490 3 systems systems PROPN ejpam-7001 490 4 technical technical PROPN ejpam-7001 490 5 journal journal NOUN ejpam-7001 490 6 , , PUNCT ejpam-7001 490 7 27 27 NUM ejpam-7001 490 8 : : PUNCT ejpam-7001 490 9 july july PROPN ejpam-7001 490 10 379–423 379–423 NUM ejpam-7001 490 11 , , PUNCT ejpam-7001 490 12 1948 1948 NUM ejpam-7001 490 13 . . PUNCT ejpam-7001 491 1 [ [ X ejpam-7001 491 2 36 36 NUM ejpam-7001 491 3 ] ] X ejpam-7001 491 4 m m VERB ejpam-7001 491 5 sanei sanei ADJ ejpam-7001 491 6 tabass tabass NOUN ejpam-7001 491 7 , , PUNCT ejpam-7001 491 8 gr gr PRON ejpam-7001 491 9 mohtashami mohtashami NOUN ejpam-7001 491 10 borzadaran borzadaran NOUN ejpam-7001 491 11 , , PUNCT ejpam-7001 491 12 and and CCONJ ejpam-7001 491 13 mohammad mohammad PROPN ejpam-7001 491 14 amini amini PROPN ejpam-7001 491 15 . . PROPN ejpam-7001 491 16 renyi renyi PROPN ejpam-7001 491 17 entropy entropy PROPN ejpam-7001 491 18 in in ADP ejpam-7001 491 19 continuous continuous ADJ ejpam-7001 491 20 case case NOUN ejpam-7001 491 21 is be AUX ejpam-7001 491 22 not not PART ejpam-7001 491 23 the the DET ejpam-7001 491 24 limit limit NOUN ejpam-7001 491 25 of of ADP ejpam-7001 491 26 discrete discrete ADJ ejpam-7001 491 27 case case NOUN ejpam-7001 491 28 . . PUNCT ejpam-7001 492 1 mathematical mathematical ADJ ejpam-7001 492 2 sciences science NOUN ejpam-7001 492 3 and and CCONJ ejpam-7001 492 4 applications application NOUN ejpam-7001 492 5 e e NOUN ejpam-7001 492 6 - - NOUN ejpam-7001 492 7 notes note NOUN ejpam-7001 492 8 , , PUNCT ejpam-7001 492 9 4(1):113–117 4(1):113–117 NUM ejpam-7001 492 10 , , PUNCT ejpam-7001 492 11 2016 2016 NUM ejpam-7001 492 12 . . PUNCT ejpam-7001 493 1 [ [ X ejpam-7001 493 2 37 37 NUM ejpam-7001 493 3 ] ] X ejpam-7001 493 4 herbert herbert PROPN ejpam-7001 493 5 a a PRON ejpam-7001 493 6 david david PROPN ejpam-7001 493 7 and and CCONJ ejpam-7001 493 8 haikady haikady PROPN ejpam-7001 493 9 n n PROPN ejpam-7001 493 10 nagaraja nagaraja PROPN ejpam-7001 493 11 . . PUNCT ejpam-7001 494 1 order order NOUN ejpam-7001 494 2 statistics statistic NOUN ejpam-7001 494 3 . . PUNCT ejpam-7001 495 1 john john PROPN ejpam-7001 495 2 wiley wiley PROPN ejpam-7001 495 3 & & CCONJ ejpam-7001 495 4 sons son NOUN ejpam-7001 495 5 , , PUNCT ejpam-7001 495 6 2004 2004 NUM ejpam-7001 495 7 . . PUNCT ejpam-7001 496 1 [ [ X ejpam-7001 496 2 38 38 NUM ejpam-7001 496 3 ] ] X ejpam-7001 496 4 bradley bradley PROPN ejpam-7001 496 5 efron efron PROPN ejpam-7001 496 6 . . PUNCT ejpam-7001 497 1 logistic logistic ADJ ejpam-7001 497 2 regression regression NOUN ejpam-7001 497 3 , , PUNCT ejpam-7001 497 4 survival survival NOUN ejpam-7001 497 5 analysis analysis NOUN ejpam-7001 497 6 , , PUNCT ejpam-7001 497 7 and and CCONJ ejpam-7001 497 8 the the DET ejpam-7001 497 9 kaplan kaplan PROPN ejpam-7001 497 10 - - PUNCT ejpam-7001 497 11 meier meier PROPN ejpam-7001 497 12 curve curve NOUN ejpam-7001 497 13 . . PUNCT ejpam-7001 498 1 journal journal NOUN ejpam-7001 498 2 of of ADP ejpam-7001 498 3 the the DET ejpam-7001 498 4 american american PROPN ejpam-7001 498 5 statistical statistical PROPN ejpam-7001 498 6 association association PROPN ejpam-7001 498 7 , , PUNCT ejpam-7001 498 8 83(402):414–425 83(402):414–425 PROPN ejpam-7001 498 9 , , PUNCT ejpam-7001 498 10 1988 1988 NUM ejpam-7001 498 11 . . PUNCT