id sid tid token lemma pos cana-6220 1 1 communications communication NOUN cana-6220 1 2 on on ADP cana-6220 1 3 applied apply VERB cana-6220 1 4 nonlinear nonlinear ADJ cana-6220 1 5 analysis analysis NOUN cana-6220 1 6 issn issn NOUN cana-6220 1 7 : : PUNCT cana-6220 1 8 1074 1074 NUM cana-6220 1 9 - - PUNCT cana-6220 1 10 133x 133x NUM cana-6220 1 11 vol vol VERB cana-6220 1 12 32 32 NUM cana-6220 1 13 no no NOUN cana-6220 1 14 . . PUNCT cana-6220 2 1 10s 10 NOUN cana-6220 2 2 ( ( PUNCT cana-6220 2 3 2025 2025 NUM cana-6220 2 4 ) ) PUNCT cana-6220 2 5 3545 3545 NUM cana-6220 2 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 2 7 classical classical ADJ cana-6220 2 8 and and CCONJ cana-6220 2 9 bayesian bayesian NOUN cana-6220 2 10 estimation estimation NOUN cana-6220 2 11 for for ADP cana-6220 2 12 a a DET cana-6220 2 13 new new ADJ cana-6220 2 14 long long ADJ cana-6220 2 15 tailed tail VERB cana-6220 2 16 distribution distribution NOUN cana-6220 2 17 : : PUNCT cana-6220 2 18 modi modi PROPN cana-6220 2 19 - - PUNCT cana-6220 2 20 lomax lomax PROPN cana-6220 2 21 distribution distribution NOUN cana-6220 2 22 surinder surinder PROPN cana-6220 2 23 kumar1 kumar1 PROPN cana-6220 2 24 , , PUNCT cana-6220 2 25 rahul rahul PROPN cana-6220 2 26 shukla1 shukla1 PROPN cana-6220 2 27 , , PUNCT cana-6220 2 28 * * PUNCT cana-6220 2 29 , , PUNCT cana-6220 2 30 bhupendra bhupendra NOUN cana-6220 2 31 meena1 meena1 NOUN cana-6220 3 1 1babasaheb 1babasaheb X cana-6220 3 2 bhimrao bhimrao PROPN cana-6220 3 3 ambedkar ambedkar PROPN cana-6220 3 4 university university PROPN cana-6220 3 5 , , PUNCT cana-6220 3 6 vidya vidya PROPN cana-6220 3 7 vihar vihar PROPN cana-6220 3 8 , , PUNCT cana-6220 3 9 raebareli raebareli PROPN cana-6220 3 10 road road NOUN cana-6220 3 11 , , PUNCT cana-6220 3 12 lucknow lucknow PROPN cana-6220 3 13 – – PUNCT cana-6220 3 14 226025 226025 NUM cana-6220 3 15 , , PUNCT cana-6220 3 16 india india PROPN cana-6220 3 17 email email NOUN cana-6220 3 18 : : PUNCT cana-6220 3 19 surinderntls@gmail.com1 surinderntls@gmail.com1 PROPN cana-6220 3 20 , , PUNCT cana-6220 3 21 rahul.shukla.stats@gmail.com1 rahul.shukla.stats@gmail.com1 NOUN cana-6220 3 22 , , PUNCT cana-6220 3 23 * * PUNCT cana-6220 3 24 ( ( PUNCT cana-6220 3 25 corresponding corresponding ADJ cana-6220 3 26 author author NOUN cana-6220 3 27 ) ) PUNCT cana-6220 3 28 , , PUNCT cana-6220 3 29 bhupendrakm57@gmail.com1 bhupendrakm57@gmail.com1 PROPN cana-6220 3 30 article article NOUN cana-6220 3 31 history history NOUN cana-6220 3 32 : : PUNCT cana-6220 3 33 received receive VERB cana-6220 3 34 : : PUNCT cana-6220 3 35 19 19 NUM cana-6220 3 36 - - PUNCT cana-6220 3 37 09 09 NUM cana-6220 3 38 - - PUNCT cana-6220 3 39 2024 2024 NUM cana-6220 3 40 revised revise VERB cana-6220 3 41 : : PUNCT cana-6220 3 42 24 24 NUM cana-6220 3 43 - - SYM cana-6220 3 44 10 10 NUM cana-6220 3 45 - - PUNCT cana-6220 3 46 2024 2024 NUM cana-6220 3 47 accepted accept VERB cana-6220 3 48 : : PUNCT cana-6220 3 49 11 11 NUM cana-6220 3 50 - - SYM cana-6220 3 51 11 11 NUM cana-6220 3 52 - - PUNCT cana-6220 3 53 2025 2025 NUM cana-6220 3 54 abstract abstract NOUN cana-6220 3 55 : : PUNCT cana-6220 3 56 this this DET cana-6220 3 57 paper paper NOUN cana-6220 3 58 presents present VERB cana-6220 3 59 the the DET cana-6220 3 60 new new ADJ cana-6220 3 61 modi modi PROPN cana-6220 3 62 - - PUNCT cana-6220 3 63 lomax lomax PROPN cana-6220 3 64 distribution distribution NOUN cana-6220 3 65 ( ( PUNCT cana-6220 3 66 mold mold NOUN cana-6220 3 67 ) ) PUNCT cana-6220 3 68 , , PUNCT cana-6220 3 69 a a DET cana-6220 3 70 three three NUM cana-6220 3 71 - - PUNCT cana-6220 3 72 parameter parameter NOUN cana-6220 3 73 distribution distribution NOUN cana-6220 3 74 obtained obtain VERB cana-6220 3 75 by by ADP cana-6220 3 76 using use VERB cana-6220 3 77 the the DET cana-6220 3 78 modi modi PROPN cana-6220 3 79 family family PROPN cana-6220 3 80 generator generator NOUN cana-6220 3 81 to to PART cana-6220 3 82 include include VERB cana-6220 3 83 one one NUM cana-6220 3 84 extra extra ADJ cana-6220 3 85 shape shape NOUN cana-6220 3 86 parameter parameter NOUN cana-6220 3 87 in in ADP cana-6220 3 88 the the DET cana-6220 3 89 standard standard ADJ cana-6220 3 90 two two NUM cana-6220 3 91 - - PUNCT cana-6220 3 92 parameter parameter NOUN cana-6220 3 93 lomax lomax PROPN cana-6220 3 94 distribution distribution NOUN cana-6220 3 95 . . PUNCT cana-6220 4 1 we we PRON cana-6220 4 2 establish establish VERB cana-6220 4 3 extensive extensive ADJ cana-6220 4 4 statistical statistical ADJ cana-6220 4 5 properties property NOUN cana-6220 4 6 such such ADJ cana-6220 4 7 as as ADP cana-6220 4 8 survival survival NOUN cana-6220 4 9 function function NOUN cana-6220 4 10 , , PUNCT cana-6220 4 11 hazard hazard NOUN cana-6220 4 12 rate rate NOUN cana-6220 4 13 function function NOUN cana-6220 4 14 , , PUNCT cana-6220 4 15 moment moment NOUN cana-6220 4 16 generating generate VERB cana-6220 4 17 function function NOUN cana-6220 4 18 , , PUNCT cana-6220 4 19 quantile quantile ADJ cana-6220 4 20 function function NOUN cana-6220 4 21 with with ADP cana-6220 4 22 quartile quartile ADJ cana-6220 4 23 representations representation NOUN cana-6220 4 24 , , PUNCT cana-6220 4 25 mean mean VERB cana-6220 4 26 residual residual ADJ cana-6220 4 27 lifetime lifetime NOUN cana-6220 4 28 , , PUNCT cana-6220 4 29 order order NOUN cana-6220 4 30 statistics statistic NOUN cana-6220 4 31 , , PUNCT cana-6220 4 32 and and CCONJ cana-6220 4 33 stress stress NOUN cana-6220 4 34 - - PUNCT cana-6220 4 35 strength strength NOUN cana-6220 4 36 reliability reliability NOUN cana-6220 4 37 . . PUNCT cana-6220 5 1 for for ADP cana-6220 5 2 parameter parameter NOUN cana-6220 5 3 estimation estimation NOUN cana-6220 5 4 , , PUNCT cana-6220 5 5 we we PRON cana-6220 5 6 use use VERB cana-6220 5 7 maximum maximum ADJ cana-6220 5 8 likelihood likelihood NOUN cana-6220 5 9 estimation estimation NOUN cana-6220 5 10 and and CCONJ cana-6220 5 11 bayesian bayesian NOUN cana-6220 5 12 methods method NOUN cana-6220 5 13 with with ADP cana-6220 5 14 gamma gamma NOUN cana-6220 5 15 priors prior NOUN cana-6220 5 16 under under ADP cana-6220 5 17 squared square VERB cana-6220 5 18 error error NOUN cana-6220 5 19 loss loss NOUN cana-6220 5 20 functions function NOUN cana-6220 5 21 , , PUNCT cana-6220 5 22 comparing compare VERB cana-6220 5 23 their their PRON cana-6220 5 24 performances performance NOUN cana-6220 5 25 based base VERB cana-6220 5 26 on on ADP cana-6220 5 27 bias bias NOUN cana-6220 5 28 and and CCONJ cana-6220 5 29 mean mean ADJ cana-6220 5 30 square square ADJ cana-6220 5 31 error error NOUN cana-6220 5 32 criteria criterion NOUN cana-6220 5 33 . . PUNCT cana-6220 6 1 the the DET cana-6220 6 2 practical practical ADJ cana-6220 6 3 usefulness usefulness NOUN cana-6220 6 4 of of ADP cana-6220 6 5 mold mold NOUN cana-6220 6 6 is be AUX cana-6220 6 7 shown show VERB cana-6220 6 8 through through ADP cana-6220 6 9 the the DET cana-6220 6 10 analysis analysis NOUN cana-6220 6 11 of of ADP cana-6220 6 12 one one NUM cana-6220 6 13 real real ADJ cana-6220 6 14 data datum NOUN cana-6220 6 15 set set VERB cana-6220 6 16 of of ADP cana-6220 6 17 bladder bladder NOUN cana-6220 6 18 cancer cancer NOUN cana-6220 6 19 patients patient NOUN cana-6220 6 20 and and CCONJ cana-6220 6 21 a a DET cana-6220 6 22 comparative comparative ADJ cana-6220 6 23 analysis analysis NOUN cana-6220 6 24 with with ADP cana-6220 6 25 a a DET cana-6220 6 26 number number NOUN cana-6220 6 27 of of ADP cana-6220 6 28 alternative alternative ADJ cana-6220 6 29 distributions distribution NOUN cana-6220 6 30 . . PUNCT cana-6220 7 1 results result NOUN cana-6220 7 2 validate validate VERB cana-6220 7 3 the the DET cana-6220 7 4 superior superior ADJ cana-6220 7 5 flexibility flexibility NOUN cana-6220 7 6 and and CCONJ cana-6220 7 7 goodness goodness NOUN cana-6220 7 8 - - PUNCT cana-6220 7 9 of of ADP cana-6220 7 10 - - PUNCT cana-6220 7 11 fit fit NOUN cana-6220 7 12 of of ADP cana-6220 7 13 the the DET cana-6220 7 14 suggested suggest VERB cana-6220 7 15 distribution distribution NOUN cana-6220 7 16 under under ADP cana-6220 7 17 different different ADJ cana-6220 7 18 test test NOUN cana-6220 7 19 criteria criterion NOUN cana-6220 7 20 , , PUNCT cana-6220 7 21 emphasizing emphasize VERB cana-6220 7 22 its its PRON cana-6220 7 23 flexibility flexibility NOUN cana-6220 7 24 to to PART cana-6220 7 25 model model VERB cana-6220 7 26 data datum NOUN cana-6220 7 27 with with ADP cana-6220 7 28 diverse diverse ADJ cana-6220 7 29 failure failure NOUN cana-6220 7 30 rate rate NOUN cana-6220 7 31 shapes shape NOUN cana-6220 7 32 and and CCONJ cana-6220 7 33 aging age VERB cana-6220 7 34 behaviours behaviour NOUN cana-6220 7 35 . . PUNCT cana-6220 8 1 this this DET cana-6220 8 2 paper paper NOUN cana-6220 8 3 makes make VERB cana-6220 8 4 mold mold NOUN cana-6220 8 5 a a DET cana-6220 8 6 great great ADJ cana-6220 8 7 contribution contribution NOUN cana-6220 8 8 to to ADP cana-6220 8 9 lifetime lifetime NOUN cana-6220 8 10 distributions distribution NOUN cana-6220 8 11 with with ADP cana-6220 8 12 prominent prominent ADJ cana-6220 8 13 practice practice NOUN cana-6220 8 14 in in ADP cana-6220 8 15 reliability reliability NOUN cana-6220 8 16 engineering engineering NOUN cana-6220 8 17 and and CCONJ cana-6220 8 18 survival survival NOUN cana-6220 8 19 analysis analysis NOUN cana-6220 8 20 . . PUNCT cana-6220 9 1 keywords keyword NOUN cana-6220 9 2 : : PUNCT cana-6220 9 3 lomax lomax PROPN cana-6220 9 4 distribution distribution NOUN cana-6220 9 5 , , PUNCT cana-6220 9 6 modi modi PROPN cana-6220 9 7 family family PROPN cana-6220 9 8 , , PUNCT cana-6220 9 9 maximum maximum ADJ cana-6220 9 10 likelihood likelihood NOUN cana-6220 9 11 estimation estimation NOUN cana-6220 9 12 , , PUNCT cana-6220 9 13 bayesian bayesian NOUN cana-6220 9 14 estimation estimation NOUN cana-6220 9 15 , , PUNCT cana-6220 9 16 stress stress NOUN cana-6220 9 17 - - PUNCT cana-6220 9 18 strength strength NOUN cana-6220 9 19 model model NOUN cana-6220 9 20 1 1 NUM cana-6220 9 21 . . PUNCT cana-6220 10 1 introduction introduction NOUN cana-6220 10 2 probability probability NOUN cana-6220 10 3 distributions distribution NOUN cana-6220 10 4 serve serve VERB cana-6220 10 5 as as ADP cana-6220 10 6 fundamental fundamental ADJ cana-6220 10 7 tools tool NOUN cana-6220 10 8 in in ADP cana-6220 10 9 statistical statistical ADJ cana-6220 10 10 modelling modelling NOUN cana-6220 10 11 across across ADP cana-6220 10 12 various various ADJ cana-6220 10 13 scientific scientific ADJ cana-6220 10 14 fields field NOUN cana-6220 10 15 . . PUNCT cana-6220 11 1 with with ADP cana-6220 11 2 the the DET cana-6220 11 3 growing grow VERB cana-6220 11 4 complexity complexity NOUN cana-6220 11 5 of of ADP cana-6220 11 6 observed observed ADJ cana-6220 11 7 phenomena phenomenon NOUN cana-6220 11 8 , , PUNCT cana-6220 11 9 statistical statistical ADJ cana-6220 11 10 research research NOUN cana-6220 11 11 has have AUX cana-6220 11 12 increasingly increasingly ADV cana-6220 11 13 focused focus VERB cana-6220 11 14 on on ADP cana-6220 11 15 developing develop VERB cana-6220 11 16 more more ADV cana-6220 11 17 adaptable adaptable ADJ cana-6220 11 18 distributions distribution NOUN cana-6220 11 19 through through ADP cana-6220 11 20 mathematical mathematical ADJ cana-6220 11 21 transformations transformation NOUN cana-6220 11 22 , , PUNCT cana-6220 11 23 weighting weight VERB cana-6220 11 24 schemes scheme NOUN cana-6220 11 25 , , PUNCT cana-6220 11 26 and and CCONJ cana-6220 11 27 mixture mixture NOUN cana-6220 11 28 techniques technique NOUN cana-6220 11 29 . . PUNCT cana-6220 12 1 in in ADP cana-6220 12 2 recent recent ADJ cana-6220 12 3 years year NOUN cana-6220 12 4 , , PUNCT cana-6220 12 5 the the DET cana-6220 12 6 generalization generalization NOUN cana-6220 12 7 of of ADP cana-6220 12 8 probability probability NOUN cana-6220 12 9 models model NOUN cana-6220 12 10 has have AUX cana-6220 12 11 become become VERB cana-6220 12 12 particularly particularly ADV cana-6220 12 13 prominent prominent ADJ cana-6220 12 14 , , PUNCT cana-6220 12 15 with with ADP cana-6220 12 16 various various ADJ cana-6220 12 17 approaches approach NOUN cana-6220 12 18 available available ADJ cana-6220 12 19 , , PUNCT cana-6220 12 20 such such ADJ cana-6220 12 21 as as ADP cana-6220 12 22 alpha alpha NOUN cana-6220 12 23 power power NOUN cana-6220 12 24 transformation transformation NOUN cana-6220 12 25 ( ( PUNCT cana-6220 12 26 apt apt ADJ cana-6220 12 27 ) ) PUNCT cana-6220 12 28 , , PUNCT cana-6220 12 29 exponentiation exponentiation NOUN cana-6220 12 30 , , PUNCT cana-6220 12 31 mixture mixture NOUN cana-6220 12 32 and and CCONJ cana-6220 12 33 weighted weight VERB cana-6220 12 34 techniques technique NOUN cana-6220 12 35 , , PUNCT cana-6220 12 36 power power NOUN cana-6220 12 37 transformations transformation NOUN cana-6220 12 38 , , PUNCT cana-6220 12 39 among among ADP cana-6220 12 40 others other NOUN cana-6220 12 41 . . PUNCT cana-6220 13 1 the the DET cana-6220 13 2 lomax lomax PROPN cana-6220 13 3 distribution distribution NOUN cana-6220 13 4 , , PUNCT cana-6220 13 5 or or CCONJ cana-6220 13 6 lomax lomax PROPN cana-6220 13 7 - - PUNCT cana-6220 13 8 pareto pareto VERB cana-6220 13 9 type type NOUN cana-6220 13 10 ii ii NOUN cana-6220 13 11 distribution distribution NOUN cana-6220 13 12 , , PUNCT cana-6220 13 13 has have AUX cana-6220 13 14 found find VERB cana-6220 13 15 its its PRON cana-6220 13 16 place place NOUN cana-6220 13 17 as as ADP cana-6220 13 18 a a DET cana-6220 13 19 useful useful ADJ cana-6220 13 20 statistical statistical ADJ cana-6220 13 21 model model NOUN cana-6220 13 22 in in ADP cana-6220 13 23 reliability reliability NOUN cana-6220 13 24 studies study NOUN cana-6220 13 25 and and CCONJ cana-6220 13 26 as as ADV cana-6220 13 27 well well ADV cana-6220 13 28 as as ADP cana-6220 13 29 distribution distribution NOUN cana-6220 13 30 theory theory NOUN cana-6220 13 31 . . PUNCT cana-6220 14 1 the the DET cana-6220 14 2 distribution distribution NOUN cana-6220 14 3 gained gain VERB cana-6220 14 4 popularity popularity NOUN cana-6220 14 5 because because SCONJ cana-6220 14 6 it it PRON cana-6220 14 7 is be AUX cana-6220 14 8 easily easily ADV cana-6220 14 9 flexible flexible ADJ cana-6220 14 10 in in ADP cana-6220 14 11 representing represent VERB cana-6220 14 12 and and CCONJ cana-6220 14 13 modelling model VERB cana-6220 14 14 heavy heavy ADJ cana-6220 14 15 - - PUNCT cana-6220 14 16 tailed tail VERB cana-6220 14 17 behaviours behaviour NOUN cana-6220 14 18 in in ADP cana-6220 14 19 various various ADJ cana-6220 14 20 fields field NOUN cana-6220 14 21 of of ADP cana-6220 14 22 mathematics mathematic NOUN cana-6220 15 1 [ [ X cana-6220 15 2 ( ( PUNCT cana-6220 15 3 harris harris PROPN cana-6220 15 4 , , PUNCT cana-6220 15 5 1968 1968 NUM cana-6220 15 6 ) ) PUNCT cana-6220 15 7 ; ; PUNCT cana-6220 15 8 ( ( PUNCT cana-6220 15 9 bryson bryson PROPN cana-6220 15 10 , , PUNCT cana-6220 15 11 1974 1974 NUM cana-6220 15 12 ) ) PUNCT cana-6220 15 13 ] ] PUNCT cana-6220 15 14 . . PUNCT cana-6220 16 1 initial initial ADJ cana-6220 16 2 theoretical theoretical ADJ cana-6220 16 3 contributions contribution NOUN cana-6220 16 4 by by ADP cana-6220 16 5 ( ( PUNCT cana-6220 16 6 balkema balkema X cana-6220 16 7 & & CCONJ cana-6220 16 8 de de X cana-6220 16 9 haan haan PROPN cana-6220 16 10 , , PUNCT cana-6220 16 11 1974 1974 NUM cana-6220 16 12 ) ) PUNCT cana-6220 16 13 laid lay VERB cana-6220 16 14 the the DET cana-6220 16 15 foundation foundation NOUN cana-6220 16 16 of of ADP cana-6220 16 17 the the DET cana-6220 16 18 lomax lomax PROPN cana-6220 16 19 distribution distribution NOUN cana-6220 16 20 's 's PART cana-6220 16 21 application application NOUN cana-6220 16 22 in in ADP cana-6220 16 23 reliability reliability NOUN cana-6220 16 24 modelling modelling NOUN cana-6220 16 25 and and CCONJ cana-6220 16 26 life life NOUN cana-6220 16 27 testing testing NOUN cana-6220 16 28 . . PUNCT cana-6220 17 1 ( ( PUNCT cana-6220 17 2 arnold arnold PROPN cana-6220 17 3 , , PUNCT cana-6220 17 4 1983 1983 NUM cana-6220 17 5 ) ) PUNCT cana-6220 17 6 further far ADV cana-6220 17 7 developed develop VERB cana-6220 17 8 a a DET cana-6220 17 9 detailed detailed ADJ cana-6220 17 10 framework framework NOUN cana-6220 17 11 that that PRON cana-6220 17 12 linked link VERB cana-6220 17 13 the the DET cana-6220 17 14 lomax lomax PROPN cana-6220 17 15 distribution distribution NOUN cana-6220 17 16 to to ADP cana-6220 17 17 the the DET cana-6220 17 18 rest rest NOUN cana-6220 17 19 of of ADP cana-6220 17 20 the the DET cana-6220 17 21 pareto pareto ADJ cana-6220 17 22 family family NOUN cana-6220 17 23 . . PUNCT cana-6220 18 1 ( ( PUNCT cana-6220 18 2 johnson johnson PROPN cana-6220 18 3 et et PROPN cana-6220 18 4 al al PROPN cana-6220 18 5 . . PROPN cana-6220 18 6 , , PUNCT cana-6220 18 7 1994 1994 NUM cana-6220 18 8 ) ) PUNCT cana-6220 18 9 continued continue VERB cana-6220 18 10 from from ADP cana-6220 18 11 such such ADJ cana-6220 18 12 foundations foundation NOUN cana-6220 18 13 , , PUNCT cana-6220 18 14 providing provide VERB cana-6220 18 15 elaborate elaborate ADJ cana-6220 18 16 details detail NOUN cana-6220 18 17 about about ADP cana-6220 18 18 the the DET cana-6220 18 19 properties property NOUN cana-6220 18 20 and and CCONJ cana-6220 18 21 features feature NOUN cana-6220 18 22 of of ADP cana-6220 18 23 the the DET cana-6220 18 24 distribution distribution NOUN cana-6220 18 25 that that PRON cana-6220 18 26 cemented cement VERB cana-6220 18 27 its its PRON cana-6220 18 28 place place NOUN cana-6220 18 29 in in ADP cana-6220 18 30 statistical statistical ADJ cana-6220 18 31 literature literature NOUN cana-6220 18 32 . . PUNCT cana-6220 19 1 mailto:surinderntls@gmail.com mailto:surinderntls@gmail.com PROPN cana-6220 19 2 mailto mailto PROPN cana-6220 19 3 : : PUNCT cana-6220 19 4 rahul.shukla.stats@gmail.com1 rahul.shukla.stats@gmail.com1 NOUN cana-6220 19 5 mailto:bhupendrakm57@gmail.com mailto:bhupendrakm57@gmail.com PROPN cana-6220 19 6 communications communication NOUN cana-6220 19 7 on on ADP cana-6220 19 8 applied apply VERB cana-6220 19 9 nonlinear nonlinear ADJ cana-6220 19 10 analysis analysis NOUN cana-6220 19 11 issn issn NOUN cana-6220 19 12 : : PUNCT cana-6220 19 13 1074 1074 NUM cana-6220 19 14 - - PUNCT cana-6220 19 15 133x 133x NUM cana-6220 19 16 vol vol VERB cana-6220 19 17 32 32 NUM cana-6220 19 18 no no NOUN cana-6220 19 19 . . PUNCT cana-6220 20 1 10s 10 NOUN cana-6220 20 2 ( ( PUNCT cana-6220 20 3 2025 2025 NUM cana-6220 20 4 ) ) PUNCT cana-6220 20 5 3546 3546 NUM cana-6220 20 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 20 7 the the DET cana-6220 20 8 statistical statistical ADJ cana-6220 20 9 properties property NOUN cana-6220 20 10 of of ADP cana-6220 20 11 lomax lomax PROPN cana-6220 20 12 distribution distribution NOUN cana-6220 20 13 have have AUX cana-6220 20 14 been be AUX cana-6220 20 15 well well ADV cana-6220 20 16 explored explore VERB cana-6220 20 17 . . PUNCT cana-6220 21 1 ( ( PUNCT cana-6220 21 2 ahsanullah ahsanullah NOUN cana-6220 21 3 , , PUNCT cana-6220 21 4 1991 1991 NUM cana-6220 21 5 ) ) PUNCT cana-6220 21 6 made make VERB cana-6220 21 7 noteworthy noteworthy ADJ cana-6220 21 8 contributions contribution NOUN cana-6220 21 9 by by ADP cana-6220 21 10 studying study VERB cana-6220 21 11 record record NOUN cana-6220 21 12 values value NOUN cana-6220 21 13 that that PRON cana-6220 21 14 came come VERB cana-6220 21 15 from from ADP cana-6220 21 16 lomax lomax NOUN cana-6220 21 17 - - PUNCT cana-6220 21 18 distributed distribute VERB cana-6220 21 19 variables variable NOUN cana-6220 21 20 . . PUNCT cana-6220 22 1 ( ( PUNCT cana-6220 22 2 balakrishnan balakrishnan PROPN cana-6220 22 3 & & CCONJ cana-6220 22 4 ahsanullah ahsanullah PROPN cana-6220 22 5 , , PUNCT cana-6220 22 6 1994 1994 NUM cana-6220 22 7 ) ) PUNCT cana-6220 22 8 derived derive VERB cana-6220 22 9 significant significant ADJ cana-6220 22 10 recurrence recurrence NOUN cana-6220 22 11 relations relation NOUN cana-6220 22 12 among among ADP cana-6220 22 13 moments moment NOUN cana-6220 22 14 of of ADP cana-6220 22 15 record record NOUN cana-6220 22 16 values value NOUN cana-6220 22 17 from from ADP cana-6220 22 18 the the DET cana-6220 22 19 lomax lomax PROPN cana-6220 22 20 distribution distribution NOUN cana-6220 22 21 . . PUNCT cana-6220 23 1 ( ( PUNCT cana-6220 23 2 atkinson atkinson PROPN cana-6220 23 3 & & CCONJ cana-6220 23 4 harrison harrison PROPN cana-6220 23 5 , , PUNCT cana-6220 23 6 1978 1978 NUM cana-6220 23 7 ) ) PUNCT cana-6220 23 8 illustrated illustrate VERB cana-6220 23 9 the the DET cana-6220 23 10 lomax lomax PROPN cana-6220 23 11 distribution distribution NOUN cana-6220 23 12 's 's PART cana-6220 23 13 suitability suitability NOUN cana-6220 23 14 in in ADP cana-6220 23 15 modelling model VERB cana-6220 23 16 income income NOUN cana-6220 23 17 and and CCONJ cana-6220 23 18 wealth wealth NOUN cana-6220 23 19 data datum NOUN cana-6220 23 20 . . PUNCT cana-6220 24 1 ( ( PUNCT cana-6220 24 2 tadikamalla tadikamalla NOUN cana-6220 24 3 , , PUNCT cana-6220 24 4 1980 1980 NUM cana-6220 24 5 ) ) PUNCT cana-6220 24 6 formulated formulate VERB cana-6220 24 7 significant significant ADJ cana-6220 24 8 relationships relationship NOUN cana-6220 24 9 among among ADP cana-6220 24 10 the the DET cana-6220 24 11 lomax lomax PROPN cana-6220 24 12 and and CCONJ cana-6220 24 13 burr burr PROPN cana-6220 24 14 family family NOUN cana-6220 24 15 of of ADP cana-6220 24 16 distributions distribution NOUN cana-6220 24 17 . . PUNCT cana-6220 25 1 the the DET cana-6220 25 2 failure failure NOUN cana-6220 25 3 rate rate NOUN cana-6220 25 4 characteristics characteristic NOUN cana-6220 25 5 of of ADP cana-6220 25 6 lomax lomax PROPN cana-6220 25 7 model model NOUN cana-6220 25 8 were be AUX cana-6220 25 9 also also ADV cana-6220 25 10 comprehensively comprehensively ADV cana-6220 25 11 studied study VERB cana-6220 25 12 by by ADP cana-6220 25 13 ( ( PUNCT cana-6220 25 14 chahkandi chahkandi PROPN cana-6220 25 15 et et PROPN cana-6220 25 16 al al PROPN cana-6220 25 17 . . PROPN cana-6220 25 18 , , PUNCT cana-6220 25 19 2009 2009 NUM cana-6220 25 20 ) ) PUNCT cana-6220 25 21 , , PUNCT cana-6220 25 22 who who PRON cana-6220 25 23 identified identify VERB cana-6220 25 24 that that SCONJ cana-6220 25 25 it it PRON cana-6220 25 26 comes come VERB cana-6220 25 27 under under ADP cana-6220 25 28 the the DET cana-6220 25 29 class class NOUN cana-6220 25 30 of of ADP cana-6220 25 31 decreasing decrease VERB cana-6220 25 32 failure failure NOUN cana-6220 25 33 rate rate NOUN cana-6220 25 34 distributions distribution NOUN cana-6220 25 35 . . PUNCT cana-6220 26 1 the the DET cana-6220 26 2 literature literature NOUN cana-6220 26 3 has have AUX cana-6220 26 4 seen see VERB cana-6220 26 5 significant significant ADJ cana-6220 26 6 development development NOUN cana-6220 26 7 in in ADP cana-6220 26 8 extensions extension NOUN cana-6220 26 9 of of ADP cana-6220 26 10 the the DET cana-6220 26 11 standard standard ADJ cana-6220 26 12 lomax lomax PROPN cana-6220 26 13 distribution distribution NOUN cana-6220 26 14 . . PUNCT cana-6220 27 1 ( ( PUNCT cana-6220 27 2 ashour ashour PROPN cana-6220 27 3 & & CCONJ cana-6220 27 4 eltehiwy eltehiwy PROPN cana-6220 27 5 , , PUNCT cana-6220 27 6 2013 2013 NUM cana-6220 27 7 ) ) PUNCT cana-6220 27 8 presented present VERB cana-6220 27 9 transmuted transmute VERB cana-6220 27 10 exponential exponential ADJ cana-6220 27 11 lomax lomax NOUN cana-6220 27 12 ( ( PUNCT cana-6220 27 13 tel tel PROPN cana-6220 27 14 ) ) PUNCT cana-6220 27 15 model model NOUN cana-6220 27 16 . . PUNCT cana-6220 28 1 ( ( PUNCT cana-6220 28 2 rady rady PROPN cana-6220 28 3 et et PROPN cana-6220 28 4 al al PROPN cana-6220 28 5 . . PROPN cana-6220 28 6 , , PUNCT cana-6220 28 7 2016 2016 NUM cana-6220 28 8 ) ) PUNCT cana-6220 28 9 used use VERB cana-6220 28 10 the the DET cana-6220 28 11 power power NOUN cana-6220 28 12 transformation transformation NOUN cana-6220 28 13 on on ADP cana-6220 28 14 lomax lomax PROPN cana-6220 28 15 distribution distribution NOUN cana-6220 28 16 ( ( PUNCT cana-6220 28 17 pol pol NOUN cana-6220 28 18 ) ) PUNCT cana-6220 28 19 . . PUNCT cana-6220 29 1 ( ( PUNCT cana-6220 29 2 shabbir shabbir PROPN cana-6220 29 3 et et PROPN cana-6220 29 4 al al PROPN cana-6220 29 5 . . PROPN cana-6220 29 6 , , PUNCT cana-6220 29 7 2018 2018 NUM cana-6220 29 8 ) ) PUNCT cana-6220 29 9 contributed contribute VERB cana-6220 29 10 to to ADP cana-6220 29 11 lomax lomax PROPN cana-6220 29 12 family family PROPN cana-6220 29 13 by by ADP cana-6220 29 14 creating create VERB cana-6220 29 15 rayleigh rayleigh PROPN cana-6220 29 16 lomax lomax PROPN cana-6220 29 17 distribution distribution NOUN cana-6220 29 18 ( ( PUNCT cana-6220 29 19 ral ral ADJ cana-6220 29 20 ) ) PUNCT cana-6220 29 21 . . PUNCT cana-6220 30 1 ( ( PUNCT cana-6220 30 2 joshi joshi PROPN cana-6220 30 3 & & CCONJ cana-6220 30 4 kumar kumar PROPN cana-6220 30 5 , , PUNCT cana-6220 30 6 2021 2021 NUM cana-6220 30 7 ) ) PUNCT cana-6220 30 8 came come VERB cana-6220 30 9 up up ADP cana-6220 30 10 with with ADP cana-6220 30 11 the the DET cana-6220 30 12 poisson poisson NOUN cana-6220 30 13 inverted invert VERB cana-6220 30 14 lomax lomax PROPN cana-6220 30 15 ( ( PUNCT cana-6220 30 16 poil poil NOUN cana-6220 30 17 ) ) PUNCT cana-6220 30 18 distribution distribution NOUN cana-6220 30 19 . . PUNCT cana-6220 31 1 another another DET cana-6220 31 2 four four NUM cana-6220 31 3 - - PUNCT cana-6220 31 4 parameter parameter NOUN cana-6220 31 5 distribution distribution NOUN cana-6220 31 6 is be AUX cana-6220 31 7 exponentiated exponentiate VERB cana-6220 31 8 odd odd ADJ cana-6220 31 9 lomax lomax PROPN cana-6220 31 10 , , PUNCT cana-6220 31 11 developed develop VERB cana-6220 31 12 by by ADP cana-6220 31 13 ( ( PUNCT cana-6220 31 14 dhungana dhungana PROPN cana-6220 31 15 & & CCONJ cana-6220 31 16 kumar kumar PROPN cana-6220 31 17 , , PUNCT cana-6220 31 18 2022 2022 NUM cana-6220 31 19 ) ) PUNCT cana-6220 31 20 . . PUNCT cana-6220 32 1 there there PRON cana-6220 32 2 is be VERB cana-6220 32 3 another another DET cana-6220 32 4 four four NUM cana-6220 32 5 - - PUNCT cana-6220 32 6 parameter parameter NOUN cana-6220 32 7 distribution distribution NOUN cana-6220 32 8 competitive competitive ADJ cana-6220 32 9 to to ADP cana-6220 32 10 our our PRON cana-6220 32 11 study study NOUN cana-6220 32 12 is be AUX cana-6220 32 13 power power NOUN cana-6220 32 14 xlindley xlindley PROPN cana-6220 32 15 ( ( PUNCT cana-6220 32 16 pxlin pxlin PROPN cana-6220 32 17 ) ) PUNCT cana-6220 32 18 by by ADP cana-6220 32 19 ( ( PUNCT cana-6220 32 20 elgarhy elgarhy PROPN cana-6220 32 21 et et PROPN cana-6220 32 22 al al PROPN cana-6220 32 23 . . PROPN cana-6220 32 24 , , PUNCT cana-6220 32 25 2025 2025 NUM cana-6220 32 26 ) ) PUNCT cana-6220 32 27 some some PRON cana-6220 32 28 of of ADP cana-6220 32 29 the the DET cana-6220 32 30 recent recent ADJ cana-6220 32 31 contributions contribution NOUN cana-6220 32 32 to to ADP cana-6220 32 33 the the DET cana-6220 32 34 lomax lomax PROPN cana-6220 32 35 family family NOUN cana-6220 32 36 is be AUX cana-6220 32 37 log log NOUN cana-6220 32 38 - - PUNCT cana-6220 32 39 lomax lomax PROPN cana-6220 32 40 ( ( PUNCT cana-6220 32 41 lol lol PROPN cana-6220 32 42 ) ) PUNCT cana-6220 32 43 by by ADP cana-6220 32 44 ( ( PUNCT cana-6220 32 45 ishaq ishaq PROPN cana-6220 32 46 et et PROPN cana-6220 32 47 al al PROPN cana-6220 32 48 . . PROPN cana-6220 32 49 , , PUNCT cana-6220 32 50 2025 2025 NUM cana-6220 32 51 ) ) PUNCT cana-6220 32 52 . . PUNCT cana-6220 33 1 ( ( PUNCT cana-6220 33 2 modi modi PROPN cana-6220 33 3 et et PROPN cana-6220 33 4 al al PROPN cana-6220 33 5 . . PROPN cana-6220 33 6 , , PUNCT cana-6220 33 7 2020 2020 NUM cana-6220 33 8 ) ) PUNCT cana-6220 33 9 introduced introduce VERB cana-6220 33 10 the the DET cana-6220 33 11 modi modi PROPN cana-6220 33 12 family family NOUN cana-6220 33 13 of of ADP cana-6220 33 14 distributions distribution NOUN cana-6220 33 15 , , PUNCT cana-6220 33 16 demonstrating demonstrate VERB cana-6220 33 17 its its PRON cana-6220 33 18 adaptability adaptability NOUN cana-6220 33 19 for for ADP cana-6220 33 20 modelling model VERB cana-6220 33 21 diverse diverse ADJ cana-6220 33 22 phenomena phenomenon NOUN cana-6220 33 23 in in ADP cana-6220 33 24 engineering engineering NOUN cana-6220 33 25 , , PUNCT cana-6220 33 26 economics economic NOUN cana-6220 33 27 , , PUNCT cana-6220 33 28 and and CCONJ cana-6220 33 29 finance finance NOUN cana-6220 33 30 . . PUNCT cana-6220 34 1 subsequent subsequent ADJ cana-6220 34 2 studies study NOUN cana-6220 34 3 have have AUX cana-6220 34 4 expanded expand VERB cana-6220 34 5 this this DET cana-6220 34 6 family family NOUN cana-6220 34 7 ( ( PUNCT cana-6220 34 8 kumawat kumawat VERB cana-6220 34 9 et et PROPN cana-6220 34 10 al al PROPN cana-6220 34 11 . . PROPN cana-6220 34 12 , , PUNCT cana-6220 34 13 2024 2024 NUM cana-6220 34 14 ) ) PUNCT cana-6220 34 15 developed develop VERB cana-6220 34 16 the the DET cana-6220 34 17 modi modi PROPN cana-6220 34 18 - - PUNCT cana-6220 34 19 weibull weibull PROPN cana-6220 34 20 distribution distribution NOUN cana-6220 34 21 , , PUNCT cana-6220 34 22 examining examine VERB cana-6220 34 23 its its PRON cana-6220 34 24 statistical statistical ADJ cana-6220 34 25 properties property NOUN cana-6220 34 26 , , PUNCT cana-6220 34 27 while while SCONJ cana-6220 34 28 ( ( PUNCT cana-6220 34 29 ndayisaba ndayisaba NOUN cana-6220 34 30 et et PROPN cana-6220 34 31 al al PROPN cana-6220 34 32 . . PROPN cana-6220 34 33 , , PUNCT cana-6220 34 34 2023 2023 NUM cana-6220 34 35 ) ) PUNCT cana-6220 34 36 proposed propose VERB cana-6220 34 37 the the DET cana-6220 34 38 modi modi PROPN cana-6220 34 39 exponentiated exponentiate VERB cana-6220 34 40 exponential exponential ADJ cana-6220 34 41 distribution distribution NOUN cana-6220 34 42 , , PUNCT cana-6220 34 43 analysing analyse VERB cana-6220 34 44 its its PRON cana-6220 34 45 mathematical mathematical ADJ cana-6220 34 46 features feature NOUN cana-6220 34 47 and and CCONJ cana-6220 34 48 practical practical ADJ cana-6220 34 49 applications application NOUN cana-6220 34 50 . . PUNCT cana-6220 35 1 in in ADP cana-6220 35 2 a a DET cana-6220 35 3 recent recent ADJ cana-6220 35 4 study study NOUN cana-6220 35 5 , , PUNCT cana-6220 35 6 ( ( PUNCT cana-6220 35 7 kumar kumar PROPN cana-6220 35 8 et et PROPN cana-6220 35 9 al al PROPN cana-6220 35 10 . . PROPN cana-6220 35 11 , , PUNCT cana-6220 35 12 2025 2025 NUM cana-6220 35 13 ) ) PUNCT cana-6220 35 14 proposed propose VERB cana-6220 35 15 a a DET cana-6220 35 16 new new ADJ cana-6220 35 17 modi modi PROPN cana-6220 35 18 - - PUNCT cana-6220 35 19 rayleigh rayleigh PROPN cana-6220 35 20 distribution distribution NOUN cana-6220 35 21 , , PUNCT cana-6220 35 22 demonstrating demonstrate VERB cana-6220 35 23 its its PRON cana-6220 35 24 superior superior ADJ cana-6220 35 25 performance performance NOUN cana-6220 35 26 relative relative ADJ cana-6220 35 27 to to ADP cana-6220 35 28 existing exist VERB cana-6220 35 29 distributions distribution NOUN cana-6220 35 30 generated generate VERB cana-6220 35 31 through through ADP cana-6220 35 32 the the DET cana-6220 35 33 identical identical ADJ cana-6220 35 34 modi modi PROPN cana-6220 35 35 transformation transformation NOUN cana-6220 35 36 approach approach NOUN cana-6220 35 37 . . PUNCT cana-6220 36 1 these these DET cana-6220 36 2 methods method NOUN cana-6220 36 3 enable enable VERB cana-6220 36 4 statisticians statistician NOUN cana-6220 36 5 to to PART cana-6220 36 6 refine refine VERB cana-6220 36 7 existing exist VERB cana-6220 36 8 distributions distribution NOUN cana-6220 36 9 to to PART cana-6220 36 10 better well ADV cana-6220 36 11 represent represent VERB cana-6220 36 12 complex complex ADJ cana-6220 36 13 data datum NOUN cana-6220 36 14 characteristics characteristic NOUN cana-6220 36 15 , , PUNCT cana-6220 36 16 such such ADJ cana-6220 36 17 as as ADP cana-6220 36 18 heavier heavy ADJ cana-6220 36 19 tails tail NOUN cana-6220 36 20 , , PUNCT cana-6220 36 21 greater great ADJ cana-6220 36 22 skewness skewness NOUN cana-6220 36 23 , , PUNCT cana-6220 36 24 or or CCONJ cana-6220 36 25 unique unique ADJ cana-6220 36 26 hazard hazard NOUN cana-6220 36 27 rate rate NOUN cana-6220 36 28 patterns pattern NOUN cana-6220 36 29 , , PUNCT cana-6220 36 30 which which DET cana-6220 36 31 conventional conventional ADJ cana-6220 36 32 distributions distribution NOUN cana-6220 36 33 may may AUX cana-6220 36 34 fail fail VERB cana-6220 36 35 to to PART cana-6220 36 36 capture capture VERB cana-6220 36 37 adequately adequately ADV cana-6220 36 38 . . PUNCT cana-6220 37 1 this this DET cana-6220 37 2 manuscript manuscript NOUN cana-6220 37 3 introduces introduce VERB cana-6220 37 4 the the DET cana-6220 37 5 modi modi PROPN cana-6220 37 6 - - PUNCT cana-6220 37 7 lomax lomax PROPN cana-6220 37 8 distribution distribution NOUN cana-6220 37 9 ( ( PUNCT cana-6220 37 10 mold mold NOUN cana-6220 37 11 ) ) PUNCT cana-6220 37 12 using use VERB cana-6220 37 13 the the DET cana-6220 37 14 modi modi PROPN cana-6220 37 15 - - PUNCT cana-6220 37 16 family family NOUN cana-6220 37 17 generator generator NOUN cana-6220 37 18 method method NOUN cana-6220 37 19 . . PUNCT cana-6220 38 1 our our PRON cana-6220 38 2 primary primary ADJ cana-6220 38 3 motivation motivation NOUN cana-6220 38 4 stems stem VERB cana-6220 38 5 from from ADP cana-6220 38 6 adding add VERB cana-6220 38 7 one one NUM cana-6220 38 8 new new ADJ cana-6220 38 9 shape shape NOUN cana-6220 38 10 parameters parameter NOUN cana-6220 38 11 to to ADP cana-6220 38 12 an an DET cana-6220 38 13 existing exist VERB cana-6220 38 14 longtailed longtaile VERB cana-6220 38 15 distribution distribution NOUN cana-6220 38 16 , , PUNCT cana-6220 38 17 enhancing enhance VERB cana-6220 38 18 its its PRON cana-6220 38 19 ability ability NOUN cana-6220 38 20 to to PART cana-6220 38 21 fit fit VERB cana-6220 38 22 failure failure NOUN cana-6220 38 23 time time NOUN cana-6220 38 24 data datum NOUN cana-6220 38 25 containing contain VERB cana-6220 38 26 extremely extremely ADV cana-6220 38 27 small small ADJ cana-6220 38 28 values value NOUN cana-6220 38 29 . . PUNCT cana-6220 39 1 we we PRON cana-6220 39 2 compare compare VERB cana-6220 39 3 our our PRON cana-6220 39 4 proposed propose VERB cana-6220 39 5 model model NOUN cana-6220 39 6 with with ADP cana-6220 39 7 well well ADV cana-6220 39 8 - - PUNCT cana-6220 39 9 established establish VERB cana-6220 39 10 lifetime lifetime NOUN cana-6220 39 11 distributions distribution NOUN cana-6220 39 12 to to PART cana-6220 39 13 demonstrate demonstrate VERB cana-6220 39 14 its its PRON cana-6220 39 15 flexibility flexibility NOUN cana-6220 39 16 in in ADP cana-6220 39 17 fitting fitting ADJ cana-6220 39 18 real real ADJ cana-6220 39 19 - - PUNCT cana-6220 39 20 world world NOUN cana-6220 39 21 datasets dataset NOUN cana-6220 39 22 . . PUNCT cana-6220 40 1 the the DET cana-6220 40 2 article article NOUN cana-6220 40 3 employs employ VERB cana-6220 40 4 both both CCONJ cana-6220 40 5 classical classical ADJ cana-6220 40 6 and and CCONJ cana-6220 40 7 bayesian bayesian NOUN cana-6220 40 8 estimation estimation NOUN cana-6220 40 9 procedures procedure NOUN cana-6220 40 10 to to PART cana-6220 40 11 estimate estimate VERB cana-6220 40 12 the the DET cana-6220 40 13 parameters parameter NOUN cana-6220 40 14 of of ADP cana-6220 40 15 our our PRON cana-6220 40 16 proposed propose VERB cana-6220 40 17 model model NOUN cana-6220 40 18 . . PUNCT cana-6220 41 1 for for ADP cana-6220 41 2 classical classical ADJ cana-6220 41 3 estimation estimation NOUN cana-6220 41 4 , , PUNCT cana-6220 41 5 we we PRON cana-6220 41 6 utilize utilize VERB cana-6220 41 7 the the DET cana-6220 41 8 maximum maximum ADJ cana-6220 41 9 likelihood likelihood NOUN cana-6220 41 10 method method NOUN cana-6220 41 11 , , PUNCT cana-6220 41 12 while while SCONJ cana-6220 41 13 our our PRON cana-6220 41 14 bayesian bayesian NOUN cana-6220 41 15 approach approach NOUN cana-6220 41 16 incorporates incorporate VERB cana-6220 41 17 gamma gamma NOUN cana-6220 41 18 priors prior NOUN cana-6220 41 19 and and CCONJ cana-6220 41 20 square square ADJ cana-6220 41 21 error error NOUN cana-6220 41 22 loss loss NOUN cana-6220 41 23 function function NOUN cana-6220 41 24 ( ( PUNCT cana-6220 41 25 self self NOUN cana-6220 41 26 ) ) PUNCT cana-6220 41 27 . . PUNCT cana-6220 42 1 the the DET cana-6220 42 2 manuscript manuscript NOUN cana-6220 42 3 is be AUX cana-6220 42 4 organized organize VERB cana-6220 42 5 as as SCONJ cana-6220 42 6 follows follow VERB cana-6220 42 7 : : PUNCT cana-6220 42 8 section section NOUN cana-6220 42 9 2 2 NUM cana-6220 42 10 introduces introduce NOUN cana-6220 42 11 the the DET cana-6220 42 12 modi modi PROPN cana-6220 42 13 - - PUNCT cana-6220 42 14 lomax lomax PROPN cana-6220 42 15 ( ( PUNCT cana-6220 42 16 mold mold NOUN cana-6220 42 17 ) ) PUNCT cana-6220 42 18 distribution distribution NOUN cana-6220 42 19 . . PUNCT cana-6220 43 1 section section NOUN cana-6220 43 2 3 3 NUM cana-6220 43 3 presents present VERB cana-6220 43 4 reliability reliability NOUN cana-6220 43 5 analysis analysis NOUN cana-6220 43 6 of of ADP cana-6220 43 7 mold mold NOUN cana-6220 43 8 . . PUNCT cana-6220 44 1 section section NOUN cana-6220 44 2 4 4 NUM cana-6220 44 3 covers cover VERB cana-6220 44 4 the the DET cana-6220 44 5 statistical statistical ADJ cana-6220 44 6 properties property NOUN cana-6220 44 7 , , PUNCT cana-6220 44 8 moment moment NOUN cana-6220 44 9 generating generating NOUN cana-6220 44 10 function function NOUN cana-6220 44 11 , , PUNCT cana-6220 44 12 quantile quantile ADJ cana-6220 44 13 function function NOUN cana-6220 44 14 and and CCONJ cana-6220 44 15 order order NOUN cana-6220 44 16 statistics statistic NOUN cana-6220 44 17 , , PUNCT cana-6220 44 18 respectively respectively ADV cana-6220 44 19 . . PUNCT cana-6220 45 1 section section NOUN cana-6220 45 2 6 6 NUM cana-6220 45 3 covered cover VERB cana-6220 45 4 the the DET cana-6220 45 5 detailed detailed ADJ cana-6220 45 6 parameter parameter NOUN cana-6220 45 7 estimation estimation NOUN cana-6220 45 8 using use VERB cana-6220 45 9 both both DET cana-6220 45 10 maximum maximum ADJ cana-6220 45 11 likelihood likelihood NOUN cana-6220 45 12 and and CCONJ cana-6220 45 13 bayesian bayesian NOUN cana-6220 45 14 approaches approach NOUN cana-6220 45 15 with with ADP cana-6220 45 16 gamma gamma NOUN cana-6220 45 17 priors prior NOUN cana-6220 45 18 and and CCONJ cana-6220 45 19 self self NOUN cana-6220 45 20 . . PUNCT cana-6220 46 1 section section NOUN cana-6220 46 2 7 7 NUM cana-6220 46 3 presents present NOUN cana-6220 46 4 simulation simulation NOUN cana-6220 46 5 studies study NOUN cana-6220 46 6 , , PUNCT cana-6220 46 7 section section NOUN cana-6220 46 8 8 8 NUM cana-6220 46 9 demonstrates demonstrate VERB cana-6220 46 10 applications application NOUN cana-6220 46 11 to to ADP cana-6220 46 12 real real ADJ cana-6220 46 13 - - PUNCT cana-6220 46 14 world world NOUN cana-6220 46 15 communications communication NOUN cana-6220 46 16 on on ADP cana-6220 46 17 applied apply VERB cana-6220 46 18 nonlinear nonlinear ADJ cana-6220 46 19 analysis analysis NOUN cana-6220 46 20 issn issn NOUN cana-6220 46 21 : : PUNCT cana-6220 46 22 1074 1074 NUM cana-6220 46 23 - - PUNCT cana-6220 46 24 133x 133x NUM cana-6220 46 25 vol vol VERB cana-6220 46 26 32 32 NUM cana-6220 46 27 no no NOUN cana-6220 46 28 . . PUNCT cana-6220 47 1 10s 10 NOUN cana-6220 47 2 ( ( PUNCT cana-6220 47 3 2025 2025 NUM cana-6220 47 4 ) ) PUNCT cana-6220 47 5 3547 3547 NUM cana-6220 47 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 47 7 datasets dataset NOUN cana-6220 47 8 with with ADP cana-6220 47 9 comparative comparative ADJ cana-6220 47 10 analysis analysis NOUN cana-6220 47 11 , , PUNCT cana-6220 47 12 and and CCONJ cana-6220 47 13 section section NOUN cana-6220 47 14 9 9 NUM cana-6220 47 15 concludes conclude VERB cana-6220 47 16 with with ADP cana-6220 47 17 a a DET cana-6220 47 18 summary summary NOUN cana-6220 47 19 of of ADP cana-6220 47 20 findings finding NOUN cana-6220 47 21 . . PUNCT cana-6220 48 1 in in ADP cana-6220 48 2 section section NOUN cana-6220 48 3 10 10 NUM cana-6220 48 4 , , PUNCT cana-6220 48 5 we we PRON cana-6220 48 6 discussed discuss VERB cana-6220 48 7 the the DET cana-6220 48 8 future future ADJ cana-6220 48 9 scope scope NOUN cana-6220 48 10 of of ADP cana-6220 48 11 the the DET cana-6220 48 12 article article NOUN cana-6220 48 13 . . PUNCT cana-6220 49 1 2 2 X cana-6220 49 2 . . X cana-6220 49 3 modi modi PROPN cana-6220 49 4 - - PUNCT cana-6220 49 5 lomax lomax PROPN cana-6220 49 6 distribution distribution NOUN cana-6220 49 7 the the DET cana-6220 49 8 modi modi PROPN cana-6220 49 9 family family PROPN cana-6220 49 10 generator generator PROPN cana-6220 49 11 ( ( PUNCT cana-6220 49 12 modi modi PROPN cana-6220 49 13 et et PROPN cana-6220 49 14 al al PROPN cana-6220 49 15 . . PROPN cana-6220 49 16 , , PUNCT cana-6220 49 17 2020 2020 NUM cana-6220 49 18 ) ) PUNCT cana-6220 49 19 is be AUX cana-6220 49 20 widely widely ADV cana-6220 49 21 employed employ VERB cana-6220 49 22 across across ADP cana-6220 49 23 various various ADJ cana-6220 49 24 fields field NOUN cana-6220 49 25 due due ADP cana-6220 49 26 to to ADP cana-6220 49 27 its its PRON cana-6220 49 28 capacity capacity NOUN cana-6220 49 29 to to PART cana-6220 49 30 introduce introduce VERB cana-6220 49 31 two two NUM cana-6220 49 32 additional additional ADJ cana-6220 49 33 shape shape NOUN cana-6220 49 34 parameters parameter NOUN cana-6220 49 35 into into ADP cana-6220 49 36 existing exist VERB cana-6220 49 37 lifetime lifetime NOUN cana-6220 49 38 models model NOUN cana-6220 49 39 , , PUNCT cana-6220 49 40 thereby thereby ADV cana-6220 49 41 enhancing enhance VERB cana-6220 49 42 their their PRON cana-6220 49 43 flexibility flexibility NOUN cana-6220 49 44 for for ADP cana-6220 49 45 modelling model VERB cana-6220 49 46 real real ADJ cana-6220 49 47 - - PUNCT cana-6220 49 48 world world NOUN cana-6220 49 49 datasets dataset NOUN cana-6220 49 50 . . PUNCT cana-6220 50 1 if if SCONJ cana-6220 50 2 f(t f(t NOUN cana-6220 50 3 ) ) PUNCT cana-6220 50 4 and and CCONJ cana-6220 50 5 f(t f(t NOUN cana-6220 50 6 ) ) PUNCT cana-6220 50 7 represent represent VERB cana-6220 50 8 the the DET cana-6220 50 9 probability probability NOUN cana-6220 50 10 density density NOUN cana-6220 50 11 function function NOUN cana-6220 50 12 ( ( PUNCT cana-6220 50 13 pdf pdf NOUN cana-6220 50 14 ) ) PUNCT cana-6220 50 15 and and CCONJ cana-6220 50 16 cumulative cumulative ADJ cana-6220 50 17 distribution distribution NOUN cana-6220 50 18 function function NOUN cana-6220 50 19 ( ( PUNCT cana-6220 50 20 cdf cdf PROPN cana-6220 50 21 ) ) PUNCT cana-6220 50 22 , , PUNCT cana-6220 50 23 respectively respectively ADV cana-6220 50 24 , , PUNCT cana-6220 50 25 of of ADP cana-6220 50 26 an an DET cana-6220 50 27 existing exist VERB cana-6220 50 28 lifetime lifetime NOUN cana-6220 50 29 distribution distribution NOUN cana-6220 50 30 , , PUNCT cana-6220 50 31 then then ADV cana-6220 50 32 the the DET cana-6220 50 33 pdf pdf NOUN cana-6220 50 34 g g NOUN cana-6220 50 35 ( ( PUNCT cana-6220 50 36 . . PUNCT cana-6220 50 37 ) ) PUNCT cana-6220 50 38 and and CCONJ cana-6220 50 39 cdf cdf PROPN cana-6220 50 40 g g PROPN cana-6220 50 41 ( ( PUNCT cana-6220 50 42 . . PUNCT cana-6220 50 43 ) ) PUNCT cana-6220 50 44 of of ADP cana-6220 50 45 the the DET cana-6220 50 46 new new ADJ cana-6220 50 47 modi modi PROPN cana-6220 50 48 family family NOUN cana-6220 50 49 distribution distribution NOUN cana-6220 50 50 are be AUX cana-6220 50 51 given give VERB cana-6220 50 52 by by ADP cana-6220 50 53 : : PUNCT cana-6220 50 54 𝑔(π‘₯ 𝑔(π‘₯ NUM cana-6220 50 55 ) ) PUNCT cana-6220 51 1 = = SYM cana-6220 51 2 𝛼𝛽(1+𝛼𝛽)𝑓(π‘₯ 𝛼𝛽(1+𝛼𝛽)𝑓(π‘₯ NOUN cana-6220 51 3 ) ) PUNCT cana-6220 51 4 ( ( PUNCT cana-6220 51 5 𝛼𝛽+𝐹(π‘₯ 𝛼𝛽+𝐹(π‘₯ ADV cana-6220 51 6 ) ) PUNCT cana-6220 51 7 ) ) PUNCT cana-6220 51 8 2 2 NUM cana-6220 51 9 ; ; PUNCT cana-6220 51 10 π‘₯ π‘₯ X cana-6220 51 11 > > X cana-6220 51 12 0 0 NUM cana-6220 51 13 , , PUNCT cana-6220 51 14 𝛼 𝛼 X cana-6220 51 15 > > X cana-6220 51 16 0 0 NUM cana-6220 51 17 , , PUNCT cana-6220 51 18 𝛽 𝛽 NOUN cana-6220 51 19 > > X cana-6220 51 20 0 0 PUNCT cana-6220 52 1 ( ( PUNCT cana-6220 52 2 1 1 NUM cana-6220 52 3 ) ) PUNCT cana-6220 52 4 𝐺(π‘₯ 𝐺(π‘₯ NOUN cana-6220 52 5 ) ) PUNCT cana-6220 52 6 = = PUNCT cana-6220 52 7 ( ( PUNCT cana-6220 52 8 1+𝛼𝛽)𝐹(π‘₯ 1+𝛼𝛽)𝐹(π‘₯ NUM cana-6220 52 9 ) ) PUNCT cana-6220 52 10 𝛼𝛽+𝐹(π‘₯ 𝛼𝛽+𝐹(π‘₯ NUM cana-6220 52 11 ) ) PUNCT cana-6220 52 12 ; ; PUNCT cana-6220 53 1 π‘₯ π‘₯ X cana-6220 53 2 > > X cana-6220 53 3 0 0 NUM cana-6220 53 4 , , PUNCT cana-6220 53 5 𝛼 𝛼 X cana-6220 53 6 > > X cana-6220 53 7 0 0 NUM cana-6220 53 8 , , PUNCT cana-6220 53 9 𝛽 𝛽 NOUN cana-6220 53 10 > > X cana-6220 53 11 0 0 PUNCT cana-6220 54 1 ( ( PUNCT cana-6220 54 2 2 2 NUM cana-6220 54 3 ) ) PUNCT cana-6220 54 4 in in ADP cana-6220 54 5 the the DET cana-6220 54 6 modi modi PROPN cana-6220 54 7 family family PROPN cana-6220 54 8 generator generator PROPN cana-6220 54 9 , , PUNCT cana-6220 54 10 there there PRON cana-6220 54 11 are be VERB cana-6220 54 12 two two NUM cana-6220 54 13 shape shape NOUN cana-6220 54 14 parameters parameter NOUN cana-6220 54 15 viz viz PROPN cana-6220 54 16 . . PUNCT cana-6220 55 1 Ξ± Ξ± PROPN cana-6220 55 2 and and CCONJ cana-6220 55 3 Ξ² Ξ² X cana-6220 55 4 . . PUNCT cana-6220 56 1 we we PRON cana-6220 56 2 combine combine VERB cana-6220 56 3 these these DET cana-6220 56 4 two two NUM cana-6220 56 5 shape shape NOUN cana-6220 56 6 parameters parameter NOUN cana-6220 56 7 and and CCONJ cana-6220 56 8 introduce introduce VERB cana-6220 56 9 single single ADJ cana-6220 56 10 shape shape NOUN cana-6220 56 11 parameter parameter NOUN cana-6220 56 12 ΞΎ ΞΎ PROPN cana-6220 57 1 = = SYM cana-6220 57 2 Ξ±Ξ² Ξ±Ξ² INTJ cana-6220 57 3 . . PUNCT cana-6220 58 1 the the DET cana-6220 58 2 motivation motivation NOUN cana-6220 58 3 behind behind ADP cana-6220 58 4 this this DET cana-6220 58 5 substitution substitution NOUN cana-6220 58 6 is be AUX cana-6220 58 7 that that SCONJ cana-6220 58 8 , , PUNCT cana-6220 58 9 we we PRON cana-6220 58 10 want want VERB cana-6220 58 11 to to PART cana-6220 58 12 check check VERB cana-6220 58 13 the the DET cana-6220 58 14 joint joint ADJ cana-6220 58 15 effect effect NOUN cana-6220 58 16 of of ADP cana-6220 58 17 these these DET cana-6220 58 18 two two NUM cana-6220 58 19 - - PUNCT cana-6220 58 20 shape shape NOUN cana-6220 58 21 parameter parameter NOUN cana-6220 58 22 after after ADP cana-6220 58 23 the the DET cana-6220 58 24 fusion fusion NOUN cana-6220 58 25 with with ADP cana-6220 58 26 lomax lomax PROPN cana-6220 58 27 distribution distribution NOUN cana-6220 58 28 . . PUNCT cana-6220 59 1 if if SCONJ cana-6220 59 2 t t PROPN cana-6220 59 3 follows follow VERB cana-6220 59 4 the the DET cana-6220 59 5 lomax lomax PROPN cana-6220 59 6 distribution distribution NOUN cana-6220 59 7 , , PUNCT cana-6220 59 8 so so CCONJ cana-6220 59 9 the the DET cana-6220 59 10 pdf pdf NOUN cana-6220 59 11 and and CCONJ cana-6220 59 12 cdf cdf PROPN cana-6220 59 13 of of ADP cana-6220 59 14 t t PROPN cana-6220 59 15 are be AUX cana-6220 59 16 as as SCONJ cana-6220 59 17 follows follow VERB cana-6220 59 18 : : PUNCT cana-6220 59 19 𝑓(𝑑 𝑓(𝑑 NOUN cana-6220 59 20 , , PUNCT cana-6220 59 21 πœ† πœ† NOUN cana-6220 59 22 , , PUNCT cana-6220 59 23 πœƒ πœƒ NOUN cana-6220 59 24 ) ) PUNCT cana-6220 59 25 = = SYM cana-6220 60 1 πœ† πœ† PRON cana-6220 60 2 πœƒ πœƒ X cana-6220 60 3 ( ( PUNCT cana-6220 60 4 1 1 NUM cana-6220 60 5 + + NUM cana-6220 60 6 𝑑 𝑑 PROPN cana-6220 60 7 πœƒ πœƒ NOUN cana-6220 60 8 ) ) PUNCT cana-6220 60 9 βˆ’(πœ†+1 βˆ’(πœ†+1 PROPN cana-6220 60 10 ) ) PUNCT cana-6220 60 11 ; ; PUNCT cana-6220 60 12 𝑑 𝑑 X cana-6220 60 13 > > X cana-6220 60 14 0 0 PROPN cana-6220 60 15 , , PUNCT cana-6220 60 16 πœ† πœ† ADJ cana-6220 60 17 > > X cana-6220 60 18 0 0 NUM cana-6220 60 19 , , PUNCT cana-6220 60 20 πœƒ πœƒ X cana-6220 60 21 > > X cana-6220 60 22 0 0 PUNCT cana-6220 61 1 ( ( PUNCT cana-6220 61 2 3 3 NUM cana-6220 61 3 ) ) PUNCT cana-6220 61 4 𝐹(𝑑 𝐹(𝑑 NUM cana-6220 61 5 , , PUNCT cana-6220 61 6 πœ† πœ† NOUN cana-6220 61 7 , , PUNCT cana-6220 61 8 πœƒ πœƒ NOUN cana-6220 61 9 ) ) PUNCT cana-6220 62 1 = = SYM cana-6220 62 2 1 1 NUM cana-6220 62 3 βˆ’ βˆ’ NOUN cana-6220 62 4 ( ( PUNCT cana-6220 62 5 1 1 NUM cana-6220 62 6 + + NUM cana-6220 62 7 𝑑 𝑑 PROPN cana-6220 62 8 πœƒ πœƒ NOUN cana-6220 62 9 ) ) PUNCT cana-6220 62 10 βˆ’πœ† βˆ’πœ† PROPN cana-6220 62 11 ; ; PUNCT cana-6220 62 12 𝑑 𝑑 X cana-6220 62 13 > > X cana-6220 62 14 0 0 PROPN cana-6220 62 15 , , PUNCT cana-6220 62 16 πœ† πœ† ADJ cana-6220 62 17 > > X cana-6220 62 18 0 0 NUM cana-6220 62 19 , , PUNCT cana-6220 62 20 πœƒ πœƒ X cana-6220 62 21 > > X cana-6220 62 22 0 0 PUNCT cana-6220 63 1 ( ( PUNCT cana-6220 63 2 4 4 X cana-6220 63 3 ) ) PUNCT cana-6220 63 4 the the DET cana-6220 63 5 mold mold NOUN cana-6220 63 6 is be AUX cana-6220 63 7 created create VERB cana-6220 63 8 from from ADP cana-6220 63 9 the the DET cana-6220 63 10 lomax lomax PROPN cana-6220 63 11 distribution distribution NOUN cana-6220 63 12 by by ADP cana-6220 63 13 putting put VERB cana-6220 63 14 eq eq NOUN cana-6220 63 15 . . PUNCT cana-6220 64 1 ( ( PUNCT cana-6220 64 2 3 3 NUM cana-6220 64 3 ) ) PUNCT cana-6220 64 4 and and CCONJ cana-6220 64 5 eq eq NOUN cana-6220 64 6 . . PUNCT cana-6220 65 1 ( ( PUNCT cana-6220 65 2 4 4 NUM cana-6220 65 3 ) ) PUNCT cana-6220 65 4 , , PUNCT cana-6220 65 5 respectively respectively ADV cana-6220 65 6 , , PUNCT cana-6220 65 7 into into ADP cana-6220 65 8 eq eq NOUN cana-6220 65 9 . . PUNCT cana-6220 66 1 ( ( PUNCT cana-6220 66 2 1 1 NUM cana-6220 66 3 ) ) PUNCT cana-6220 66 4 and and CCONJ cana-6220 66 5 eq eq NOUN cana-6220 66 6 . . PUNCT cana-6220 67 1 ( ( PUNCT cana-6220 67 2 2 2 NUM cana-6220 67 3 ) ) PUNCT cana-6220 67 4 . . PUNCT cana-6220 68 1 as as ADP cana-6220 68 2 a a DET cana-6220 68 3 result result NOUN cana-6220 68 4 , , PUNCT cana-6220 68 5 the the DET cana-6220 68 6 mold mold NOUN cana-6220 68 7 's 's PART cana-6220 68 8 pdf pdf NOUN cana-6220 68 9 is be AUX cana-6220 68 10 ascertained ascertain VERB cana-6220 68 11 as as ADP cana-6220 68 12 𝑔(𝑑 𝑔(𝑑 PROPN cana-6220 68 13 ) ) PUNCT cana-6220 68 14 = = SYM cana-6220 68 15 πœ‰(1+πœ‰)πœ†πœƒβˆ’πœ†(πœƒ+𝑑)βˆ’(πœ†+1 πœ‰(1+πœ‰)πœ†πœƒβˆ’πœ†(πœƒ+𝑑)βˆ’(πœ†+1 NOUN cana-6220 68 16 ) ) PUNCT cana-6220 69 1 [ [ X cana-6220 69 2 ( ( PUNCT cana-6220 69 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 69 4 ] ] X cana-6220 69 5 2 2 NUM cana-6220 69 6 ; ; PUNCT cana-6220 69 7 𝑑 𝑑 X cana-6220 69 8 > > X cana-6220 69 9 0 0 NUM cana-6220 69 10 , , PUNCT cana-6220 69 11 πœ‰ πœ‰ X cana-6220 69 12 > > X cana-6220 69 13 0 0 PROPN cana-6220 69 14 , , PUNCT cana-6220 69 15 πœ† πœ† ADJ cana-6220 69 16 > > X cana-6220 69 17 0 0 NUM cana-6220 69 18 , , PUNCT cana-6220 69 19 πœƒ πœƒ X cana-6220 69 20 > > X cana-6220 69 21 0 0 PUNCT cana-6220 69 22 ( ( PUNCT cana-6220 69 23 5 5 NUM cana-6220 69 24 ) ) PUNCT cana-6220 70 1 the the DET cana-6220 70 2 corresponding correspond VERB cana-6220 70 3 cdf cdf PROPN cana-6220 70 4 of of ADP cana-6220 70 5 mold mold NOUN cana-6220 70 6 is be AUX cana-6220 70 7 given give VERB cana-6220 70 8 as as ADP cana-6220 70 9 𝐺(𝑑 𝐺(𝑑 NOUN cana-6220 70 10 ) ) PUNCT cana-6220 70 11 = = PUNCT cana-6220 71 1 ( ( PUNCT cana-6220 71 2 1+πœ‰)[πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)[πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 71 3 ] ] X cana-6220 72 1 [ [ X cana-6220 72 2 ( ( PUNCT cana-6220 72 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 72 4 ] ] PUNCT cana-6220 72 5 ; ; PUNCT cana-6220 72 6 𝑑 𝑑 X cana-6220 72 7 > > X cana-6220 72 8 0 0 NUM cana-6220 72 9 , , PUNCT cana-6220 72 10 πœ‰ πœ‰ X cana-6220 72 11 > > X cana-6220 72 12 0 0 PROPN cana-6220 72 13 , , PUNCT cana-6220 72 14 πœ† πœ† ADJ cana-6220 72 15 > > X cana-6220 72 16 0 0 NUM cana-6220 72 17 , , PUNCT cana-6220 72 18 πœƒ πœƒ X cana-6220 72 19 > > X cana-6220 72 20 0 0 PUNCT cana-6220 73 1 ( ( PUNCT cana-6220 73 2 6 6 NUM cana-6220 73 3 ) ) PUNCT cana-6220 73 4 communications communication NOUN cana-6220 73 5 on on ADP cana-6220 73 6 applied apply VERB cana-6220 73 7 nonlinear nonlinear ADJ cana-6220 73 8 analysis analysis NOUN cana-6220 73 9 issn issn NOUN cana-6220 73 10 : : PUNCT cana-6220 73 11 1074 1074 NUM cana-6220 73 12 - - PUNCT cana-6220 73 13 133x 133x NUM cana-6220 73 14 vol vol VERB cana-6220 73 15 32 32 NUM cana-6220 73 16 no no NOUN cana-6220 73 17 . . PUNCT cana-6220 74 1 10s 10 NOUN cana-6220 74 2 ( ( PUNCT cana-6220 74 3 2025 2025 NUM cana-6220 74 4 ) ) PUNCT cana-6220 74 5 3548 3548 NUM cana-6220 74 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 74 7 figure figure NOUN cana-6220 74 8 1 1 NUM cana-6220 74 9 . . PUNCT cana-6220 75 1 pdf pdf NOUN cana-6220 75 2 plots plot NOUN cana-6220 75 3 of of ADP cana-6220 75 4 mold mold NOUN cana-6220 75 5 for for ADP cana-6220 75 6 different different ADJ cana-6220 75 7 parametric parametric ADJ cana-6220 75 8 values value NOUN cana-6220 75 9 of of ADP cana-6220 75 10 ΞΎ ΞΎ PROPN cana-6220 75 11 , , PUNCT cana-6220 75 12 Ξ» Ξ» PROPN cana-6220 75 13 and and CCONJ cana-6220 75 14 ΞΈ ΞΈ PROPN cana-6220 75 15 . . PROPN cana-6220 75 16 figure figure NOUN cana-6220 75 17 2 2 NUM cana-6220 75 18 . . X cana-6220 75 19 3d 3d PROPN cana-6220 75 20 pdf pdf NOUN cana-6220 75 21 plots plot NOUN cana-6220 75 22 of of ADP cana-6220 75 23 mold mold NOUN cana-6220 75 24 for for ADP cana-6220 75 25 varying vary VERB cana-6220 75 26 ΞΎ ΞΎ PROPN cana-6220 75 27 , , PUNCT cana-6220 75 28 Ξ» Ξ» PROPN cana-6220 75 29 and and CCONJ cana-6220 75 30 ΞΈ ΞΈ PROPN cana-6220 75 31 values value NOUN cana-6220 75 32 . . PUNCT cana-6220 76 1 3 3 X cana-6220 76 2 . . X cana-6220 76 3 reliability reliability NOUN cana-6220 76 4 characteristics characteristic NOUN cana-6220 76 5 of of ADP cana-6220 76 6 mold mold NOUN cana-6220 76 7 this this DET cana-6220 76 8 section section NOUN cana-6220 76 9 presents present VERB cana-6220 76 10 the the DET cana-6220 76 11 derivation derivation NOUN cana-6220 76 12 of of ADP cana-6220 76 13 essential essential ADJ cana-6220 76 14 reliability reliability NOUN cana-6220 76 15 characteristics characteristic NOUN cana-6220 76 16 for for ADP cana-6220 76 17 the the DET cana-6220 76 18 mold mold NOUN cana-6220 76 19 distribution distribution NOUN cana-6220 76 20 , , PUNCT cana-6220 76 21 specifically specifically ADV cana-6220 76 22 addressing address VERB cana-6220 76 23 survival survival NOUN cana-6220 76 24 function function NOUN cana-6220 76 25 , , PUNCT cana-6220 76 26 hazard hazard NOUN cana-6220 76 27 rate rate NOUN cana-6220 76 28 , , PUNCT cana-6220 76 29 reverse reverse VERB cana-6220 76 30 hazard hazard NOUN cana-6220 76 31 rate rate NOUN cana-6220 76 32 , , PUNCT cana-6220 76 33 cumulative cumulative ADJ cana-6220 76 34 failure failure NOUN cana-6220 76 35 rate rate NOUN cana-6220 76 36 , , PUNCT cana-6220 76 37 and and CCONJ cana-6220 76 38 the the DET cana-6220 76 39 mills mill NOUN cana-6220 76 40 ratio ratio NOUN cana-6220 76 41 . . PUNCT cana-6220 77 1 3.1 3.1 NUM cana-6220 77 2 . . PUNCT cana-6220 77 3 survival survival NOUN cana-6220 77 4 function function VERB cana-6220 77 5 the the DET cana-6220 77 6 survival survival NOUN cana-6220 77 7 function function PROPN cana-6220 77 8 s(t s(t PROPN cana-6220 77 9 ) ) PUNCT cana-6220 77 10 is be AUX cana-6220 77 11 one one NUM cana-6220 77 12 of of ADP cana-6220 77 13 important important ADJ cana-6220 77 14 reliability reliability NOUN cana-6220 77 15 measure measure NOUN cana-6220 77 16 in in ADP cana-6220 77 17 the the DET cana-6220 77 18 reliability reliability NOUN cana-6220 77 19 realm realm NOUN cana-6220 77 20 . . PUNCT cana-6220 78 1 it it PRON cana-6220 78 2 is be AUX cana-6220 78 3 defined define VERB cana-6220 78 4 as as ADP cana-6220 78 5 s(t s(t PROPN cana-6220 78 6 ) ) PUNCT cana-6220 78 7 β€ˆ β€ˆ SPACE cana-6220 79 1 = = SYM cana-6220 79 2 β€ˆ β€ˆ SPACE cana-6220 79 3 1 1 NUM cana-6220 79 4 β€ˆ β€ˆ SPACE cana-6220 79 5 βˆ’ βˆ’ PROPN cana-6220 79 6 β€ˆ β€ˆ SPACE cana-6220 79 7 g(t g(t PROPN cana-6220 79 8 ) ) PUNCT cana-6220 80 1 where where SCONJ cana-6220 80 2 g(t g(t PROPN cana-6220 80 3 ) ) PUNCT cana-6220 80 4 is be AUX cana-6220 80 5 the the DET cana-6220 80 6 cumulative cumulative ADJ cana-6220 80 7 density density NOUN cana-6220 80 8 function function NOUN cana-6220 80 9 . . PUNCT cana-6220 81 1 from from ADP cana-6220 81 2 eq eq ADP cana-6220 81 3 . . PUNCT cana-6220 82 1 ( ( PUNCT cana-6220 82 2 6 6 NUM cana-6220 82 3 ) ) PUNCT cana-6220 82 4 , , PUNCT cana-6220 82 5 we we PRON cana-6220 82 6 get get VERB cana-6220 82 7 the the DET cana-6220 82 8 survival survival NOUN cana-6220 82 9 function function NOUN cana-6220 82 10 for for ADP cana-6220 82 11 mold mold NOUN cana-6220 82 12 as as ADP cana-6220 82 13 following follow VERB cana-6220 82 14 𝑆(𝑑 𝑆(𝑑 NOUN cana-6220 82 15 ) ) PUNCT cana-6220 82 16 = = PUNCT cana-6220 83 1 πœ‰(πœƒ+𝑑)βˆ’πœ† πœ‰(πœƒ+𝑑)βˆ’πœ† ADP cana-6220 83 2 πœƒβˆ’πœ†(1+πœ‰)βˆ’(πœƒ+𝑑)βˆ’πœ† πœƒβˆ’πœ†(1+πœ‰)βˆ’(πœƒ+𝑑)βˆ’πœ† PROPN cana-6220 83 3 ( ( PUNCT cana-6220 83 4 7 7 NUM cana-6220 83 5 ) ) PUNCT cana-6220 83 6 communications communication NOUN cana-6220 83 7 on on ADP cana-6220 83 8 applied apply VERB cana-6220 83 9 nonlinear nonlinear ADJ cana-6220 83 10 analysis analysis NOUN cana-6220 83 11 issn issn NOUN cana-6220 83 12 : : PUNCT cana-6220 83 13 1074 1074 NUM cana-6220 83 14 - - PUNCT cana-6220 83 15 133x 133x NUM cana-6220 83 16 vol vol VERB cana-6220 83 17 32 32 NUM cana-6220 83 18 no no NOUN cana-6220 83 19 . . PUNCT cana-6220 84 1 10s 10 NOUN cana-6220 84 2 ( ( PUNCT cana-6220 84 3 2025 2025 NUM cana-6220 84 4 ) ) PUNCT cana-6220 84 5 3549 3549 NUM cana-6220 84 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 84 7 figure figure NOUN cana-6220 84 8 3 3 NUM cana-6220 84 9 . . PUNCT cana-6220 84 10 survival survival NOUN cana-6220 84 11 function function NOUN cana-6220 84 12 plots plot NOUN cana-6220 84 13 for for ADP cana-6220 84 14 mold mold NOUN cana-6220 84 15 distribution distribution NOUN cana-6220 84 16 . . PUNCT cana-6220 85 1 3.2 3.2 NUM cana-6220 85 2 . . PUNCT cana-6220 85 3 hazard hazard NOUN cana-6220 85 4 rate rate NOUN cana-6220 85 5 and and CCONJ cana-6220 85 6 inverse inverse ADJ cana-6220 85 7 hazard hazard NOUN cana-6220 85 8 rate rate NOUN cana-6220 85 9 function function VERB cana-6220 85 10 the the DET cana-6220 85 11 hazard hazard NOUN cana-6220 85 12 rate rate NOUN cana-6220 85 13 function function NOUN cana-6220 85 14 h(t h(t PROPN cana-6220 85 15 ) ) PUNCT cana-6220 85 16 β€ˆ β€ˆ SPACE cana-6220 85 17 = = SYM cana-6220 85 18 β€ˆ β€ˆ SPACE cana-6220 85 19 g(t g(t PROPN cana-6220 85 20 ) ) PUNCT cana-6220 85 21 s(t s(t PROPN cana-6220 85 22 ) ) PUNCT cana-6220 85 23 β€ˆ β€ˆ SPACE cana-6220 85 24 and and CCONJ cana-6220 85 25 the the DET cana-6220 85 26 reversed reverse VERB cana-6220 85 27 hazard hazard NOUN cana-6220 85 28 rate rate NOUN cana-6220 85 29 function function NOUN cana-6220 85 30 hβ€²(t hβ€²(t NOUN cana-6220 85 31 ) ) PUNCT cana-6220 85 32 = = SYM cana-6220 85 33 g(t g(t PROPN cana-6220 85 34 ) ) PUNCT cana-6220 85 35 g(t g(t PROPN cana-6220 85 36 ) ) PUNCT cana-6220 85 37 are be AUX cana-6220 85 38 important important ADJ cana-6220 85 39 quantities quantity NOUN cana-6220 85 40 characterizing characterize VERB cana-6220 85 41 life life NOUN cana-6220 85 42 time time NOUN cana-6220 85 43 phenomena phenomena PROPN cana-6220 85 44 . . PUNCT cana-6220 86 1 for for ADP cana-6220 86 2 the the DET cana-6220 86 3 mold mold NOUN cana-6220 86 4 distribution distribution NOUN cana-6220 86 5 , , PUNCT cana-6220 86 6 they they PRON cana-6220 86 7 are be AUX cana-6220 86 8 given give VERB cana-6220 86 9 as as ADP cana-6220 86 10 𝐻(𝑑 𝐻(𝑑 NOUN cana-6220 86 11 ) ) PUNCT cana-6220 86 12 = = SYM cana-6220 86 13 πœ†(1+πœ‰ πœ†(1+πœ‰ NUM cana-6220 86 14 ) ) PUNCT cana-6220 86 15 ( ( PUNCT cana-6220 86 16 πœƒ+𝑑)(1+πœ‰)βˆ’πœƒπœ†(πœƒ+𝑑)1βˆ’πœ† πœƒ+𝑑)(1+πœ‰)βˆ’πœƒπœ†(πœƒ+𝑑)1βˆ’πœ† X cana-6220 86 17 ( ( PUNCT cana-6220 86 18 8) 8) NUM cana-6220 86 19 and and CCONJ cana-6220 86 20 𝐻′(𝑑 𝐻′(𝑑 NOUN cana-6220 86 21 ) ) PUNCT cana-6220 86 22 = = SYM cana-6220 86 23 πœ‰πœ†πœƒβˆ’πœ†(πœƒ+𝑑)βˆ’(πœ†+1 πœ‰πœ†πœƒβˆ’πœ†(πœƒ+𝑑)βˆ’(πœ†+1 X cana-6220 86 24 ) ) PUNCT cana-6220 87 1 [ [ X cana-6220 87 2 ( ( PUNCT cana-6220 87 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ†][πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ†][πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 87 4 ] ] X cana-6220 87 5 ( ( PUNCT cana-6220 87 6 9 9 NUM cana-6220 87 7 ) ) PUNCT cana-6220 87 8 3.3 3.3 NUM cana-6220 87 9 . . PUNCT cana-6220 88 1 cumulative cumulative ADJ cana-6220 88 2 hazard hazard NOUN cana-6220 88 3 rate rate NOUN cana-6220 88 4 the the DET cana-6220 88 5 cumulative cumulative ADJ cana-6220 88 6 hazard hazard NOUN cana-6220 88 7 rate rate NOUN cana-6220 88 8 , , PUNCT cana-6220 88 9 measures measure VERB cana-6220 88 10 the the DET cana-6220 88 11 total total ADJ cana-6220 88 12 risk risk NOUN cana-6220 88 13 that that SCONJ cana-6220 88 14 an an DET cana-6220 88 15 event event NOUN cana-6220 88 16 will will AUX cana-6220 88 17 occur occur VERB cana-6220 88 18 by by ADP cana-6220 88 19 some some DET cana-6220 88 20 specified specify VERB cana-6220 88 21 time time NOUN cana-6220 88 22 . . PUNCT cana-6220 89 1 the the DET cana-6220 89 2 function function NOUN cana-6220 89 3 is be AUX cana-6220 89 4 actually actually ADV cana-6220 89 5 the the DET cana-6220 89 6 integration integration NOUN cana-6220 89 7 of of ADP cana-6220 89 8 the the DET cana-6220 89 9 hazard hazard NOUN cana-6220 89 10 rate rate NOUN cana-6220 89 11 over over ADP cana-6220 89 12 time time NOUN cana-6220 89 13 intervals interval NOUN cana-6220 89 14 , , PUNCT cana-6220 89 15 which which PRON cana-6220 89 16 illustrates illustrate VERB cana-6220 89 17 how how SCONJ cana-6220 89 18 probability probability NOUN cana-6220 89 19 of of ADP cana-6220 89 20 the the DET cana-6220 89 21 event event NOUN cana-6220 89 22 occurrence occurrence NOUN cana-6220 89 23 increases increase VERB cana-6220 89 24 with with ADP cana-6220 89 25 time time NOUN cana-6220 89 26 . . PUNCT cana-6220 90 1 it it PRON cana-6220 90 2 is be AUX cana-6220 90 3 defined define VERB cana-6220 90 4 as as ADP cana-6220 90 5 Ξ΄(𝑑 Ξ΄(𝑑 NOUN cana-6220 90 6 ) ) PUNCT cana-6220 90 7 = = SYM cana-6220 91 1 βˆ’ βˆ’ PROPN cana-6220 91 2 log(𝑆(𝑑 log(𝑆(𝑑 NOUN cana-6220 91 3 ) ) PUNCT cana-6220 91 4 ) ) PUNCT cana-6220 91 5 hence hence ADV cana-6220 91 6 for for ADP cana-6220 91 7 the the DET cana-6220 91 8 mold mold NOUN cana-6220 91 9 , , PUNCT cana-6220 91 10 it it PRON cana-6220 91 11 is be AUX cana-6220 91 12 given give VERB cana-6220 91 13 as as ADP cana-6220 91 14 Ξ΄(𝑑 Ξ΄(𝑑 NOUN cana-6220 91 15 ) ) PUNCT cana-6220 91 16 = = PUNCT cana-6220 92 1 βˆ’ βˆ’ PROPN cana-6220 92 2 log log NOUN cana-6220 92 3 [ [ PUNCT cana-6220 92 4 ΞΎ(ΞΈ ΞΎ(ΞΈ PROPN cana-6220 92 5 + + CCONJ cana-6220 92 6 𝑑)βˆ’Ξ» 𝑑)βˆ’Ξ» PROPN cana-6220 92 7 ΞΈβˆ’Ξ»(1 ΞΈβˆ’Ξ»(1 PROPN cana-6220 92 8 + + CCONJ cana-6220 92 9 ΞΎ ΞΎ NOUN cana-6220 92 10 ) ) PUNCT cana-6220 92 11 βˆ’ βˆ’ PROPN cana-6220 92 12 ( ( PUNCT cana-6220 92 13 ΞΈ ΞΈ PROPN cana-6220 92 14 + + X cana-6220 92 15 𝑑)βˆ’Ξ» 𝑑)βˆ’Ξ» X cana-6220 92 16 ] ] PUNCT cana-6220 92 17 π›₯(𝑑 π›₯(𝑑 NUM cana-6220 92 18 ) ) PUNCT cana-6220 92 19 = = SYM cana-6220 92 20 βˆ’ βˆ’ PROPN cana-6220 92 21 π‘™π‘œπ‘”(πœ‰ π‘™π‘œπ‘”(πœ‰ PROPN cana-6220 92 22 ) ) PUNCT cana-6220 92 23 + + CCONJ cana-6220 92 24 πœ† πœ† PROPN cana-6220 92 25 π‘™π‘œπ‘”(πœƒ π‘™π‘œπ‘”(πœƒ PROPN cana-6220 92 26 + + CCONJ cana-6220 92 27 𝑑 𝑑 NOUN cana-6220 92 28 ) ) PUNCT cana-6220 92 29 + + CCONJ cana-6220 92 30 π‘™π‘œπ‘”[πœƒβˆ’πœ†(1 π‘™π‘œπ‘”[πœƒβˆ’πœ†(1 ADJ cana-6220 92 31 + + NUM cana-6220 92 32 πœ‰ πœ‰ X cana-6220 92 33 ) ) PUNCT cana-6220 92 34 βˆ’ βˆ’ PROPN cana-6220 92 35 ( ( PUNCT cana-6220 92 36 πœƒ πœƒ X cana-6220 92 37 + + PUNCT cana-6220 92 38 𝑑)βˆ’πœ† 𝑑)βˆ’πœ† ADP cana-6220 92 39 ] ] X cana-6220 92 40 ( ( PUNCT cana-6220 92 41 10 10 NUM cana-6220 92 42 ) ) PUNCT cana-6220 92 43 3.4 3.4 NUM cana-6220 92 44 . . PUNCT cana-6220 93 1 mills mill NOUN cana-6220 93 2 ratio ratio VERB cana-6220 93 3 the the DET cana-6220 93 4 mills mill NOUN cana-6220 93 5 ratio ratio NOUN cana-6220 93 6 ( ( PUNCT cana-6220 93 7 m.r m.r PROPN cana-6220 93 8 ) ) PUNCT cana-6220 93 9 for for ADP cana-6220 93 10 the the DET cana-6220 93 11 mold mold NOUN cana-6220 93 12 is be AUX cana-6220 93 13 obtained obtain VERB cana-6220 93 14 as as ADP cana-6220 93 15 m.r m.r PROPN cana-6220 93 16 = = PROPN cana-6220 93 17 𝐺(𝑑 𝐺(𝑑 NOUN cana-6220 93 18 ) ) PUNCT cana-6220 93 19 𝑆(𝑑 𝑆(𝑑 NUM cana-6220 93 20 ) ) PUNCT cana-6220 93 21 m.r m.r NOUN cana-6220 93 22 = = PUNCT cana-6220 93 23 ( ( PUNCT cana-6220 93 24 1 1 NUM cana-6220 93 25 + + NUM cana-6220 93 26 πœ‰ πœ‰ X cana-6220 93 27 ) ) PUNCT cana-6220 94 1 [ [ X cana-6220 94 2 ( ( PUNCT cana-6220 94 3 1 1 NUM cana-6220 94 4 + + NUM cana-6220 94 5 𝑑 𝑑 PROPN cana-6220 94 6 πœƒ πœƒ NOUN cana-6220 94 7 ) ) PUNCT cana-6220 95 1 πœ† πœ† DET cana-6220 95 2 βˆ’ βˆ’ PROPN cana-6220 95 3 1 1 NUM cana-6220 95 4 ] ] X cana-6220 95 5 ( ( PUNCT cana-6220 95 6 11 11 NUM cana-6220 95 7 ) ) PUNCT cana-6220 95 8 communications communication NOUN cana-6220 95 9 on on ADP cana-6220 95 10 applied apply VERB cana-6220 95 11 nonlinear nonlinear ADJ cana-6220 95 12 analysis analysis NOUN cana-6220 95 13 issn issn NOUN cana-6220 95 14 : : PUNCT cana-6220 95 15 1074 1074 NUM cana-6220 95 16 - - PUNCT cana-6220 95 17 133x 133x NUM cana-6220 95 18 vol vol VERB cana-6220 95 19 32 32 NUM cana-6220 95 20 no no NOUN cana-6220 95 21 . . PUNCT cana-6220 96 1 10s 10 NOUN cana-6220 96 2 ( ( PUNCT cana-6220 96 3 2025 2025 NUM cana-6220 96 4 ) ) PUNCT cana-6220 96 5 3550 3550 NUM cana-6220 96 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 96 7 figure figure NOUN cana-6220 96 8 4 4 NUM cana-6220 96 9 . . PUNCT cana-6220 96 10 hazard hazard NOUN cana-6220 96 11 function function NOUN cana-6220 96 12 plots plot NOUN cana-6220 96 13 for for ADP cana-6220 96 14 mold mold NOUN cana-6220 96 15 distribution distribution NOUN cana-6220 96 16 3.5 3.5 NUM cana-6220 96 17 . . PUNCT cana-6220 97 1 cumulative cumulative ADJ cana-6220 97 2 hazard hazard NOUN cana-6220 97 3 rate rate NOUN cana-6220 97 4 the the DET cana-6220 97 5 mean mean ADJ cana-6220 97 6 residual residual ADJ cana-6220 97 7 lifetime lifetime NOUN cana-6220 97 8 ( ( PUNCT cana-6220 97 9 mrl mrl PROPN cana-6220 97 10 ) ) PUNCT cana-6220 97 11 represents represent VERB cana-6220 97 12 the the DET cana-6220 97 13 expected expect VERB cana-6220 97 14 remaining remain VERB cana-6220 97 15 lifespan lifespan NOUN cana-6220 97 16 of of ADP cana-6220 97 17 a a DET cana-6220 97 18 subject subject NOUN cana-6220 97 19 given give VERB cana-6220 97 20 that that SCONJ cana-6220 97 21 it it PRON cana-6220 97 22 has have AUX cana-6220 97 23 survived survive VERB cana-6220 97 24 to to ADP cana-6220 97 25 a a DET cana-6220 97 26 particular particular ADJ cana-6220 97 27 time time NOUN cana-6220 97 28 point point NOUN cana-6220 97 29 . . PUNCT cana-6220 98 1 this this DET cana-6220 98 2 measure measure NOUN cana-6220 98 3 provides provide VERB cana-6220 98 4 valuable valuable ADJ cana-6220 98 5 insight insight NOUN cana-6220 98 6 into into ADP cana-6220 98 7 the the DET cana-6220 98 8 conditional conditional ADJ cana-6220 98 9 life life NOUN cana-6220 98 10 expectancy expectancy NOUN cana-6220 98 11 and and CCONJ cana-6220 98 12 is be AUX cana-6220 98 13 particularly particularly ADV cana-6220 98 14 useful useful ADJ cana-6220 98 15 for for ADP cana-6220 98 16 understanding understand VERB cana-6220 98 17 survival survival NOUN cana-6220 98 18 patterns pattern NOUN cana-6220 98 19 in in ADP cana-6220 98 20 different different ADJ cana-6220 98 21 phases phase NOUN cana-6220 98 22 of of ADP cana-6220 98 23 the the DET cana-6220 98 24 study study NOUN cana-6220 98 25 period period NOUN cana-6220 98 26 . . PUNCT cana-6220 99 1 mrl mrl NOUN cana-6220 99 2 = = PUNCT cana-6220 99 3 e[(π‘₯ e[(π‘₯ PROPN cana-6220 99 4 βˆ’ βˆ’ NOUN cana-6220 99 5 𝑑)|π‘₯ 𝑑)|π‘₯ NOUN cana-6220 99 6 > > X cana-6220 99 7 𝑑 𝑑 X cana-6220 99 8 ] ] PUNCT cana-6220 99 9 = = SYM cana-6220 99 10 ∫ ∫ PROPN cana-6220 99 11 ( ( PUNCT cana-6220 99 12 π‘₯ π‘₯ NOUN cana-6220 99 13 βˆ’ βˆ’ PROPN cana-6220 99 14 𝑑)𝑓(π‘₯)𝑑π‘₯ 𝑑)𝑓(π‘₯)𝑑π‘₯ PROPN cana-6220 99 15 ∞ ∞ NUM cana-6220 99 16 𝑑 𝑑 PROPN cana-6220 99 17 𝑆(𝑑 𝑆(𝑑 NOUN cana-6220 99 18 ) ) PUNCT cana-6220 99 19 for for ADP cana-6220 99 20 the the DET cana-6220 99 21 mold mold NOUN cana-6220 99 22 , , PUNCT cana-6220 99 23 mrl mrl PROPN cana-6220 99 24 is be AUX cana-6220 99 25 derived derive VERB cana-6220 99 26 as as ADP cana-6220 99 27 mrl mrl PROPN cana-6220 99 28 = = PUNCT cana-6220 99 29 ( ( PUNCT cana-6220 99 30 ΞΈ ΞΈ PROPN cana-6220 99 31 + + CCONJ cana-6220 99 32 𝑑 𝑑 NOUN cana-6220 99 33 ) ) PUNCT cana-6220 99 34 Ξ» Ξ» NOUN cana-6220 99 35 βˆ’ βˆ’ NOUN cana-6220 99 36 1 1 NUM cana-6220 99 37 ; ; PUNCT cana-6220 99 38 Ξ» Ξ» X cana-6220 99 39 > > X cana-6220 99 40 1 1 NUM cana-6220 99 41 this this PRON cana-6220 99 42 shows show VERB cana-6220 99 43 that that SCONJ cana-6220 99 44 the the DET cana-6220 99 45 mrl mrl PROPN cana-6220 99 46 for for ADP cana-6220 99 47 the the DET cana-6220 99 48 mold mold NOUN cana-6220 99 49 increases increase VERB cana-6220 99 50 linearly linearly ADV cana-6220 99 51 with with ADP cana-6220 99 52 t t PROPN cana-6220 99 53 , , PUNCT cana-6220 99 54 with with ADP cana-6220 99 55 the the DET cana-6220 99 56 rate rate NOUN cana-6220 99 57 determined determine VERB cana-6220 99 58 by by ADP cana-6220 99 59 the the DET cana-6220 99 60 parameter parameter PROPN cana-6220 99 61 Ξ» Ξ» PROPN cana-6220 99 62 . . PUNCT cana-6220 100 1 this this PRON cana-6220 100 2 is be AUX cana-6220 100 3 a a DET cana-6220 100 4 characteristic characteristic NOUN cana-6220 100 5 of of ADP cana-6220 100 6 distributions distribution NOUN cana-6220 100 7 with with ADP cana-6220 100 8 the the DET cana-6220 100 9 lack lack NOUN cana-6220 100 10 of of ADP cana-6220 100 11 memory memory NOUN cana-6220 100 12 property property NOUN cana-6220 100 13 similar similar ADJ cana-6220 100 14 to to ADP cana-6220 100 15 the the DET cana-6220 100 16 exponential exponential ADJ cana-6220 100 17 distribution distribution NOUN cana-6220 100 18 , , PUNCT cana-6220 100 19 but but CCONJ cana-6220 100 20 with with ADP cana-6220 100 21 a a DET cana-6220 100 22 different different ADJ cana-6220 100 23 structure structure NOUN cana-6220 100 24 . . PUNCT cana-6220 101 1 4 4 X cana-6220 101 2 . . X cana-6220 101 3 statistical statistical ADJ cana-6220 101 4 properties property NOUN cana-6220 101 5 of of ADP cana-6220 101 6 mold mold NOUN cana-6220 101 7 4.1 4.1 NUM cana-6220 101 8 . . PUNCT cana-6220 102 1 moment moment NOUN cana-6220 102 2 generating generate VERB cana-6220 102 3 function function NOUN cana-6220 102 4 theorem theorem VERB cana-6220 102 5 1 1 NUM cana-6220 102 6 . . PUNCT cana-6220 103 1 if if SCONJ cana-6220 103 2 x x PRON cana-6220 103 3 is be AUX cana-6220 103 4 the the DET cana-6220 103 5 mold mold NOUN cana-6220 103 6 variable variable NOUN cana-6220 103 7 having have VERB cana-6220 103 8 pdf pdf NOUN cana-6220 103 9 given give VERB cana-6220 103 10 in in ADP cana-6220 103 11 eq eq ADP cana-6220 103 12 . . PUNCT cana-6220 104 1 ( ( PUNCT cana-6220 104 2 5 5 NUM cana-6220 104 3 ) ) PUNCT cana-6220 104 4 , , PUNCT cana-6220 104 5 then then ADV cana-6220 104 6 its its PRON cana-6220 104 7 moment moment NOUN cana-6220 104 8 generating generate VERB cana-6220 104 9 function function NOUN cana-6220 104 10 𝑀π‘₯(𝑠 𝑀π‘₯(𝑠 NOUN cana-6220 104 11 ) ) PUNCT cana-6220 104 12 is be AUX cana-6220 104 13 given give VERB cana-6220 104 14 by by ADP cana-6220 104 15 𝑀π‘₯(𝑠 𝑀π‘₯(𝑠 NOUN cana-6220 104 16 ) ) PUNCT cana-6220 104 17 = = SYM cana-6220 105 1 πœ‰(1 πœ‰(1 PROPN cana-6220 105 2 + + NUM cana-6220 105 3 πœ‰)πœ†πœƒβˆ’πœ†π‘’βˆ’π‘ πœƒ πœ‰)πœ†πœƒβˆ’πœ†π‘’βˆ’π‘ πœƒ PROPN cana-6220 105 4 ∫ ∫ PROPN cana-6220 105 5 π‘’π‘ π‘’π‘’βˆ’(πœ†+1 π‘’π‘ π‘’π‘’βˆ’(πœ†+1 PROPN cana-6220 105 6 ) ) PUNCT cana-6220 106 1 [ [ X cana-6220 106 2 ( ( PUNCT cana-6220 106 3 1+πœ‰)πœƒβˆ’πœ†βˆ’π‘’βˆ’πœ†]2 1+πœ‰)πœƒβˆ’πœ†βˆ’π‘’βˆ’πœ†]2 NUM cana-6220 106 4 𝑑𝑒 𝑑𝑒 NOUN cana-6220 106 5 ∞ ∞ PROPN cana-6220 106 6 πœƒ πœƒ PROPN cana-6220 106 7 ( ( PUNCT cana-6220 106 8 12 12 NUM cana-6220 106 9 ) ) PUNCT cana-6220 106 10 proof proof NOUN cana-6220 106 11 . . PUNCT cana-6220 107 1 the the DET cana-6220 107 2 mgf mgf PROPN cana-6220 107 3 of of ADP cana-6220 107 4 mold mold NOUN cana-6220 107 5 is be AUX cana-6220 107 6 obtained obtain VERB cana-6220 107 7 from from ADP cana-6220 107 8 𝑀π‘₯(𝑠 𝑀π‘₯(𝑠 NOUN cana-6220 107 9 ) ) PUNCT cana-6220 107 10 = = SYM cana-6220 107 11 𝐸[𝑒𝑠π‘₯ 𝐸[𝑒𝑠π‘₯ NOUN cana-6220 107 12 ] ] X cana-6220 107 13 = = SYM cana-6220 107 14 ∫ ∫ PROPN cana-6220 107 15 𝑒𝑠𝑑 𝑒𝑠𝑑 NOUN cana-6220 107 16 ∞ ∞ PROPN cana-6220 107 17 0 0 NUM cana-6220 107 18 𝑔(𝑑)𝑑𝑑 𝑔(𝑑)𝑑𝑑 ADJ cana-6220 107 19 if if SCONJ cana-6220 107 20 we we PRON cana-6220 107 21 define define VERB cana-6220 107 22 l[g(t)](s)as l[g(t)](s)as ADP cana-6220 107 23 the the DET cana-6220 107 24 laplace laplace NOUN cana-6220 107 25 transformation transformation NOUN cana-6220 107 26 of of ADP cana-6220 107 27 g(t g(t PROPN cana-6220 107 28 ) ) PUNCT cana-6220 107 29 , , PUNCT cana-6220 107 30 then then ADV cana-6220 107 31 𝑀π‘₯(𝑠 𝑀π‘₯(𝑠 NOUN cana-6220 107 32 ) ) PUNCT cana-6220 107 33 = = SYM cana-6220 107 34 𝐿[𝑔(𝑑)](βˆ’π‘  𝐿[𝑔(𝑑)](βˆ’π‘  NOUN cana-6220 107 35 ) ) PUNCT cana-6220 107 36 communications communication NOUN cana-6220 107 37 on on ADP cana-6220 107 38 applied apply VERB cana-6220 107 39 nonlinear nonlinear ADJ cana-6220 107 40 analysis analysis NOUN cana-6220 107 41 issn issn NOUN cana-6220 107 42 : : PUNCT cana-6220 107 43 1074 1074 NUM cana-6220 107 44 - - PUNCT cana-6220 107 45 133x 133x NUM cana-6220 107 46 vol vol VERB cana-6220 107 47 32 32 NUM cana-6220 107 48 no no NOUN cana-6220 107 49 . . PUNCT cana-6220 107 50 10s 10 NOUN cana-6220 107 51 ( ( PUNCT cana-6220 107 52 2025 2025 NUM cana-6220 107 53 ) ) PUNCT cana-6220 107 54 3551 3551 NUM cana-6220 107 55 https://internationalpubls.com https://internationalpubls.com X cana-6220 107 56 where where SCONJ cana-6220 107 57 𝐿[𝑔(𝑑)](𝑠 𝐿[𝑔(𝑑)](𝑠 ADP cana-6220 107 58 ) ) PUNCT cana-6220 108 1 = = SYM cana-6220 108 2 ∫ ∫ PROPN cana-6220 109 1 π‘’βˆ’π‘ π‘‘βˆž π‘’βˆ’π‘ π‘‘βˆž X cana-6220 109 2 0 0 NUM cana-6220 109 3 𝑔(𝑑)𝑑𝑑 𝑔(𝑑)𝑑𝑑 NOUN cana-6220 109 4 hence hence ADV cana-6220 109 5 , , PUNCT cana-6220 109 6 we we PRON cana-6220 109 7 get get VERB cana-6220 109 8 𝑀π‘₯(𝑠 𝑀π‘₯(𝑠 NOUN cana-6220 109 9 ) ) PUNCT cana-6220 109 10 = = SYM cana-6220 110 1 ΞΎ(1 ΞΎ(1 PROPN cana-6220 110 2 + + PUNCT cana-6220 110 3 ΞΎ)Ξ»ΞΈβˆ’Ξ»π‘’βˆ’π‘ ΞΈ ΞΎ)Ξ»ΞΈβˆ’Ξ»π‘’βˆ’π‘ ΞΈ ADP cana-6220 110 4 ∫ ∫ PROPN cana-6220 110 5 π‘’π‘ π‘’π‘’βˆ’(πœ†+1 π‘’π‘ π‘’π‘’βˆ’(πœ†+1 PROPN cana-6220 110 6 ) ) PUNCT cana-6220 111 1 [ [ X cana-6220 111 2 ( ( PUNCT cana-6220 111 3 1 1 NUM cana-6220 111 4 + + NUM cana-6220 111 5 πœ‰)πœƒβˆ’πœ† πœ‰)πœƒβˆ’πœ† NOUN cana-6220 111 6 βˆ’ βˆ’ PROPN cana-6220 111 7 π‘’βˆ’πœ†]2 π‘’βˆ’πœ†]2 NOUN cana-6220 111 8 𝑑𝑒 𝑑𝑒 PROPN cana-6220 111 9 ∞ ∞ PROPN cana-6220 111 10 πœƒ πœƒ PROPN cana-6220 111 11 theorem theorem VERB cana-6220 111 12 2 2 NUM cana-6220 111 13 . . PUNCT cana-6220 112 1 the the DET cana-6220 112 2 rth rth PROPN cana-6220 112 3 moment moment NOUN cana-6220 112 4 about about ADP cana-6220 112 5 origin origin NOUN cana-6220 112 6 of of ADP cana-6220 112 7 mold mold NOUN cana-6220 112 8 is be AUX cana-6220 112 9 defined define VERB cana-6220 112 10 as as ADP cana-6220 112 11 ΞΌπ‘Ÿ ΞΌπ‘Ÿ ADP cana-6220 112 12 β€² β€² NUM cana-6220 112 13 = = SYM cana-6220 112 14 𝐸(π‘‘π‘Ÿ 𝐸(π‘‘π‘Ÿ PROPN cana-6220 112 15 ) ) PUNCT cana-6220 113 1 = = SYM cana-6220 113 2 ΞΈπ‘Ÿ+Ξ» ΞΈπ‘Ÿ+Ξ» NOUN cana-6220 113 3 Ξ» Ξ» INTJ cana-6220 113 4 βˆ‘ βˆ‘ PUNCT cana-6220 113 5 ( ( PUNCT cana-6220 113 6 π‘Ÿ π‘Ÿ PRON cana-6220 113 7 π‘˜ π‘˜ NOUN cana-6220 113 8 ) ) PUNCT cana-6220 113 9 ( ( PUNCT cana-6220 113 10 βˆ’1)π‘˜b βˆ’1)π‘˜b PROPN cana-6220 113 11 ( ( PUNCT cana-6220 113 12 1 1 NUM cana-6220 113 13 βˆ’ βˆ’ PROPN cana-6220 113 14 ( ( PUNCT cana-6220 113 15 π‘Ÿ π‘Ÿ NOUN cana-6220 113 16 βˆ’ βˆ’ X cana-6220 113 17 π‘˜ π‘˜ X cana-6220 113 18 ) ) PUNCT cana-6220 113 19 Ξ» Ξ» NOUN cana-6220 113 20 + + NOUN cana-6220 113 21 1,1 1,1 NUM cana-6220 113 22 ) ) PUNCT cana-6220 113 23 ( ( PUNCT cana-6220 113 24 1 1 NUM cana-6220 113 25 + + CCONJ cana-6220 113 26 ΞΎ)1βˆ’(π‘Ÿβˆ’π‘˜)/Ξ»βˆ’2 ΞΎ)1βˆ’(π‘Ÿβˆ’π‘˜)/Ξ»βˆ’2 ADP cana-6220 113 27 π‘Ÿ π‘Ÿ NOUN cana-6220 113 28 π‘˜=0 π‘˜=0 ADP cana-6220 113 29 where where SCONJ cana-6220 113 30 , , PUNCT cana-6220 113 31 b(x b(x NOUN cana-6220 113 32 , , PUNCT cana-6220 113 33 y y NOUN cana-6220 113 34 ) ) PUNCT cana-6220 113 35 is be AUX cana-6220 113 36 the the DET cana-6220 113 37 beta beta ADJ cana-6220 113 38 function function NOUN cana-6220 113 39 . . PUNCT cana-6220 114 1 proof proof NOUN cana-6220 114 2 . . PUNCT cana-6220 115 1 the the DET cana-6220 115 2 rth rth PROPN cana-6220 115 3 moment moment NOUN cana-6220 115 4 about about ADP cana-6220 115 5 origin origin NOUN cana-6220 115 6 for for ADP cana-6220 115 7 the the DET cana-6220 115 8 mold mold NOUN cana-6220 115 9 is be AUX cana-6220 115 10 obtained obtain VERB cana-6220 115 11 from from ADP cana-6220 115 12 the the DET cana-6220 115 13 following follow VERB cana-6220 115 14 expression expression NOUN cana-6220 115 15 using use VERB cana-6220 115 16 eq.(5 eq.(5 NOUN cana-6220 115 17 ) ) PUNCT cana-6220 115 18 ΞΌπ‘Ÿ ΞΌπ‘Ÿ ADP cana-6220 115 19 β€² β€² NUM cana-6220 115 20 = = SYM cana-6220 115 21 𝐸(π‘‘π‘Ÿ 𝐸(π‘‘π‘Ÿ PROPN cana-6220 115 22 ) ) PUNCT cana-6220 115 23 = = SYM cana-6220 116 1 ∫ ∫ PROPN cana-6220 116 2 π‘‘π‘Ÿπ‘”(𝑑)𝑑𝑑 π‘‘π‘Ÿπ‘”(𝑑)𝑑𝑑 X cana-6220 117 1 ∞ ∞ NOUN cana-6220 117 2 0 0 PUNCT cana-6220 117 3 let let VERB cana-6220 117 4 𝑒 𝑒 X cana-6220 117 5 = = SYM cana-6220 117 6 ΞΈ ΞΈ PROPN cana-6220 117 7 + + CCONJ cana-6220 117 8 𝑑 𝑑 PROPN cana-6220 117 9 𝐸(π‘‘π‘Ÿ 𝐸(π‘‘π‘Ÿ NOUN cana-6220 117 10 ) ) PUNCT cana-6220 118 1 = = SYM cana-6220 118 2 ∫ ∫ PROPN cana-6220 118 3 ( ( PUNCT cana-6220 118 4 𝑒 𝑒 PROPN cana-6220 118 5 βˆ’ βˆ’ PROPN cana-6220 118 6 ΞΈ)π‘ŸΞΎΞ»ΞΈβˆ’Ξ»(𝑒)βˆ’(Ξ»+1)(1 ΞΈ)π‘ŸΞΎΞ»ΞΈβˆ’Ξ»(𝑒)βˆ’(Ξ»+1)(1 NOUN cana-6220 118 7 + + CCONJ cana-6220 118 8 ΞΎ ΞΎ X cana-6220 118 9 ) ) PUNCT cana-6220 119 1 [ [ X cana-6220 119 2 ( ( PUNCT cana-6220 119 3 1 1 NUM cana-6220 119 4 + + PROPN cana-6220 119 5 ΞΎ)ΞΈβˆ’Ξ» ΞΎ)ΞΈβˆ’Ξ» ADJ cana-6220 119 6 βˆ’ βˆ’ PROPN cana-6220 119 7 π‘’βˆ’Ξ»]2 π‘’βˆ’Ξ»]2 NOUN cana-6220 119 8 𝑑𝑒 𝑑𝑒 NOUN cana-6220 119 9 ∞ ∞ PROPN cana-6220 119 10 ΞΈ ΞΈ PROPN cana-6220 119 11 now now ADV cana-6220 119 12 we we PRON cana-6220 119 13 use use VERB cana-6220 119 14 second second ADJ cana-6220 119 15 substitution substitution NOUN cana-6220 119 16 𝑣 𝑣 ADP cana-6220 119 17 = = PUNCT cana-6220 119 18 ( ( PUNCT cana-6220 119 19 ΞΈ ΞΈ NOUN cana-6220 119 20 𝑒 𝑒 X cana-6220 119 21 ) ) PUNCT cana-6220 119 22 Ξ» Ξ» PROPN cana-6220 119 23 𝐸(π‘‘π‘Ÿ 𝐸(π‘‘π‘Ÿ NOUN cana-6220 119 24 ) ) PUNCT cana-6220 119 25 = = SYM cana-6220 120 1 ΞΈπ‘Ÿ+Ξ» ΞΈπ‘Ÿ+Ξ» PROPN cana-6220 120 2 Ξ» Ξ» X cana-6220 120 3 ∫ ∫ PROPN cana-6220 120 4 ( ( PUNCT cana-6220 120 5 π‘£βˆ’1 π‘£βˆ’1 NOUN cana-6220 120 6 / / SYM cana-6220 120 7 Ξ» Ξ» NOUN cana-6220 120 8 βˆ’ βˆ’ NOUN cana-6220 120 9 1 1 NUM cana-6220 120 10 ) ) PUNCT cana-6220 120 11 π‘Ÿ π‘Ÿ NOUN cana-6220 120 12 𝑣1 𝑣1 PROPN cana-6220 120 13 / / SYM cana-6220 120 14 Ξ» Ξ» PROPN cana-6220 120 15 ( ( PUNCT cana-6220 120 16 1 1 NUM cana-6220 120 17 + + SYM cana-6220 120 18 ΞΎ ΞΎ PROPN cana-6220 120 19 βˆ’ βˆ’ X cana-6220 120 20 𝑣)2 𝑣)2 PROPN cana-6220 120 21 𝑑𝑣 𝑑𝑣 X cana-6220 120 22 1 1 NUM cana-6220 120 23 0 0 NUM cana-6220 120 24 now now ADV cana-6220 120 25 expanding expand VERB cana-6220 120 26 ( ( PUNCT cana-6220 120 27 π‘£βˆ’1 π‘£βˆ’1 NOUN cana-6220 120 28 / / SYM cana-6220 120 29 Ξ» Ξ» NOUN cana-6220 120 30 βˆ’ βˆ’ NOUN cana-6220 120 31 1 1 NUM cana-6220 120 32 ) ) PUNCT cana-6220 120 33 π‘Ÿ π‘Ÿ NOUN cana-6220 121 1 = = SYM cana-6220 121 2 βˆ‘ βˆ‘ PUNCT cana-6220 121 3 ( ( PUNCT cana-6220 121 4 π‘Ÿ π‘Ÿ X cana-6220 121 5 π‘˜ π‘˜ NOUN cana-6220 121 6 ) ) PUNCT cana-6220 121 7 ( ( PUNCT cana-6220 121 8 π‘£βˆ’1 π‘£βˆ’1 NOUN cana-6220 121 9 / / SYM cana-6220 121 10 Ξ» Ξ» NOUN cana-6220 121 11 ) ) PUNCT cana-6220 121 12 π‘Ÿβˆ’π‘˜ π‘Ÿβˆ’π‘˜ X cana-6220 122 1 ( ( PUNCT cana-6220 122 2 βˆ’1)π‘˜π‘Ÿ βˆ’1)π‘˜π‘Ÿ NOUN cana-6220 122 3 π‘˜=0 π‘˜=0 ADP cana-6220 122 4 using use VERB cana-6220 122 5 binomial binomial ADJ cana-6220 122 6 expression expression NOUN cana-6220 122 7 , , PUNCT cana-6220 122 8 we we PRON cana-6220 122 9 get get AUX cana-6220 122 10 𝐸(π‘‘π‘Ÿ 𝐸(π‘‘π‘Ÿ VERB cana-6220 122 11 ) ) PUNCT cana-6220 123 1 = = SYM cana-6220 123 2 ΞΈπ‘Ÿ+Ξ» ΞΈπ‘Ÿ+Ξ» NOUN cana-6220 123 3 Ξ» Ξ» INTJ cana-6220 123 4 βˆ‘ βˆ‘ PUNCT cana-6220 123 5 ( ( PUNCT cana-6220 123 6 π‘Ÿ π‘Ÿ PRON cana-6220 123 7 π‘˜ π‘˜ NOUN cana-6220 123 8 ) ) PUNCT cana-6220 123 9 ( ( PUNCT cana-6220 123 10 βˆ’1)π‘˜b βˆ’1)π‘˜b PROPN cana-6220 123 11 ( ( PUNCT cana-6220 123 12 1 1 NUM cana-6220 123 13 βˆ’ βˆ’ PROPN cana-6220 123 14 ( ( PUNCT cana-6220 123 15 π‘Ÿ π‘Ÿ NOUN cana-6220 123 16 βˆ’ βˆ’ X cana-6220 123 17 π‘˜ π‘˜ X cana-6220 123 18 ) ) PUNCT cana-6220 123 19 Ξ» Ξ» NOUN cana-6220 123 20 + + NOUN cana-6220 123 21 1,1 1,1 NUM cana-6220 123 22 ) ) PUNCT cana-6220 123 23 ( ( PUNCT cana-6220 123 24 1 1 NUM cana-6220 123 25 + + CCONJ cana-6220 123 26 ΞΎ)1βˆ’(π‘Ÿβˆ’π‘˜)/Ξ»βˆ’2 ΞΎ)1βˆ’(π‘Ÿβˆ’π‘˜)/Ξ»βˆ’2 ADP cana-6220 123 27 π‘Ÿ π‘Ÿ NOUN cana-6220 123 28 π‘˜=0 π‘˜=0 ADP cana-6220 123 29 4.2 4.2 NUM cana-6220 123 30 quantile quantile ADJ cana-6220 123 31 function function NOUN cana-6220 123 32 let let VERB cana-6220 123 33 𝑑 𝑑 PRON cana-6220 123 34 ∼ ∼ VERB cana-6220 123 35 mold(ΞΎ mold(ΞΎ PROPN cana-6220 123 36 , , PUNCT cana-6220 123 37 Ξ» Ξ» PROPN cana-6220 123 38 , , PUNCT cana-6220 123 39 ΞΈ ΞΈ NOUN cana-6220 123 40 ) ) PUNCT cana-6220 123 41 and and CCONJ cana-6220 123 42 g(t g(t PROPN cana-6220 123 43 ) ) PUNCT cana-6220 124 1 = = PRON cana-6220 125 1 p p NOUN cana-6220 125 2 be be AUX cana-6220 125 3 the the DET cana-6220 125 4 cdf cdf PROPN cana-6220 125 5 of of ADP cana-6220 125 6 t t PROPN cana-6220 125 7 , , PUNCT cana-6220 125 8 so so ADV cana-6220 125 9 the the DET cana-6220 125 10 quantile quantile ADJ cana-6220 125 11 function function NOUN cana-6220 125 12 is be AUX cana-6220 125 13 defined define VERB cana-6220 125 14 as as ADP cana-6220 125 15 𝑄(𝑝 𝑄(𝑝 NOUN cana-6220 125 16 ) ) PUNCT cana-6220 125 17 = = PUNCT cana-6220 125 18 πΊβˆ’1(𝑝 πΊβˆ’1(𝑝 PROPN cana-6220 125 19 ) ) PUNCT cana-6220 125 20 , , PUNCT cana-6220 125 21 for for ADP cana-6220 125 22 0 0 NUM cana-6220 125 23 < < X cana-6220 125 24 𝑝 𝑝 X cana-6220 125 25 < < X cana-6220 125 26 1 1 NUM cana-6220 125 27 hence hence ADV cana-6220 125 28 the the DET cana-6220 125 29 quantile quantile ADJ cana-6220 125 30 function function NOUN cana-6220 125 31 of of ADP cana-6220 125 32 mold mold NOUN cana-6220 125 33 is be AUX cana-6220 125 34 obtained obtain VERB cana-6220 125 35 as as ADP cana-6220 125 36 follows follow NOUN cana-6220 125 37 𝑄(𝑝 𝑄(𝑝 PROPN cana-6220 125 38 ) ) PUNCT cana-6220 125 39 = = PUNCT cana-6220 126 1 πœƒ πœƒ X cana-6220 127 1 [ [ X cana-6220 127 2 ( ( PUNCT cana-6220 127 3 1+πœ‰βˆ’π‘ 1+πœ‰βˆ’π‘ NUM cana-6220 127 4 ( ( PUNCT cana-6220 127 5 1+πœ‰)(1βˆ’π‘ 1+πœ‰)(1βˆ’π‘ NUM cana-6220 127 6 ) ) PUNCT cana-6220 127 7 ) ) PUNCT cana-6220 128 1 1/πœ† 1/πœ† NUM cana-6220 128 2 βˆ’ βˆ’ NOUN cana-6220 128 3 1 1 NUM cana-6220 128 4 ] ] PUNCT cana-6220 128 5 , , PUNCT cana-6220 128 6 0 0 PUNCT cana-6220 128 7 < < X cana-6220 128 8 𝑝 𝑝 X cana-6220 128 9 < < X cana-6220 128 10 ( ( PUNCT cana-6220 128 11 1 1 NUM cana-6220 128 12 + + NUM cana-6220 128 13 πœ‰ πœ‰ X cana-6220 128 14 ) ) PUNCT cana-6220 128 15 ( ( PUNCT cana-6220 128 16 13 13 NUM cana-6220 128 17 ) ) PUNCT cana-6220 128 18 the the DET cana-6220 128 19 first first ADJ cana-6220 128 20 , , PUNCT cana-6220 128 21 second second ADJ cana-6220 128 22 and and CCONJ cana-6220 128 23 third third ADJ cana-6220 128 24 quartile quartile NOUN cana-6220 128 25 can can AUX cana-6220 128 26 be be AUX cana-6220 128 27 obtained obtain VERB cana-6220 128 28 from from ADP cana-6220 128 29 eq eq PROPN cana-6220 128 30 . . PUNCT cana-6220 129 1 ( ( PUNCT cana-6220 129 2 13 13 NUM cana-6220 129 3 ) ) PUNCT cana-6220 129 4 by by ADP cana-6220 129 5 putting put VERB cana-6220 129 6 p p NOUN cana-6220 129 7 = = NOUN cana-6220 129 8 1/4 1/4 NUM cana-6220 129 9 , , PUNCT cana-6220 129 10 1/2 1/2 NUM cana-6220 129 11 and and CCONJ cana-6220 129 12 3/4 3/4 NUM cana-6220 129 13 , , PUNCT cana-6220 129 14 respectively respectively ADV cana-6220 129 15 . . PUNCT cana-6220 130 1 communications communication NOUN cana-6220 130 2 on on ADP cana-6220 130 3 applied apply VERB cana-6220 130 4 nonlinear nonlinear ADJ cana-6220 130 5 analysis analysis NOUN cana-6220 130 6 issn issn NOUN cana-6220 130 7 : : PUNCT cana-6220 130 8 1074 1074 NUM cana-6220 130 9 - - PUNCT cana-6220 130 10 133x 133x NUM cana-6220 130 11 vol vol VERB cana-6220 130 12 32 32 NUM cana-6220 130 13 no no NOUN cana-6220 130 14 . . PUNCT cana-6220 131 1 10s 10 NOUN cana-6220 131 2 ( ( PUNCT cana-6220 131 3 2025 2025 NUM cana-6220 131 4 ) ) PUNCT cana-6220 131 5 3552 3552 NUM cana-6220 131 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 131 7 the the DET cana-6220 131 8 first first ADJ cana-6220 131 9 quartile quartile ADJ cana-6220 131 10 𝑄1 𝑄1 NOUN cana-6220 131 11 = = PUNCT cana-6220 132 1 πœƒ πœƒ X cana-6220 133 1 [ [ X cana-6220 133 2 ( ( PUNCT cana-6220 133 3 3 3 NUM cana-6220 133 4 + + NOUN cana-6220 133 5 4πœ‰ 4πœ‰ NOUN cana-6220 133 6 3(1+πœ‰ 3(1+πœ‰ NUM cana-6220 133 7 ) ) PUNCT cana-6220 133 8 ) ) PUNCT cana-6220 134 1 1/πœ† 1/πœ† NUM cana-6220 134 2 βˆ’ βˆ’ NOUN cana-6220 134 3 1 1 NUM cana-6220 134 4 ] ] X cana-6220 134 5 ( ( PUNCT cana-6220 134 6 14 14 NUM cana-6220 134 7 ) ) PUNCT cana-6220 134 8 the the DET cana-6220 134 9 second second ADJ cana-6220 134 10 quartile quartile NOUN cana-6220 134 11 𝑄2 𝑄2 PROPN cana-6220 135 1 = = SYM cana-6220 135 2 πœƒ πœƒ X cana-6220 136 1 [ [ X cana-6220 136 2 ( ( PUNCT cana-6220 136 3 1 1 NUM cana-6220 136 4 + + NOUN cana-6220 136 5 2πœ‰ 2πœ‰ NUM cana-6220 136 6 ( ( PUNCT cana-6220 136 7 1+πœ‰ 1+πœ‰ NUM cana-6220 136 8 ) ) PUNCT cana-6220 136 9 ) ) PUNCT cana-6220 137 1 1/πœ† 1/πœ† NUM cana-6220 137 2 βˆ’ βˆ’ NOUN cana-6220 137 3 1 1 NUM cana-6220 137 4 ] ] X cana-6220 137 5 ( ( PUNCT cana-6220 137 6 15 15 NUM cana-6220 137 7 ) ) PUNCT cana-6220 137 8 the the DET cana-6220 137 9 third third ADJ cana-6220 137 10 quartile quartile NOUN cana-6220 137 11 𝑄3 𝑄3 ADV cana-6220 138 1 = = PUNCT cana-6220 138 2 πœƒ πœƒ SYM cana-6220 139 1 [ [ X cana-6220 139 2 ( ( PUNCT cana-6220 139 3 1 1 NUM cana-6220 139 4 + + NOUN cana-6220 139 5 4πœ‰ 4πœ‰ NOUN cana-6220 139 6 ( ( PUNCT cana-6220 139 7 1+πœ‰ 1+πœ‰ NUM cana-6220 139 8 ) ) PUNCT cana-6220 139 9 ) ) PUNCT cana-6220 140 1 1/πœ† 1/πœ† NUM cana-6220 140 2 βˆ’ βˆ’ NOUN cana-6220 140 3 1 1 NUM cana-6220 140 4 ] ] X cana-6220 140 5 ( ( PUNCT cana-6220 140 6 16 16 NUM cana-6220 140 7 ) ) PUNCT cana-6220 140 8 4.3 4.3 NUM cana-6220 140 9 order order NOUN cana-6220 140 10 statistics statistic NOUN cana-6220 140 11 consider consider VERB cana-6220 140 12 a a DET cana-6220 140 13 finite finite ADJ cana-6220 140 14 random random ADJ cana-6220 140 15 sample sample NOUN cana-6220 140 16 consisting consist VERB cana-6220 140 17 of of ADP cana-6220 140 18 observations observation NOUN cana-6220 140 19 t1 t1 PROPN cana-6220 140 20 , , PUNCT cana-6220 140 21 t2 t2 NOUN cana-6220 140 22 , , PUNCT cana-6220 140 23 … … PUNCT cana-6220 140 24 , , PUNCT cana-6220 140 25 tn tn NOUN cana-6220 140 26 drawn draw VERB cana-6220 140 27 from from ADP cana-6220 140 28 the the DET cana-6220 140 29 mold mold NOUN cana-6220 140 30 with with ADP cana-6220 140 31 pdf pdf NOUN cana-6220 140 32 g(t g(t PROPN cana-6220 140 33 ) ) PUNCT cana-6220 140 34 and and CCONJ cana-6220 140 35 cdf cdf PROPN cana-6220 140 36 g(t g(t PROPN cana-6220 140 37 ) ) PUNCT cana-6220 140 38 . . PUNCT cana-6220 141 1 when when SCONJ cana-6220 141 2 these these DET cana-6220 141 3 sample sample NOUN cana-6220 141 4 values value NOUN cana-6220 141 5 are be AUX cana-6220 141 6 rearranged rearrange VERB cana-6220 141 7 in in ADP cana-6220 141 8 non non ADJ cana-6220 141 9 - - ADJ cana-6220 141 10 decreasing decrease VERB cana-6220 141 11 sequence sequence NOUN cana-6220 141 12 , , PUNCT cana-6220 141 13 the the DET cana-6220 141 14 resulting result VERB cana-6220 141 15 ordered order VERB cana-6220 141 16 observations observation NOUN cana-6220 141 17 t1 t1 PROPN cana-6220 141 18 , , PUNCT cana-6220 141 19 t2 t2 NOUN cana-6220 141 20 , , PUNCT cana-6220 141 21 … … PUNCT cana-6220 141 22 , , PUNCT cana-6220 141 23 tn tn PROPN cana-6220 141 24 are be AUX cana-6220 141 25 called call VERB cana-6220 141 26 the the DET cana-6220 141 27 order order NOUN cana-6220 141 28 statistics statistic NOUN cana-6220 141 29 of of ADP cana-6220 141 30 the the DET cana-6220 141 31 sample sample NOUN cana-6220 141 32 , , PUNCT cana-6220 141 33 where where SCONJ cana-6220 141 34 : : PUNCT cana-6220 141 35 𝑑(1 𝑑(1 NOUN cana-6220 141 36 ) ) PUNCT cana-6220 141 37 ≀ ≀ NUM cana-6220 141 38 𝑑(2 𝑑(2 NOUN cana-6220 141 39 ) ) PUNCT cana-6220 141 40 ≀ ≀ NOUN cana-6220 141 41 β‹― β‹― NOUN cana-6220 141 42 ≀ ≀ NOUN cana-6220 141 43 𝑑(𝑛 𝑑(𝑛 NOUN cana-6220 141 44 ) ) PUNCT cana-6220 141 45 the the DET cana-6220 141 46 order order NOUN cana-6220 141 47 statistic statistic NOUN cana-6220 141 48 𝑑(π‘Ÿ 𝑑(π‘Ÿ NUM cana-6220 141 49 ) ) PUNCT cana-6220 141 50 corresponds correspond VERB cana-6220 141 51 to to ADP cana-6220 141 52 the the DET cana-6220 141 53 π‘Ÿπ‘‘β„Ž π‘Ÿπ‘‘β„Ž NOUN cana-6220 141 54 smallest small ADJ cana-6220 141 55 observation observation NOUN cana-6220 141 56 among among ADP cana-6220 141 57 the the DET cana-6220 141 58 sorted sorted ADJ cana-6220 141 59 sample sample NOUN cana-6220 141 60 values value NOUN cana-6220 141 61 . . PUNCT cana-6220 142 1 specifically specifically ADV cana-6220 142 2 , , PUNCT cana-6220 142 3 𝑑(1 𝑑(1 PROPN cana-6220 142 4 ) ) PUNCT cana-6220 142 5 is be AUX cana-6220 142 6 the the DET cana-6220 142 7 minimum minimum ADJ cana-6220 142 8 value value NOUN cana-6220 142 9 , , PUNCT cana-6220 142 10 𝑑(2 𝑑(2 PROPN cana-6220 142 11 ) ) PUNCT cana-6220 142 12 is be AUX cana-6220 142 13 the the DET cana-6220 142 14 second second ADJ cana-6220 142 15 minimum minimum NOUN cana-6220 142 16 , , PUNCT cana-6220 142 17 and and CCONJ cana-6220 142 18 this this DET cana-6220 142 19 pattern pattern NOUN cana-6220 142 20 continues continue VERB cana-6220 142 21 until until ADP cana-6220 142 22 𝑑(𝑛 𝑑(𝑛 PROPN cana-6220 142 23 ) ) PUNCT cana-6220 142 24 which which PRON cana-6220 142 25 represents represent VERB cana-6220 142 26 the the DET cana-6220 142 27 maximum maximum ADJ cana-6220 142 28 value value NOUN cana-6220 142 29 in in ADP cana-6220 142 30 the the DET cana-6220 142 31 sample sample NOUN cana-6220 142 32 . . PUNCT cana-6220 143 1 for for ADP cana-6220 143 2 any any DET cana-6220 143 3 r r NOUN cana-6220 143 4 where where SCONJ cana-6220 143 5 1 1 NUM cana-6220 143 6 ≀ ≀ NUM cana-6220 143 7 π‘Ÿ π‘Ÿ NOUN cana-6220 143 8 ≀ ≀ NUM cana-6220 143 9 𝑛 𝑛 ADP cana-6220 143 10 the the DET cana-6220 143 11 pdf pdf NOUN cana-6220 143 12 of of ADP cana-6220 143 13 the the DET cana-6220 143 14 π‘Ÿπ‘‘β„Ž π‘Ÿπ‘‘β„Ž NOUN cana-6220 143 15 order order NOUN cana-6220 143 16 statistic statistic NOUN cana-6220 143 17 is be AUX cana-6220 143 18 expressed express VERB cana-6220 143 19 as as ADP cana-6220 143 20 : : PUNCT cana-6220 143 21 π‘ž(π‘Ÿ)(𝑑 π‘ž(π‘Ÿ)(𝑑 NUM cana-6220 143 22 ) ) PUNCT cana-6220 143 23 = = SYM cana-6220 143 24 𝑛 𝑛 PROPN cana-6220 143 25 ! ! PUNCT cana-6220 143 26 ( ( PUNCT cana-6220 143 27 π‘Ÿβˆ’1)!(π‘›βˆ’π‘Ÿ π‘Ÿβˆ’1)!(π‘›βˆ’π‘Ÿ NOUN cana-6220 143 28 ) ) PUNCT cana-6220 143 29 ! ! PUNCT cana-6220 143 30 𝑔(𝑑)[𝐺(𝑑)]π‘Ÿβˆ’1[1 𝑔(𝑑)[𝐺(𝑑)]π‘Ÿβˆ’1[1 X cana-6220 143 31 βˆ’ βˆ’ NOUN cana-6220 143 32 𝐺(𝑑)]π‘›βˆ’π‘Ÿ 𝐺(𝑑)]π‘›βˆ’π‘Ÿ INTJ cana-6220 143 33 ( ( PUNCT cana-6220 143 34 17 17 NUM cana-6220 143 35 ) ) PUNCT cana-6220 143 36 putting put VERB cana-6220 143 37 the the DET cana-6220 143 38 expression expression NOUN cana-6220 143 39 of of ADP cana-6220 143 40 pdf pdf NOUN cana-6220 143 41 and and CCONJ cana-6220 143 42 cdf cdf PROPN cana-6220 143 43 of of ADP cana-6220 143 44 mold mold NOUN cana-6220 143 45 from from ADP cana-6220 143 46 eq eq PROPN cana-6220 143 47 . . PUNCT cana-6220 143 48 ( ( PUNCT cana-6220 143 49 5 5 NUM cana-6220 143 50 ) ) PUNCT cana-6220 143 51 and and CCONJ cana-6220 143 52 eq eq NOUN cana-6220 143 53 . . PUNCT cana-6220 144 1 ( ( PUNCT cana-6220 144 2 6 6 NUM cana-6220 144 3 ) ) PUNCT cana-6220 144 4 respectively respectively ADV cana-6220 144 5 in in ADP cana-6220 144 6 eq.(17 eq.(17 NOUN cana-6220 144 7 ) ) PUNCT cana-6220 144 8 , , PUNCT cana-6220 144 9 π‘ž(π‘Ÿ)(𝑑 π‘ž(π‘Ÿ)(𝑑 X cana-6220 144 10 ) ) PUNCT cana-6220 144 11 = = PUNCT cana-6220 144 12 π‘š π‘š ADP cana-6220 144 13 πœ†πœ‰(1+π‘›βˆ’π‘Ÿ)(1+πœ‰)π‘Ÿ(πœƒ+𝑑)πœ†(π‘Ÿ+π‘›βˆ’1)βˆ’1πœƒβˆ’πœ†π‘Ÿ[1βˆ’(1 πœ†πœ‰(1+π‘›βˆ’π‘Ÿ)(1+πœ‰)π‘Ÿ(πœƒ+𝑑)πœ†(π‘Ÿ+π‘›βˆ’1)βˆ’1πœƒβˆ’πœ†π‘Ÿ[1βˆ’(1 PROPN cana-6220 144 14 + + CCONJ cana-6220 144 15 𝑑 𝑑 PROPN cana-6220 144 16 πœƒ πœƒ NOUN cana-6220 144 17 ) ) PUNCT cana-6220 144 18 βˆ’πœ† βˆ’πœ† ADV cana-6220 144 19 ] ] PUNCT cana-6220 145 1 π‘Ÿβˆ’1 π‘Ÿβˆ’1 PROPN cana-6220 146 1 [ [ X cana-6220 146 2 ( ( PUNCT cana-6220 146 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 146 4 ] ] X cana-6220 146 5 𝑛+1 𝑛+1 PROPN cana-6220 146 6 ( ( PUNCT cana-6220 146 7 18 18 NUM cana-6220 146 8 ) ) PUNCT cana-6220 146 9 where where SCONJ cana-6220 146 10 , , PUNCT cana-6220 146 11 π‘š π‘š PROPN cana-6220 146 12 = = SYM cana-6220 146 13 𝑛 𝑛 PROPN cana-6220 146 14 ! ! PUNCT cana-6220 146 15 ( ( PUNCT cana-6220 146 16 π‘Ÿβˆ’1)!(π‘›βˆ’π‘Ÿ π‘Ÿβˆ’1)!(π‘›βˆ’π‘Ÿ NOUN cana-6220 146 17 ) ) PUNCT cana-6220 146 18 ! ! PUNCT cana-6220 147 1 the the DET cana-6220 147 2 pdf pdf NOUN cana-6220 147 3 for for ADP cana-6220 147 4 first first ADJ cana-6220 147 5 order order NOUN cana-6220 147 6 statistics statistic NOUN cana-6220 147 7 of of ADP cana-6220 147 8 mold mold NOUN cana-6220 147 9 , , PUNCT cana-6220 147 10 when when SCONJ cana-6220 147 11 the the DET cana-6220 147 12 value value NOUN cana-6220 147 13 of of ADP cana-6220 147 14 r r NOUN cana-6220 147 15 is be AUX cana-6220 147 16 1 1 NUM cana-6220 147 17 , , PUNCT cana-6220 147 18 and and CCONJ cana-6220 147 19 given give VERB cana-6220 147 20 by by ADP cana-6220 147 21 π‘ž(1)(𝑑 π‘ž(1)(𝑑 NOUN cana-6220 147 22 ) ) PUNCT cana-6220 147 23 = = PUNCT cana-6220 148 1 π‘›πœ†πœ‰π‘›(1+πœ‰)(πœƒ+𝑑)βˆ’(πœ†π‘›+1)πœƒβˆ’πœ† π‘›πœ†πœ‰π‘›(1+πœ‰)(πœƒ+𝑑)βˆ’(πœ†π‘›+1)πœƒβˆ’πœ† X cana-6220 149 1 [ [ X cana-6220 149 2 ( ( PUNCT cana-6220 149 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 149 4 ] ] X cana-6220 149 5 𝑛+1 𝑛+1 PROPN cana-6220 149 6 ( ( PUNCT cana-6220 149 7 19 19 NUM cana-6220 149 8 ) ) PUNCT cana-6220 149 9 the the DET cana-6220 149 10 pdf pdf NOUN cana-6220 149 11 of of ADP cana-6220 149 12 nth nth PROPN cana-6220 149 13 order order NOUN cana-6220 149 14 statistics statistic NOUN cana-6220 149 15 of of ADP cana-6220 149 16 the the DET cana-6220 149 17 mold mold NOUN cana-6220 149 18 when when SCONJ cana-6220 149 19 the the DET cana-6220 149 20 value value NOUN cana-6220 149 21 of of ADP cana-6220 149 22 r r NOUN cana-6220 149 23 is be AUX cana-6220 149 24 n n CCONJ cana-6220 149 25 , , PUNCT cana-6220 149 26 and and CCONJ cana-6220 149 27 is be AUX cana-6220 149 28 given give VERB cana-6220 149 29 by by ADP cana-6220 149 30 π‘ž(𝑛)(𝑑 π‘ž(𝑛)(𝑑 NOUN cana-6220 149 31 ) ) PUNCT cana-6220 149 32 = = SYM cana-6220 149 33 π‘›πœ†πœ‰(1+πœ‰)𝑛(πœƒ+𝑑)βˆ’(πœ†+1)πœƒβˆ’πœ†π‘›[1βˆ’(1 π‘›πœ†πœ‰(1+πœ‰)𝑛(πœƒ+𝑑)βˆ’(πœ†+1)πœƒβˆ’πœ†π‘›[1βˆ’(1 PROPN cana-6220 149 34 + + CCONJ cana-6220 149 35 𝑑 𝑑 PROPN cana-6220 149 36 πœƒ πœƒ NOUN cana-6220 149 37 ) ) PUNCT cana-6220 150 1 βˆ’πœ† βˆ’πœ† ADV cana-6220 150 2 ] ] X cana-6220 151 1 π‘›βˆ’1 π‘›βˆ’1 NUM cana-6220 151 2 [ [ X cana-6220 151 3 ( ( PUNCT cana-6220 151 4 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑)βˆ’πœ† NUM cana-6220 151 5 ] ] X cana-6220 151 6 𝑛+1 𝑛+1 PROPN cana-6220 151 7 ( ( PUNCT cana-6220 151 8 20 20 NUM cana-6220 151 9 ) ) PUNCT cana-6220 151 10 communications communication NOUN cana-6220 151 11 on on ADP cana-6220 151 12 applied apply VERB cana-6220 151 13 nonlinear nonlinear ADJ cana-6220 151 14 analysis analysis NOUN cana-6220 151 15 issn issn NOUN cana-6220 151 16 : : PUNCT cana-6220 151 17 1074 1074 NUM cana-6220 151 18 - - PUNCT cana-6220 151 19 133x 133x NUM cana-6220 151 20 vol vol VERB cana-6220 151 21 32 32 NUM cana-6220 151 22 no no NOUN cana-6220 151 23 . . PUNCT cana-6220 152 1 10s 10 NOUN cana-6220 152 2 ( ( PUNCT cana-6220 152 3 2025 2025 NUM cana-6220 152 4 ) ) PUNCT cana-6220 152 5 3553 3553 NUM cana-6220 152 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 152 7 4.4 4.4 NUM cana-6220 152 8 stress stress NOUN cana-6220 152 9 - - PUNCT cana-6220 152 10 strength strength NOUN cana-6220 152 11 reliability reliability NOUN cana-6220 152 12 the the DET cana-6220 152 13 reliability reliability NOUN cana-6220 152 14 model model NOUN cana-6220 152 15 based base VERB cana-6220 152 16 on on ADP cana-6220 152 17 stress stress NOUN cana-6220 152 18 - - PUNCT cana-6220 152 19 strength strength NOUN cana-6220 152 20 analysis analysis NOUN cana-6220 152 21 is be AUX cana-6220 152 22 expressed express VERB cana-6220 152 23 as as ADP cana-6220 152 24 r r NOUN cana-6220 152 25 = = SYM cana-6220 152 26 p(x p(x PROPN cana-6220 152 27 > > X cana-6220 152 28 y y PROPN cana-6220 152 29 ) ) PUNCT cana-6220 152 30 , , PUNCT cana-6220 152 31 where where SCONJ cana-6220 152 32 x x PRON cana-6220 152 33 denotes denote VERB cana-6220 152 34 the the DET cana-6220 152 35 random random ADJ cana-6220 152 36 strength strength NOUN cana-6220 152 37 capacity capacity NOUN cana-6220 152 38 of of ADP cana-6220 152 39 a a DET cana-6220 152 40 system system NOUN cana-6220 152 41 or or CCONJ cana-6220 152 42 its its PRON cana-6220 152 43 component component NOUN cana-6220 152 44 , , PUNCT cana-6220 152 45 while while SCONJ cana-6220 152 46 y y PROPN cana-6220 152 47 represents represent VERB cana-6220 152 48 the the DET cana-6220 152 49 random random ADJ cana-6220 152 50 stress stress NOUN cana-6220 152 51 applied apply VERB cana-6220 152 52 to to ADP cana-6220 152 53 the the DET cana-6220 152 54 system system NOUN cana-6220 152 55 or or CCONJ cana-6220 152 56 component component NOUN cana-6220 152 57 at at ADP cana-6220 152 58 any any DET cana-6220 152 59 given give VERB cana-6220 152 60 moment moment NOUN cana-6220 152 61 . . PUNCT cana-6220 153 1 in in ADP cana-6220 153 2 this this DET cana-6220 153 3 study study NOUN cana-6220 153 4 , , PUNCT cana-6220 153 5 we we PRON cana-6220 153 6 compute compute VERB cana-6220 153 7 the the DET cana-6220 153 8 stress stress NOUN cana-6220 153 9 - - PUNCT cana-6220 153 10 strength strength NOUN cana-6220 153 11 reliability reliability NOUN cana-6220 153 12 by by ADP cana-6220 153 13 assuming assume VERB cana-6220 153 14 that that SCONJ cana-6220 153 15 the the DET cana-6220 153 16 stress stress NOUN cana-6220 153 17 y y PROPN cana-6220 153 18 follows follow VERB cana-6220 153 19 an an DET cana-6220 153 20 exponential exponential ADJ cana-6220 153 21 distribution distribution NOUN cana-6220 153 22 and and CCONJ cana-6220 153 23 the the DET cana-6220 153 24 strength strength NOUN cana-6220 153 25 x x PUNCT cana-6220 153 26 follows follow VERB cana-6220 153 27 a a DET cana-6220 153 28 mold mold NOUN cana-6220 153 29 distribution distribution NOUN cana-6220 153 30 . . PUNCT cana-6220 154 1 the the DET cana-6220 154 2 rationale rationale NOUN cana-6220 154 3 for for ADP cana-6220 154 4 modeling model VERB cana-6220 154 5 y y PROPN cana-6220 154 6 with with ADP cana-6220 154 7 an an DET cana-6220 154 8 exponential exponential ADJ cana-6220 154 9 distribution distribution NOUN cana-6220 154 10 is be AUX cana-6220 154 11 that that SCONJ cana-6220 154 12 in in ADP cana-6220 154 13 many many ADJ cana-6220 154 14 practical practical ADJ cana-6220 154 15 engineering engineering NOUN cana-6220 154 16 scenarios scenario NOUN cana-6220 154 17 , , PUNCT cana-6220 154 18 stress stress NOUN cana-6220 154 19 tends tend VERB cana-6220 154 20 to to PART cana-6220 154 21 grow grow VERB cana-6220 154 22 exponentially exponentially ADV cana-6220 154 23 over over ADP cana-6220 154 24 time time NOUN cana-6220 154 25 . . PUNCT cana-6220 155 1 let let VERB cana-6220 155 2 𝑋 𝑋 NOUN cana-6220 155 3 ∼ ∼ NOUN cana-6220 155 4 𝑀𝑂𝐿𝐷(ΞΎ1 𝑀𝑂𝐿𝐷(ΞΎ1 NOUN cana-6220 155 5 , , PUNCT cana-6220 155 6 Ξ» Ξ» NOUN cana-6220 155 7 , , PUNCT cana-6220 155 8 ΞΈ ΞΈ NOUN cana-6220 155 9 ) ) PUNCT cana-6220 155 10 and and CCONJ cana-6220 155 11 π‘Œ π‘Œ PROPN cana-6220 155 12 ∼ ∼ NOUN cana-6220 155 13 𝑀𝑂𝐿𝐷(ΞΎ2 𝑀𝑂𝐿𝐷(ΞΎ2 NOUN cana-6220 155 14 , , PUNCT cana-6220 155 15 Ξ» Ξ» NOUN cana-6220 155 16 , , PUNCT cana-6220 155 17 ΞΈ ΞΈ NOUN cana-6220 155 18 ) ) PUNCT cana-6220 155 19 with with ADP cana-6220 155 20 the the DET cana-6220 155 21 pdf pdf NOUN cana-6220 155 22 and and CCONJ cana-6220 155 23 cdf cdf NOUN cana-6220 155 24 function function NOUN cana-6220 155 25 given give VERB cana-6220 155 26 in in ADP cana-6220 155 27 eq eq ADP cana-6220 155 28 . . PUNCT cana-6220 156 1 ( ( PUNCT cana-6220 156 2 5 5 NUM cana-6220 156 3 ) ) PUNCT cana-6220 156 4 and and CCONJ cana-6220 156 5 ( ( PUNCT cana-6220 156 6 6 6 NUM cana-6220 156 7 ) ) PUNCT cana-6220 156 8 respectively respectively ADV cana-6220 156 9 . . PUNCT cana-6220 157 1 hence hence ADV cana-6220 157 2 𝑅 𝑅 PROPN cana-6220 157 3 = = PUNCT cana-6220 157 4 𝑃(𝑋 𝑃(𝑋 PROPN cana-6220 157 5 > > X cana-6220 157 6 π‘Œ π‘Œ PROPN cana-6220 157 7 ) ) PUNCT cana-6220 157 8 𝑅 𝑅 PROPN cana-6220 157 9 = = PUNCT cana-6220 157 10 ∫ ∫ PROPN cana-6220 157 11 𝑃 𝑃 NOUN cana-6220 157 12 ∞ ∞ PROPN cana-6220 157 13 0 0 NUM cana-6220 158 1 ( ( PUNCT cana-6220 158 2 𝑋 𝑋 NOUN cana-6220 158 3 > > X cana-6220 158 4 π‘Œ)𝑓(π‘₯)𝑑π‘₯ π‘Œ)𝑓(π‘₯)𝑑π‘₯ PROPN cana-6220 158 5 𝑅 𝑅 PROPN cana-6220 158 6 = = PUNCT cana-6220 158 7 ∫ ∫ PROPN cana-6220 158 8 ( ( PUNCT cana-6220 158 9 1 1 NUM cana-6220 158 10 + + CCONJ cana-6220 158 11 ΞΎ2)[ΞΈβˆ’Ξ» ΞΎ2)[ΞΈβˆ’Ξ» ADJ cana-6220 158 12 βˆ’ βˆ’ PROPN cana-6220 158 13 ( ( PUNCT cana-6220 158 14 ΞΈ ΞΈ PROPN cana-6220 158 15 + + X cana-6220 158 16 π‘₯)βˆ’Ξ» π‘₯)βˆ’Ξ» X cana-6220 158 17 ] ] X cana-6220 159 1 [ [ X cana-6220 159 2 ( ( PUNCT cana-6220 159 3 1 1 NUM cana-6220 159 4 + + CCONJ cana-6220 159 5 ΞΎ2)ΞΈβˆ’Ξ» ΞΎ2)ΞΈβˆ’Ξ» PROPN cana-6220 159 6 βˆ’ βˆ’ PROPN cana-6220 159 7 ( ( PUNCT cana-6220 159 8 ΞΈ ΞΈ PROPN cana-6220 159 9 + + X cana-6220 159 10 π‘₯)βˆ’Ξ» π‘₯)βˆ’Ξ» X cana-6220 159 11 ] ] X cana-6220 159 12 ∞ ∞ NUM cana-6220 159 13 0 0 NUM cana-6220 159 14 . . PUNCT cana-6220 160 1 ΞΎ1(1 ΞΎ1(1 ADV cana-6220 160 2 + + CCONJ cana-6220 160 3 ΞΎ1)Ξ»ΞΈβˆ’Ξ»(ΞΈ ΞΎ1)Ξ»ΞΈβˆ’Ξ»(ΞΈ ADJ cana-6220 160 4 + + CCONJ cana-6220 160 5 π‘₯)βˆ’(Ξ»+1 π‘₯)βˆ’(Ξ»+1 NOUN cana-6220 160 6 ) ) PUNCT cana-6220 161 1 [ [ X cana-6220 161 2 ( ( PUNCT cana-6220 161 3 1 1 NUM cana-6220 161 4 + + CCONJ cana-6220 161 5 ΞΎ1)ΞΈβˆ’Ξ» ΞΎ1)ΞΈβˆ’Ξ» PROPN cana-6220 161 6 βˆ’ βˆ’ PROPN cana-6220 161 7 ( ( PUNCT cana-6220 161 8 ΞΈ ΞΈ NOUN cana-6220 161 9 + + NOUN cana-6220 161 10 π‘₯)βˆ’Ξ»]2 π‘₯)βˆ’Ξ»]2 ADV cana-6220 161 11 𝑑π‘₯ 𝑑π‘₯ AUX cana-6220 161 12 putting put VERB cana-6220 161 13 two two NUM cana-6220 161 14 substitutions substitution NOUN cana-6220 161 15 in in ADP cana-6220 161 16 sequence sequence NOUN cana-6220 161 17 , , PUNCT cana-6220 161 18 u u NOUN cana-6220 161 19 = = PUNCT cana-6220 161 20 ( ( PUNCT cana-6220 161 21 ΞΈ ΞΈ PROPN cana-6220 161 22 + + PUNCT cana-6220 161 23 x)βˆ’Ξ» x)βˆ’Ξ» PROPN cana-6220 161 24 and and CCONJ cana-6220 161 25 𝑣 𝑣 X cana-6220 161 26 = = SYM cana-6220 161 27 𝑒/ΞΈβˆ’Ξ» 𝑒/ΞΈβˆ’Ξ» PROPN cana-6220 161 28 , , PUNCT cana-6220 161 29 we we PRON cana-6220 161 30 get get VERB cana-6220 161 31 𝑅 𝑅 PROPN cana-6220 161 32 = = PUNCT cana-6220 161 33 ΞΎ1(1 ΞΎ1(1 NOUN cana-6220 161 34 + + NUM cana-6220 161 35 ΞΎ1)(1 ΞΎ1)(1 PRON cana-6220 161 36 + + CCONJ cana-6220 161 37 ΞΎ2 ΞΎ2 ADJ cana-6220 161 38 ) ) PUNCT cana-6220 161 39 ∫ ∫ PROPN cana-6220 161 40 ( ( PUNCT cana-6220 161 41 1 1 NUM cana-6220 161 42 βˆ’ βˆ’ PROPN cana-6220 161 43 𝑣 𝑣 X cana-6220 161 44 ) ) PUNCT cana-6220 162 1 [ [ X cana-6220 162 2 ( ( PUNCT cana-6220 162 3 1 1 NUM cana-6220 162 4 + + NUM cana-6220 162 5 ΞΎ1 ΞΎ1 NOUN cana-6220 162 6 ) ) PUNCT cana-6220 162 7 βˆ’ βˆ’ PROPN cana-6220 163 1 𝑣]2[(1 𝑣]2[(1 INTJ cana-6220 163 2 + + CCONJ cana-6220 163 3 ΞΎ2 ΞΎ2 ADJ cana-6220 163 4 ) ) PUNCT cana-6220 164 1 βˆ’ βˆ’ PROPN cana-6220 165 1 𝑣 𝑣 X cana-6220 165 2 ] ] X cana-6220 165 3 𝑑𝑣 𝑑𝑣 X cana-6220 165 4 1 1 NUM cana-6220 165 5 0 0 NUM cana-6220 165 6 after after ADP cana-6220 165 7 using use VERB cana-6220 165 8 by by ADP cana-6220 165 9 - - PUNCT cana-6220 165 10 part part NOUN cana-6220 165 11 method method NOUN cana-6220 165 12 from from ADP cana-6220 165 13 calculus calculus NOUN cana-6220 165 14 , , PUNCT cana-6220 165 15 we we PRON cana-6220 165 16 get get VERB cana-6220 165 17 𝑅 𝑅 PROPN cana-6220 165 18 = = PUNCT cana-6220 165 19 πœ‰1(1+πœ‰2 πœ‰1(1+πœ‰2 PROPN cana-6220 165 20 ) ) PUNCT cana-6220 165 21 ( ( PUNCT cana-6220 165 22 πœ‰1βˆ’πœ‰2 πœ‰1βˆ’πœ‰2 NOUN cana-6220 165 23 ) ) PUNCT cana-6220 165 24 + + NUM cana-6220 165 25 πœ‰1πœ‰2(1+πœ‰1)(1+πœ‰2 πœ‰1πœ‰2(1+πœ‰1)(1+πœ‰2 NUM cana-6220 165 26 ) ) PUNCT cana-6220 165 27 ) ) PUNCT cana-6220 166 1 ( ( PUNCT cana-6220 166 2 πœ‰1βˆ’πœ‰2)2 πœ‰1βˆ’πœ‰2)2 NOUN cana-6220 166 3 π‘™π‘œπ‘” π‘™π‘œπ‘” PROPN cana-6220 166 4 ( ( PUNCT cana-6220 166 5 [ [ PUNCT cana-6220 166 6 ( ( PUNCT cana-6220 166 7 1+πœ‰1)πœ‰2 1+πœ‰1)πœ‰2 INTJ cana-6220 166 8 ( ( PUNCT cana-6220 166 9 1+πœ‰2)πœ‰1 1+πœ‰2)πœ‰1 NUM cana-6220 166 10 ] ] PUNCT cana-6220 166 11 ) ) PUNCT cana-6220 166 12 ( ( PUNCT cana-6220 166 13 21 21 NUM cana-6220 166 14 ) ) PUNCT cana-6220 166 15 6 6 NUM cana-6220 166 16 . . PUNCT cana-6220 167 1 parameter parameter NOUN cana-6220 167 2 estimation estimation NOUN cana-6220 167 3 6.1 6.1 NUM cana-6220 167 4 classical classical ADJ cana-6220 167 5 estimation estimation NOUN cana-6220 167 6 procedure procedure NOUN cana-6220 167 7 the the DET cana-6220 167 8 method method NOUN cana-6220 167 9 of of ADP cana-6220 167 10 maximum maximum ADJ cana-6220 167 11 likelihood likelihood NOUN cana-6220 167 12 estimation estimation NOUN cana-6220 167 13 ( ( PUNCT cana-6220 167 14 mle mle PROPN cana-6220 167 15 ) ) PUNCT cana-6220 167 16 is be AUX cana-6220 167 17 a a DET cana-6220 167 18 key key ADJ cana-6220 167 19 classical classical ADJ cana-6220 167 20 statistical statistical ADJ cana-6220 167 21 methodology methodology NOUN cana-6220 167 22 for for ADP cana-6220 167 23 the the DET cana-6220 167 24 inference inference NOUN cana-6220 167 25 of of ADP cana-6220 167 26 parameters parameter NOUN cana-6220 167 27 of of ADP cana-6220 167 28 probability probability NOUN cana-6220 167 29 distributions distribution NOUN cana-6220 167 30 . . PUNCT cana-6220 168 1 the the DET cana-6220 168 2 method method NOUN cana-6220 168 3 operates operate VERB cana-6220 168 4 by by ADP cana-6220 168 5 identifying identify VERB cana-6220 168 6 the the DET cana-6220 168 7 set set NOUN cana-6220 168 8 of of ADP cana-6220 168 9 parameters parameter NOUN cana-6220 168 10 which which PRON cana-6220 168 11 maximizes maximize VERB cana-6220 168 12 the the DET cana-6220 168 13 value value NOUN cana-6220 168 14 of of ADP cana-6220 168 15 the the DET cana-6220 168 16 likelihood likelihood NOUN cana-6220 168 17 function function NOUN cana-6220 168 18 , , PUNCT cana-6220 168 19 which which PRON cana-6220 168 20 is be AUX cana-6220 168 21 defined define VERB cana-6220 168 22 as as ADP cana-6220 168 23 the the DET cana-6220 168 24 probability probability NOUN cana-6220 168 25 of of ADP cana-6220 168 26 the the DET cana-6220 168 27 observed observe VERB cana-6220 168 28 data datum NOUN cana-6220 168 29 under under ADP cana-6220 168 30 a a DET cana-6220 168 31 specified specified ADJ cana-6220 168 32 model model NOUN cana-6220 168 33 . . PUNCT cana-6220 169 1 for for ADP cana-6220 169 2 a a DET cana-6220 169 3 series series NOUN cana-6220 169 4 of of ADP cana-6220 169 5 i.i.d i.i.d PROPN cana-6220 169 6 . . PUNCT cana-6220 169 7 observations observation NOUN cana-6220 169 8 t1 t1 PROPN cana-6220 169 9 , , PUNCT cana-6220 169 10 t2 t2 NOUN cana-6220 169 11 , , PUNCT cana-6220 169 12 … … PUNCT cana-6220 169 13 , , PUNCT cana-6220 169 14 tn tn NOUN cana-6220 169 15 constituting constitute VERB cana-6220 169 16 a a DET cana-6220 169 17 sample sample NOUN cana-6220 169 18 of of ADP cana-6220 169 19 size size NOUN cana-6220 169 20 n n CCONJ cana-6220 169 21 from from ADP cana-6220 169 22 the the DET cana-6220 169 23 mold mold NOUN cana-6220 169 24 ( ( PUNCT cana-6220 169 25 ΞΎ ΞΎ PROPN cana-6220 169 26 , , PUNCT cana-6220 169 27 Ξ» Ξ» PROPN cana-6220 169 28 , , PUNCT cana-6220 169 29 ΞΈ ΞΈ NOUN cana-6220 169 30 ) ) PUNCT cana-6220 169 31 distribution distribution NOUN cana-6220 169 32 , , PUNCT cana-6220 169 33 we we PRON cana-6220 169 34 can can AUX cana-6220 169 35 write write VERB cana-6220 169 36 the the DET cana-6220 169 37 likelihood likelihood NOUN cana-6220 169 38 function function NOUN cana-6220 169 39 as as ADP cana-6220 169 40 : : PUNCT cana-6220 169 41 𝐿 𝐿 PROPN cana-6220 169 42 ( ( PUNCT cana-6220 169 43 𝑑 𝑑 PROPN cana-6220 169 44 , , PUNCT cana-6220 169 45 πœ‰ πœ‰ X cana-6220 169 46 , , PUNCT cana-6220 169 47 πœ† πœ† NOUN cana-6220 169 48 , , PUNCT cana-6220 169 49 πœƒ πœƒ NOUN cana-6220 169 50 ) ) PUNCT cana-6220 169 51 = = PUNCT cana-6220 170 1 πœ‰π‘›πœ†π‘›πœƒβˆ’π‘›πœ†(1 πœ‰π‘›πœ†π‘›πœƒβˆ’π‘›πœ†(1 X cana-6220 171 1 + + CCONJ cana-6220 171 2 πœ‰)𝑛 πœ‰)𝑛 X cana-6220 171 3 ∏ ∏ X cana-6220 171 4 ( ( PUNCT cana-6220 171 5 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 NOUN cana-6220 171 6 𝑖=1 𝑖=1 PUNCT cana-6220 171 7 ∏ ∏ PROPN cana-6220 171 8 [ [ X cana-6220 171 9 ( ( PUNCT cana-6220 171 10 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 171 11 ] ] PUNCT cana-6220 171 12 2𝑛 2𝑛 PROPN cana-6220 171 13 𝑖=1 𝑖=1 PROPN cana-6220 171 14 ( ( PUNCT cana-6220 171 15 22 22 NUM cana-6220 171 16 ) ) PUNCT cana-6220 171 17 using use VERB cana-6220 171 18 the the DET cana-6220 171 19 eq eq NOUN cana-6220 171 20 . . PUNCT cana-6220 171 21 ( ( PUNCT cana-6220 171 22 22 22 NUM cana-6220 171 23 ) ) PUNCT cana-6220 171 24 the the DET cana-6220 171 25 log log NOUN cana-6220 171 26 - - PUNCT cana-6220 171 27 likelihood likelihood NOUN cana-6220 171 28 function function NOUN cana-6220 171 29 is be AUX cana-6220 171 30 given give VERB cana-6220 171 31 as as ADP cana-6220 171 32 log(𝐿 log(𝐿 NOUN cana-6220 171 33 ) ) PUNCT cana-6220 171 34 = = SYM cana-6220 171 35 𝑛 𝑛 PRON cana-6220 171 36 log(ΞΎ log(ΞΎ PROPN cana-6220 171 37 ) ) PUNCT cana-6220 171 38 + + NUM cana-6220 171 39 𝑛 𝑛 PRON cana-6220 171 40 log(Ξ» log(Ξ» PROPN cana-6220 171 41 ) ) PUNCT cana-6220 171 42 βˆ’ βˆ’ PROPN cana-6220 172 1 ( ( PUNCT cana-6220 172 2 Ξ» Ξ» X cana-6220 172 3 + + NOUN cana-6220 172 4 1 1 NUM cana-6220 172 5 ) ) PUNCT cana-6220 172 6 βˆ‘ βˆ‘ PUNCT cana-6220 172 7 log(ΞΈ log(ΞΈ PROPN cana-6220 172 8 + + NOUN cana-6220 172 9 𝑑𝑖 𝑑𝑖 NOUN cana-6220 172 10 ) ) PUNCT cana-6220 172 11 𝑛 𝑛 PRON cana-6220 172 12 𝑖=1 𝑖=1 PROPN cana-6220 172 13 βˆ’ βˆ’ X cana-6220 172 14 𝑛λ 𝑛λ NUM cana-6220 172 15 log(ΞΈ log(ΞΈ PROPN cana-6220 172 16 ) ) PUNCT cana-6220 172 17 + + NOUN cana-6220 172 18 𝑛 𝑛 PRON cana-6220 172 19 π‘™π‘œπ‘”(1 π‘™π‘œπ‘”(1 NOUN cana-6220 172 20 + + CCONJ cana-6220 172 21 πœ‰ πœ‰ X cana-6220 172 22 ) ) PUNCT cana-6220 172 23 βˆ’ βˆ’ PROPN cana-6220 172 24 2 2 NUM cana-6220 172 25 βˆ‘ βˆ‘ NOUN cana-6220 172 26 π‘™π‘œπ‘” π‘™π‘œπ‘” X cana-6220 172 27 ( ( PUNCT cana-6220 172 28 ( ( PUNCT cana-6220 172 29 1 1 NUM cana-6220 172 30 + + NUM cana-6220 172 31 πœ‰)πœƒβˆ’πœ† πœ‰)πœƒβˆ’πœ† NOUN cana-6220 173 1 βˆ’ βˆ’ NOUN cana-6220 173 2 ( ( PUNCT cana-6220 173 3 πœƒ πœƒ X cana-6220 173 4 + + NUM cana-6220 173 5 𝑑𝑖 𝑑𝑖 NOUN cana-6220 173 6 ) ) PUNCT cana-6220 173 7 βˆ’πœ†)𝑛 βˆ’πœ†)𝑛 NOUN cana-6220 173 8 𝑖=1 𝑖=1 PROPN cana-6220 174 1 ( ( PUNCT cana-6220 174 2 23 23 NUM cana-6220 174 3 ) ) PUNCT cana-6220 174 4 communications communication NOUN cana-6220 174 5 on on ADP cana-6220 174 6 applied apply VERB cana-6220 174 7 nonlinear nonlinear ADJ cana-6220 174 8 analysis analysis NOUN cana-6220 174 9 issn issn NOUN cana-6220 174 10 : : PUNCT cana-6220 174 11 1074 1074 NUM cana-6220 174 12 - - PUNCT cana-6220 174 13 133x 133x NUM cana-6220 174 14 vol vol VERB cana-6220 174 15 32 32 NUM cana-6220 174 16 no no NOUN cana-6220 174 17 . . PUNCT cana-6220 175 1 10s 10 NOUN cana-6220 175 2 ( ( PUNCT cana-6220 175 3 2025 2025 NUM cana-6220 175 4 ) ) PUNCT cana-6220 175 5 3554 3554 NUM cana-6220 175 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 175 7 by by ADP cana-6220 175 8 partially partially ADV cana-6220 175 9 differentiating differentiate VERB cana-6220 175 10 log log NOUN cana-6220 175 11 likelihood likelihood NOUN cana-6220 175 12 in in ADP cana-6220 175 13 eq eq ADP cana-6220 175 14 . . PUNCT cana-6220 176 1 ( ( PUNCT cana-6220 176 2 23 23 NUM cana-6220 176 3 ) ) PUNCT cana-6220 176 4 with with ADP cana-6220 176 5 respect respect NOUN cana-6220 176 6 to to ADP cana-6220 176 7 each each DET cana-6220 176 8 parameter parameter NOUN cana-6220 176 9 , , PUNCT cana-6220 176 10 we we PRON cana-6220 176 11 get get VERB cana-6220 176 12 the the DET cana-6220 176 13 following follow VERB cana-6220 176 14 closed closed ADJ cana-6220 176 15 form form NOUN cana-6220 176 16 equations equation NOUN cana-6220 176 17 for for ADP cana-6220 176 18 the the DET cana-6220 176 19 mle mle PROPN cana-6220 176 20 for for ADP cana-6220 176 21 the the DET cana-6220 176 22 parameters parameter NOUN cana-6220 176 23 ΞΎ ΞΎ PROPN cana-6220 176 24 , , PUNCT cana-6220 176 25 Ξ» Ξ» PROPN cana-6220 176 26 and and CCONJ cana-6220 176 27 ΞΈ ΞΈ PROPN cana-6220 176 28 , , PUNCT cana-6220 176 29 respectively respectively ADV cana-6220 176 30 as as SCONJ cana-6220 176 31 πœ• πœ• NOUN cana-6220 176 32 π‘™π‘œπ‘”(𝐿 π‘™π‘œπ‘”(𝐿 NUM cana-6220 176 33 ) ) PUNCT cana-6220 176 34 πœ•πœ‰ πœ•πœ‰ VERB cana-6220 176 35 = = SYM cana-6220 176 36 𝑛 𝑛 PRON cana-6220 176 37 πœ‰ πœ‰ NOUN cana-6220 176 38 + + X cana-6220 176 39 𝑛 𝑛 PROPN cana-6220 176 40 ( ( PUNCT cana-6220 176 41 1+πœ‰ 1+πœ‰ NUM cana-6220 176 42 ) ) PUNCT cana-6220 176 43 βˆ’ βˆ’ PROPN cana-6220 176 44 2 2 NUM cana-6220 176 45 βˆ‘ βˆ‘ NOUN cana-6220 176 46 πœƒβˆ’πœ† πœƒβˆ’πœ† NOUN cana-6220 176 47 ( ( PUNCT cana-6220 176 48 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 177 1 𝑛 𝑛 PRON cana-6220 177 2 𝑖=1 𝑖=1 PROPN cana-6220 177 3 ( ( PUNCT cana-6220 177 4 24 24 NUM cana-6220 177 5 ) ) PUNCT cana-6220 177 6 πœ• πœ• NOUN cana-6220 177 7 π‘™π‘œπ‘”(𝐿 π‘™π‘œπ‘”(𝐿 NOUN cana-6220 177 8 ) ) PUNCT cana-6220 177 9 πœ•πœ† πœ•πœ† NOUN cana-6220 177 10 = = PUNCT cana-6220 177 11 𝑛 𝑛 PROPN cana-6220 177 12 πœ† πœ† PRON cana-6220 177 13 βˆ’ βˆ’ PROPN cana-6220 177 14 𝑛 𝑛 PROPN cana-6220 177 15 π‘™π‘œπ‘”(πœƒ π‘™π‘œπ‘”(πœƒ PROPN cana-6220 177 16 ) ) PUNCT cana-6220 177 17 βˆ’ βˆ’ NOUN cana-6220 178 1 βˆ‘ βˆ‘ PUNCT cana-6220 178 2 π‘™π‘œπ‘”(πœƒ π‘™π‘œπ‘”(πœƒ PROPN cana-6220 178 3 + + CCONJ cana-6220 178 4 𝑑𝑖 𝑑𝑖 NOUN cana-6220 178 5 ) ) PUNCT cana-6220 178 6 𝑛 𝑛 PRON cana-6220 178 7 𝑖=1 𝑖=1 PUNCT cana-6220 179 1 + + CCONJ cana-6220 179 2 2 2 NUM cana-6220 179 3 βˆ‘ βˆ‘ PUNCT cana-6220 179 4 ( ( PUNCT cana-6220 179 5 1+πœ‰)πœƒβˆ’πœ† 1+πœ‰)πœƒβˆ’πœ† NUM cana-6220 179 6 π‘™π‘œπ‘”(πœƒ)βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† π‘™π‘œπ‘”(πœƒ)βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† PROPN cana-6220 179 7 π‘™π‘œπ‘”(πœƒ+𝑑𝑖 π‘™π‘œπ‘”(πœƒ+𝑑𝑖 NOUN cana-6220 179 8 ) ) PUNCT cana-6220 179 9 ( ( PUNCT cana-6220 179 10 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 179 11 𝑛 𝑛 PRON cana-6220 179 12 𝑖=1 𝑖=1 PROPN cana-6220 179 13 ( ( PUNCT cana-6220 179 14 25 25 NUM cana-6220 179 15 ) ) PUNCT cana-6220 179 16 πœ• πœ• NOUN cana-6220 179 17 π‘™π‘œπ‘”(𝐿 π‘™π‘œπ‘”(𝐿 NOUN cana-6220 179 18 ) ) PUNCT cana-6220 179 19 πœ•πœƒ πœ•πœƒ NOUN cana-6220 180 1 = = SYM cana-6220 180 2 βˆ’π‘›πœ† βˆ’π‘›πœ† PROPN cana-6220 180 3 πœƒ πœƒ NOUN cana-6220 180 4 βˆ’ βˆ’ PROPN cana-6220 180 5 ( ( PUNCT cana-6220 180 6 πœ†+1 πœ†+1 X cana-6220 180 7 ) ) PUNCT cana-6220 180 8 πœƒ πœƒ NOUN cana-6220 180 9 βˆ‘ βˆ‘ ADP cana-6220 180 10 1 1 NUM cana-6220 180 11 1+𝑑𝑖/πœƒ 1+𝑑𝑖/πœƒ NUM cana-6220 180 12 𝑛 𝑛 PRON cana-6220 180 13 𝑖=1 𝑖=1 PUNCT cana-6220 181 1 + + CCONJ cana-6220 181 2 2 2 NUM cana-6220 181 3 βˆ‘ βˆ‘ NOUN cana-6220 181 4 πœ†(1+πœ‰)πœƒβˆ’(πœ†+1)βˆ’πœ†(πœƒ+𝑑𝑖)βˆ’(πœ†+1 πœ†(1+πœ‰)πœƒβˆ’(πœ†+1)βˆ’πœ†(πœƒ+𝑑𝑖)βˆ’(πœ†+1 NOUN cana-6220 181 5 ) ) PUNCT cana-6220 181 6 ( ( PUNCT cana-6220 181 7 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 181 8 𝑛 𝑛 PRON cana-6220 181 9 𝑖=1 𝑖=1 PROPN cana-6220 181 10 ( ( PUNCT cana-6220 181 11 26 26 NUM cana-6220 181 12 ) ) PUNCT cana-6220 181 13 the the DET cana-6220 181 14 above above ADJ cana-6220 181 15 non non ADJ cana-6220 181 16 - - ADJ cana-6220 181 17 linear linear ADJ cana-6220 181 18 equations equation NOUN cana-6220 181 19 can can AUX cana-6220 181 20 not not PART cana-6220 181 21 be be AUX cana-6220 181 22 solved solve VERB cana-6220 181 23 analytically analytically ADV cana-6220 181 24 so so ADV cana-6220 181 25 , , PUNCT cana-6220 181 26 the the DET cana-6220 181 27 mle mle NOUN cana-6220 181 28 of of ADP cana-6220 181 29 the the DET cana-6220 181 30 parameters parameter NOUN cana-6220 181 31 ΞΎ ΞΎ PROPN cana-6220 181 32 , , PUNCT cana-6220 181 33 Ξ» Ξ» PROPN cana-6220 181 34 and and CCONJ cana-6220 181 35 ΞΈ ΞΈ PROPN cana-6220 181 36 can can AUX cana-6220 181 37 be be AUX cana-6220 181 38 obtained obtain VERB cana-6220 181 39 as as ADP cana-6220 181 40 the the DET cana-6220 181 41 numerical numerical ADJ cana-6220 181 42 solution solution NOUN cana-6220 181 43 of of ADP cana-6220 181 44 the the DET cana-6220 181 45 eq eq NOUN cana-6220 181 46 . . PUNCT cana-6220 182 1 ( ( PUNCT cana-6220 182 2 24 24 NUM cana-6220 182 3 ) ) PUNCT cana-6220 182 4 , , PUNCT cana-6220 182 5 ( ( PUNCT cana-6220 182 6 25 25 NUM cana-6220 182 7 ) ) PUNCT cana-6220 182 8 and and CCONJ cana-6220 182 9 ( ( PUNCT cana-6220 182 10 26 26 NUM cana-6220 182 11 ) ) PUNCT cana-6220 182 12 , , PUNCT cana-6220 182 13 respectively respectively ADV cana-6220 182 14 . . PUNCT cana-6220 183 1 6.2 6.2 NUM cana-6220 183 2 bayesian bayesian NOUN cana-6220 183 3 estimation estimation NOUN cana-6220 183 4 in in ADP cana-6220 183 5 this this DET cana-6220 183 6 section section NOUN cana-6220 183 7 we we PRON cana-6220 183 8 used use VERB cana-6220 183 9 bayesian bayesian NOUN cana-6220 183 10 parameter parameter NOUN cana-6220 183 11 estimation estimation NOUN cana-6220 183 12 methods method NOUN cana-6220 183 13 for for ADP cana-6220 183 14 the the DET cana-6220 183 15 modi modi PROPN cana-6220 183 16 - - PUNCT cana-6220 183 17 lomax lomax PROPN cana-6220 183 18 distribution distribution NOUN cana-6220 183 19 's 's PART cana-6220 183 20 parameters parameter NOUN cana-6220 183 21 . . PUNCT cana-6220 184 1 bayesian bayesian NOUN cana-6220 184 2 inference inference NOUN cana-6220 184 3 demands demand VERB cana-6220 184 4 appropriate appropriate ADJ cana-6220 184 5 prior prior ADJ cana-6220 184 6 distribution distribution NOUN cana-6220 184 7 selection selection NOUN cana-6220 184 8 to to PART cana-6220 184 9 incorporate incorporate VERB cana-6220 184 10 available available ADJ cana-6220 184 11 information information NOUN cana-6220 184 12 or or CCONJ cana-6220 184 13 parameter parameter NOUN cana-6220 184 14 assumptions assumption NOUN cana-6220 184 15 . . PUNCT cana-6220 185 1 here here ADV cana-6220 185 2 , , PUNCT cana-6220 185 3 we we PRON cana-6220 185 4 employ employ VERB cana-6220 185 5 gamma gamma NOUN cana-6220 185 6 prior prior ADJ cana-6220 185 7 distributions distribution NOUN cana-6220 185 8 for for ADP cana-6220 185 9 estimating estimate VERB cana-6220 185 10 parameters parameter NOUN cana-6220 185 11 , , PUNCT cana-6220 185 12 which which PRON cana-6220 185 13 are be AUX cana-6220 185 14 suitable suitable ADJ cana-6220 185 15 due due ADJ cana-6220 185 16 to to ADP cana-6220 185 17 positive positive ADJ cana-6220 185 18 parameter parameter NOUN cana-6220 185 19 space space NOUN cana-6220 185 20 restrictions restriction NOUN cana-6220 185 21 . . PUNCT cana-6220 186 1 the the DET cana-6220 186 2 parameters parameter NOUN cana-6220 186 3 are be AUX cana-6220 186 4 assumed assume VERB cana-6220 186 5 to to PART cana-6220 186 6 be be AUX cana-6220 186 7 independent independent ADJ cana-6220 186 8 and and CCONJ cana-6220 186 9 have have VERB cana-6220 186 10 gamma gamma NOUN cana-6220 186 11 prior prior ADJ cana-6220 186 12 distributions distribution NOUN cana-6220 186 13 such such ADJ cana-6220 186 14 that that SCONJ cana-6220 186 15 ΞΎ ΞΎ ADP cana-6220 186 16 ∼ ∼ NOUN cana-6220 186 17 gamma(a1 gamma(a1 NOUN cana-6220 186 18 , , PUNCT cana-6220 186 19 b1 b1 NOUN cana-6220 186 20 ) ) PUNCT cana-6220 186 21 , , PUNCT cana-6220 186 22 Ξ» Ξ» PROPN cana-6220 186 23 ∼ ∼ NOUN cana-6220 186 24 gamma(a2 gamma(a2 NOUN cana-6220 186 25 , , PUNCT cana-6220 186 26 b2 b2 NOUN cana-6220 186 27 ) ) PUNCT cana-6220 186 28 and and CCONJ cana-6220 186 29 ΞΈ ΞΈ PROPN cana-6220 186 30 ∼ ∼ NOUN cana-6220 186 31 gamma(a3 gamma(a3 NOUN cana-6220 186 32 , , PUNCT cana-6220 186 33 b3 b3 PROPN cana-6220 186 34 ) ) PUNCT cana-6220 186 35 . . PUNCT cana-6220 187 1 hence hence ADV cana-6220 187 2 the the DET cana-6220 187 3 joint joint ADJ cana-6220 187 4 prior prior ADJ cana-6220 187 5 density density NOUN cana-6220 187 6 of of ADP cana-6220 187 7 ΞΎ ΞΎ PROPN cana-6220 187 8 , , PUNCT cana-6220 187 9 Ξ» Ξ» PROPN cana-6220 187 10 and and CCONJ cana-6220 187 11 ΞΈ ΞΈ PROPN cana-6220 187 12 is be AUX cana-6220 187 13 given give VERB cana-6220 187 14 by by ADP cana-6220 187 15 πœ“(πœ‰ πœ“(πœ‰ NOUN cana-6220 187 16 , , PUNCT cana-6220 187 17 πœ† πœ† NOUN cana-6220 187 18 , , PUNCT cana-6220 187 19 πœƒ πœƒ NOUN cana-6220 187 20 ) ) PUNCT cana-6220 187 21 ∝ ∝ PROPN cana-6220 187 22 πœ‰π‘Ž1βˆ’1π‘’βˆ’π‘1πœ‰πœ†π‘Ž2βˆ’1π‘’βˆ’π‘2πœ†πœƒπ‘Ž3βˆ’1π‘’βˆ’π‘3πœƒ πœ‰π‘Ž1βˆ’1π‘’βˆ’π‘1πœ‰πœ†π‘Ž2βˆ’1π‘’βˆ’π‘2πœ†πœƒπ‘Ž3βˆ’1π‘’βˆ’π‘3πœƒ PROPN cana-6220 187 23 ( ( PUNCT cana-6220 187 24 27 27 NUM cana-6220 187 25 ) ) PUNCT cana-6220 187 26 where where SCONJ cana-6220 187 27 a1 a1 NOUN cana-6220 187 28 , , PUNCT cana-6220 187 29 b1 b1 NOUN cana-6220 187 30 , , PUNCT cana-6220 187 31 a2 a2 PROPN cana-6220 187 32 , , PUNCT cana-6220 187 33 b2 b2 NOUN cana-6220 187 34 , , PUNCT cana-6220 187 35 a3 a3 NOUN cana-6220 187 36 and and CCONJ cana-6220 187 37 b3 b3 PROPN cana-6220 187 38 are be AUX cana-6220 187 39 the the DET cana-6220 187 40 hyper hyper ADJ cana-6220 187 41 parameters parameter NOUN cana-6220 187 42 . . PUNCT cana-6220 188 1 the the DET cana-6220 188 2 hyper hyper NOUN cana-6220 188 3 - - NOUN cana-6220 188 4 parameters parameter NOUN cana-6220 188 5 in in ADP cana-6220 188 6 the the DET cana-6220 188 7 prior prior ADJ cana-6220 188 8 distributions distribution NOUN cana-6220 188 9 are be AUX cana-6220 188 10 assumed assume VERB cana-6220 188 11 to to PART cana-6220 188 12 be be AUX cana-6220 188 13 known know VERB cana-6220 188 14 . . PUNCT cana-6220 189 1 the the DET cana-6220 189 2 choice choice NOUN cana-6220 189 3 of of ADP cana-6220 189 4 loss loss NOUN cana-6220 189 5 function function NOUN cana-6220 189 6 is be AUX cana-6220 189 7 pivotal pivotal ADJ cana-6220 189 8 in in ADP cana-6220 189 9 bayesian bayesian NOUN cana-6220 189 10 decision decision NOUN cana-6220 189 11 theory theory NOUN cana-6220 189 12 , , PUNCT cana-6220 189 13 as as SCONJ cana-6220 189 14 it it PRON cana-6220 189 15 quantifies quantify VERB cana-6220 189 16 the the DET cana-6220 189 17 penalty penalty NOUN cana-6220 189 18 for for ADP cana-6220 189 19 estimation estimation NOUN cana-6220 189 20 errors error NOUN cana-6220 189 21 . . PUNCT cana-6220 190 1 here here ADV cana-6220 190 2 , , PUNCT cana-6220 190 3 we we PRON cana-6220 190 4 adopt adopt VERB cana-6220 190 5 the the DET cana-6220 190 6 squared square VERB cana-6220 190 7 error error NOUN cana-6220 190 8 loss loss NOUN cana-6220 190 9 function function NOUN cana-6220 190 10 ( ( PUNCT cana-6220 190 11 self self NOUN cana-6220 190 12 ) ) PUNCT cana-6220 190 13 , , PUNCT cana-6220 190 14 defined define VERB cana-6220 190 15 as as ADP cana-6220 190 16 : : PUNCT cana-6220 190 17 𝐿𝑠(Ξ± 𝐿𝑠(Ξ± NOUN cana-6220 190 18 , , PUNCT cana-6220 190 19 Ξ±Μ‚ Ξ±Μ‚ NUM cana-6220 190 20 ) ) PUNCT cana-6220 191 1 = = PRON cana-6220 191 2 ( ( PUNCT cana-6220 191 3 Ξ± Ξ± X cana-6220 191 4 , , PUNCT cana-6220 191 5 Ξ±Μ‚)2 Ξ±Μ‚)2 NOUN cana-6220 191 6 where where SCONJ cana-6220 191 7 Ξ± Ξ± NOUN cana-6220 191 8 is be AUX cana-6220 191 9 the the DET cana-6220 191 10 true true ADJ cana-6220 191 11 parameter parameter NOUN cana-6220 191 12 and and CCONJ cana-6220 191 13 Ξ±Μ‚ Ξ±Μ‚ NUM cana-6220 191 14 is be AUX cana-6220 191 15 its its PRON cana-6220 191 16 estimator estimator NOUN cana-6220 191 17 . . PUNCT cana-6220 192 1 the the DET cana-6220 192 2 self self NOUN cana-6220 192 3 is be AUX cana-6220 192 4 symmetric symmetric ADJ cana-6220 192 5 and and CCONJ cana-6220 192 6 penalizes penalize NOUN cana-6220 192 7 over over ADP cana-6220 192 8 and and CCONJ cana-6220 192 9 under under ADP cana-6220 192 10 estimation estimation NOUN cana-6220 192 11 equally equally ADV cana-6220 192 12 , , PUNCT cana-6220 192 13 yielding yield VERB cana-6220 192 14 the the DET cana-6220 192 15 posterior posterior ADJ cana-6220 192 16 mean mean NOUN cana-6220 192 17 as as ADP cana-6220 192 18 the the DET cana-6220 192 19 optimal optimal ADJ cana-6220 192 20 estimator estimator NOUN cana-6220 192 21 . . PUNCT cana-6220 193 1 this this DET cana-6220 193 2 approach approach NOUN cana-6220 193 3 balances balance VERB cana-6220 193 4 computational computational ADJ cana-6220 193 5 tractability tractability NOUN cana-6220 193 6 with with ADP cana-6220 193 7 theoretical theoretical ADJ cana-6220 193 8 rigor rigor NOUN cana-6220 193 9 , , PUNCT cana-6220 193 10 making make VERB cana-6220 193 11 it it PRON cana-6220 193 12 widely widely ADV cana-6220 193 13 used use VERB cana-6220 193 14 in in ADP cana-6220 193 15 reliability reliability NOUN cana-6220 193 16 and and CCONJ cana-6220 193 17 survival survival NOUN cana-6220 193 18 analysis analysis NOUN cana-6220 193 19 . . PUNCT cana-6220 194 1 by by ADP cana-6220 194 2 employing employ VERB cana-6220 194 3 the the DET cana-6220 194 4 likelihood likelihood NOUN cana-6220 194 5 function function NOUN cana-6220 194 6 in in ADP cana-6220 194 7 eq eq ADP cana-6220 194 8 . . PUNCT cana-6220 195 1 ( ( PUNCT cana-6220 195 2 22 22 NUM cana-6220 195 3 ) ) PUNCT cana-6220 195 4 with with ADP cana-6220 195 5 the the DET cana-6220 195 6 joint joint ADJ cana-6220 195 7 prior prior ADJ cana-6220 195 8 distribution distribution NOUN cana-6220 195 9 in in ADP cana-6220 195 10 eq eq ADP cana-6220 195 11 . . PUNCT cana-6220 196 1 ( ( PUNCT cana-6220 196 2 28 28 NUM cana-6220 196 3 ) ) PUNCT cana-6220 196 4 , , PUNCT cana-6220 196 5 the the DET cana-6220 196 6 joint joint ADJ cana-6220 196 7 posterior posterior ADJ cana-6220 196 8 distribution distribution NOUN cana-6220 196 9 of of ADP cana-6220 196 10 ΞΎ ΞΎ PROPN cana-6220 196 11 , , PUNCT cana-6220 196 12 Ξ» Ξ» PROPN cana-6220 196 13 and and CCONJ cana-6220 196 14 ΞΈ ΞΈ PROPN cana-6220 196 15 can can AUX cana-6220 196 16 be be AUX cana-6220 196 17 expressed express VERB cana-6220 196 18 in in ADP cana-6220 196 19 the the DET cana-6220 196 20 following follow VERB cana-6220 196 21 form form NOUN cana-6220 196 22 : : PUNCT cana-6220 196 23 Ο€(ΞΎ Ο€(ΞΎ PROPN cana-6220 196 24 , , PUNCT cana-6220 196 25 Ξ» Ξ» PROPN cana-6220 196 26 , , PUNCT cana-6220 196 27 ΞΈ ΞΈ NOUN cana-6220 196 28 ) ) PUNCT cana-6220 196 29 ∝ ∝ PROPN cana-6220 196 30 ΞΎπ‘Ž1+π‘›βˆ’1Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 ΞΎπ‘Ž1+π‘›βˆ’1Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 PROPN cana-6220 196 31 + + CCONJ cana-6220 196 32 ΞΎ)𝑛 ΞΎ)𝑛 ADJ cana-6220 196 33 ∏ ∏ X cana-6220 196 34 ( ( PUNCT cana-6220 196 35 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 196 36 𝑖=1 𝑖=1 PUNCT cana-6220 196 37 ∏ ∏ PROPN cana-6220 197 1 [ [ X cana-6220 197 2 ( ( PUNCT cana-6220 197 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 197 4 ] ] PUNCT cana-6220 197 5 2𝑛 2𝑛 PROPN cana-6220 197 6 𝑖=1 𝑖=1 PROPN cana-6220 197 7 ( ( PUNCT cana-6220 197 8 28 28 NUM cana-6220 197 9 ) ) PUNCT cana-6220 197 10 communications communication NOUN cana-6220 197 11 on on ADP cana-6220 197 12 applied apply VERB cana-6220 197 13 nonlinear nonlinear ADJ cana-6220 197 14 analysis analysis NOUN cana-6220 197 15 issn issn NOUN cana-6220 197 16 : : PUNCT cana-6220 197 17 1074 1074 NUM cana-6220 197 18 - - PUNCT cana-6220 197 19 133x 133x NUM cana-6220 197 20 vol vol VERB cana-6220 197 21 32 32 NUM cana-6220 197 22 no no NOUN cana-6220 197 23 . . PUNCT cana-6220 198 1 10s 10 NOUN cana-6220 198 2 ( ( PUNCT cana-6220 198 3 2025 2025 NUM cana-6220 198 4 ) ) PUNCT cana-6220 198 5 3555 3555 NUM cana-6220 198 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 199 1 the the DET cana-6220 199 2 bayes bayes PROPN cana-6220 199 3 estimators estimator NOUN cana-6220 199 4 under under ADP cana-6220 199 5 the the DET cana-6220 199 6 self self NOUN cana-6220 199 7 loss loss NOUN cana-6220 199 8 function function NOUN cana-6220 199 9 is be AUX cana-6220 199 10 the the DET cana-6220 199 11 posterior posterior ADJ cana-6220 199 12 mean mean NOUN cana-6220 199 13 of of ADP cana-6220 199 14 the the DET cana-6220 199 15 posterior posterior ADJ cana-6220 199 16 distribution distribution NOUN cana-6220 199 17 , , PUNCT cana-6220 199 18 are be AUX cana-6220 199 19 given give VERB cana-6220 199 20 as as ADP cana-6220 199 21 , , PUNCT cana-6220 199 22 ΞΎΜ‚ ΞΎΜ‚ NUM cana-6220 199 23 = = SYM cana-6220 199 24 1 1 NUM cana-6220 199 25 Ξ΄ Ξ΄ NOUN cana-6220 199 26 ∫ ∫ PROPN cana-6220 199 27 ∫ ∫ PROPN cana-6220 199 28 βˆ«ΞΎπ‘Ž1+𝑛 βˆ«ΞΎπ‘Ž1+𝑛 PROPN cana-6220 199 29 θλξ θλξ NOUN cana-6220 199 30 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 X cana-6220 199 31 + + CCONJ cana-6220 199 32 ΞΎ)𝑛 ΞΎ)𝑛 ADJ cana-6220 199 33 ∏ ∏ X cana-6220 199 34 ( ( PUNCT cana-6220 199 35 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 199 36 𝑖=1 𝑖=1 PUNCT cana-6220 199 37 ∏ ∏ PROPN cana-6220 200 1 [ [ X cana-6220 200 2 ( ( PUNCT cana-6220 200 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 200 4 ] ] PUNCT cana-6220 200 5 2𝑛 2𝑛 PROPN cana-6220 200 6 𝑖=1 𝑖=1 PUNCT cana-6220 200 7     SPACE cana-6220 200 8 π‘‘πœ‰ π‘‘πœ‰ ADP cana-6220 200 9     SPACE cana-6220 200 10 π‘‘πœ† π‘‘πœ† NOUN cana-6220 200 11     SPACE cana-6220 200 12 𝑑 𝑑 PROPN cana-6220 200 13 ( ( PUNCT cana-6220 200 14 29 29 NUM cana-6220 200 15 ) ) PUNCT cana-6220 200 16 Ξ»Μ‚ Ξ»Μ‚ X cana-6220 201 1 = = SYM cana-6220 201 2 1 1 NUM cana-6220 201 3 Ξ΄ Ξ΄ NOUN cana-6220 201 4 ∫ ∫ PROPN cana-6220 201 5 ∫ ∫ PROPN cana-6220 201 6 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 NOUN cana-6220 201 7 θλξ θλξ AUX cana-6220 201 8 Ξ»π‘Ž2+π‘›ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 Ξ»π‘Ž2+π‘›ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 PROPN cana-6220 201 9 + + CCONJ cana-6220 201 10 ΞΎ)𝑛 ΞΎ)𝑛 ADJ cana-6220 201 11 ∏ ∏ X cana-6220 201 12 ( ( PUNCT cana-6220 201 13 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 201 14 𝑖=1 𝑖=1 PUNCT cana-6220 201 15 ∏ ∏ PROPN cana-6220 202 1 [ [ X cana-6220 202 2 ( ( PUNCT cana-6220 202 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 202 4 ] ] PUNCT cana-6220 202 5 2𝑛 2𝑛 PROPN cana-6220 202 6 𝑖=1 𝑖=1 PUNCT cana-6220 202 7     SPACE cana-6220 202 8 π‘‘πœ‰ π‘‘πœ‰ ADP cana-6220 202 9     SPACE cana-6220 202 10 π‘‘πœ† π‘‘πœ† NOUN cana-6220 202 11     SPACE cana-6220 202 12 𝑑 𝑑 PROPN cana-6220 202 13 ( ( PUNCT cana-6220 202 14 30 30 NUM cana-6220 202 15 ) ) PUNCT cana-6220 202 16 and and CCONJ cana-6220 202 17 ΞΈΜ‚ ΞΈΜ‚ NUM cana-6220 202 18 = = SYM cana-6220 202 19 1 1 NUM cana-6220 202 20 Ξ΄ Ξ΄ NOUN cana-6220 202 21 ∫ ∫ PROPN cana-6220 202 22 ∫ ∫ PROPN cana-6220 203 1 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 NOUN cana-6220 203 2 θλξ θλξ AUX cana-6220 203 3 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 PROPN cana-6220 203 4 + + CCONJ cana-6220 203 5 ΞΎ)𝑛 ΞΎ)𝑛 ADJ cana-6220 203 6 ∏ ∏ X cana-6220 203 7 ( ( PUNCT cana-6220 203 8 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 203 9 𝑖=1 𝑖=1 PUNCT cana-6220 203 10 ∏ ∏ PROPN cana-6220 204 1 [ [ X cana-6220 204 2 ( ( PUNCT cana-6220 204 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 204 4 ] ] PUNCT cana-6220 204 5 2𝑛 2𝑛 PROPN cana-6220 204 6 𝑖=1 𝑖=1 PUNCT cana-6220 204 7     SPACE cana-6220 204 8 π‘‘πœ‰ π‘‘πœ‰ ADP cana-6220 204 9     SPACE cana-6220 204 10 π‘‘πœ† π‘‘πœ† NOUN cana-6220 204 11     SPACE cana-6220 204 12 𝑑 𝑑 PROPN cana-6220 204 13 ( ( PUNCT cana-6220 204 14 31 31 NUM cana-6220 204 15 ) ) PUNCT cana-6220 204 16 respectively respectively ADV cana-6220 204 17 , , PUNCT cana-6220 204 18 where where SCONJ cana-6220 204 19 Ξ΄ Ξ΄ PROPN cana-6220 204 20 = = SYM cana-6220 204 21 ∫ ∫ PROPN cana-6220 204 22 ∫ ∫ PROPN cana-6220 204 23 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 βˆ«ΞΎπ‘Ž1+π‘›βˆ’1 NOUN cana-6220 204 24 θλξ θλξ ADJ cana-6220 204 25 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 Ξ»π‘Ž2+π‘›βˆ’1ΞΈπ‘Ž3βˆ’π‘›Ξ»βˆ’1π‘’βˆ’π‘1ΞΎβˆ’π‘2Ξ»βˆ’π‘3ΞΈ(1 X cana-6220 204 26 + + CCONJ cana-6220 204 27 ΞΎ)𝑛 ΞΎ)𝑛 ADJ cana-6220 204 28 ∏ ∏ X cana-6220 204 29 ( ( PUNCT cana-6220 204 30 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 204 31 𝑖=1 𝑖=1 PUNCT cana-6220 204 32 ∏ ∏ PROPN cana-6220 205 1 [ [ X cana-6220 205 2 ( ( PUNCT cana-6220 205 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 205 4 ] ] PUNCT cana-6220 205 5 2𝑛 2𝑛 PROPN cana-6220 205 6 𝑖=1 𝑖=1 PUNCT cana-6220 205 7     SPACE cana-6220 205 8 π‘‘πœ‰ π‘‘πœ‰ ADP cana-6220 205 9     SPACE cana-6220 205 10 π‘‘πœ† π‘‘πœ† NOUN cana-6220 205 11     SPACE cana-6220 205 12 𝑑 𝑑 VERB cana-6220 205 13 the the DET cana-6220 205 14 mathematical mathematical ADJ cana-6220 205 15 intricacy intricacy NOUN cana-6220 205 16 of of ADP cana-6220 205 17 posterior posterior ADJ cana-6220 205 18 expectations expectation NOUN cana-6220 205 19 from from ADP cana-6220 205 20 mathematically mathematically ADV cana-6220 205 21 formulated formulate VERB cana-6220 205 22 expressions expression NOUN cana-6220 205 23 inherently inherently ADV cana-6220 205 24 renders render VERB cana-6220 205 25 it it PRON cana-6220 205 26 difficult difficult ADJ cana-6220 205 27 to to PART cana-6220 205 28 obtain obtain VERB cana-6220 205 29 closed closed ADJ cana-6220 205 30 - - PUNCT cana-6220 205 31 form form NOUN cana-6220 205 32 analytical analytical ADJ cana-6220 205 33 solutions solution NOUN cana-6220 205 34 . . PUNCT cana-6220 206 1 to to PART cana-6220 206 2 avoid avoid VERB cana-6220 206 3 this this DET cana-6220 206 4 computational computational ADJ cana-6220 206 5 hurdle hurdle NOUN cana-6220 206 6 , , PUNCT cana-6220 206 7 researchers researcher NOUN cana-6220 206 8 can can AUX cana-6220 206 9 utilize utilize VERB cana-6220 206 10 a a DET cana-6220 206 11 number number NOUN cana-6220 206 12 of of ADP cana-6220 206 13 bayesian bayesian NOUN cana-6220 206 14 approximation approximation NOUN cana-6220 206 15 techniques technique NOUN cana-6220 206 16 , , PUNCT cana-6220 206 17 including include VERB cana-6220 206 18 lindley lindley NOUN cana-6220 206 19 's 's PART cana-6220 206 20 approximation approximation NOUN cana-6220 206 21 , , PUNCT cana-6220 206 22 tierney tierney PROPN cana-6220 206 23 - - PUNCT cana-6220 206 24 kadane kadane PROPN cana-6220 206 25 's 's PART cana-6220 206 26 method method NOUN cana-6220 206 27 , , PUNCT cana-6220 206 28 or or CCONJ cana-6220 206 29 markov markov NOUN cana-6220 206 30 chain chain NOUN cana-6220 206 31 monte monte PROPN cana-6220 206 32 carlo carlo PROPN cana-6220 206 33 ( ( PUNCT cana-6220 206 34 mcmc mcmc PROPN cana-6220 206 35 ) ) PUNCT cana-6220 206 36 techniques technique NOUN cana-6220 206 37 . . PUNCT cana-6220 207 1 in in ADP cana-6220 207 2 our our PRON cana-6220 207 3 study study NOUN cana-6220 207 4 , , PUNCT cana-6220 207 5 we we PRON cana-6220 207 6 use use VERB cana-6220 207 7 mcmc mcmc NOUN cana-6220 207 8 sampling sample VERB cana-6220 207 9 to to PART cana-6220 207 10 approximate approximate VERB cana-6220 207 11 the the DET cana-6220 207 12 posterior posterior ADJ cana-6220 207 13 expectations expectation NOUN cana-6220 207 14 , , PUNCT cana-6220 207 15 as as SCONJ cana-6220 207 16 described describe VERB cana-6220 207 17 in in ADP cana-6220 207 18 the the DET cana-6220 207 19 next next ADJ cana-6220 207 20 section section NOUN cana-6220 207 21 . . PUNCT cana-6220 208 1 6.3 6.3 NUM cana-6220 208 2 markov markov PROPN cana-6220 208 3 chain chain NOUN cana-6220 208 4 monte monte PROPN cana-6220 208 5 carlo carlo PROPN cana-6220 208 6 ( ( PUNCT cana-6220 208 7 mcmc mcmc PROPN cana-6220 208 8 ) ) PUNCT cana-6220 208 9 method method NOUN cana-6220 208 10 we we PRON cana-6220 208 11 must must AUX cana-6220 208 12 first first ADV cana-6220 208 13 determine determine VERB cana-6220 208 14 the the DET cana-6220 208 15 complete complete ADJ cana-6220 208 16 conditional conditional ADJ cana-6220 208 17 distributions distribution NOUN cana-6220 208 18 of of ADP cana-6220 208 19 the the DET cana-6220 208 20 ΞΎ ΞΎ PROPN cana-6220 208 21 , , PUNCT cana-6220 208 22 Ξ» Ξ» PROPN cana-6220 208 23 , , PUNCT cana-6220 208 24 and and CCONJ cana-6220 208 25 ΞΈ ΞΈ NOUN cana-6220 208 26 in in ADP cana-6220 208 27 order order NOUN cana-6220 208 28 to to PART cana-6220 208 29 apply apply VERB cana-6220 208 30 the the DET cana-6220 208 31 mcmc mcmc PROPN cana-6220 208 32 approach approach NOUN cana-6220 208 33 , , PUNCT cana-6220 208 34 as as SCONJ cana-6220 208 35 indicated indicate VERB cana-6220 208 36 below below ADV cana-6220 208 37 . . PUNCT cana-6220 209 1 πœ‹βˆ—(πœ‰|πœ† πœ‹βˆ—(πœ‰|πœ† NOUN cana-6220 209 2 , , PUNCT cana-6220 209 3 πœƒ πœƒ NOUN cana-6220 209 4 , , PUNCT cana-6220 209 5 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 209 6 ) ) PUNCT cana-6220 209 7 ∝ ∝ PROPN cana-6220 209 8 πœ‰π‘Ž1+π‘›βˆ’1π‘’βˆ’π‘1πœ‰(1 πœ‰π‘Ž1+π‘›βˆ’1π‘’βˆ’π‘1πœ‰(1 PROPN cana-6220 210 1 + + CCONJ cana-6220 210 2 πœ‰)𝑛 πœ‰)𝑛 ADJ cana-6220 210 3 1 1 NUM cana-6220 210 4 ∏ ∏ NUM cana-6220 210 5 [ [ X cana-6220 210 6 ( ( PUNCT cana-6220 210 7 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 210 8 ] ] PUNCT cana-6220 210 9 2𝑛 2𝑛 PROPN cana-6220 210 10 𝑖=1 𝑖=1 PROPN cana-6220 210 11 ( ( PUNCT cana-6220 210 12 32 32 NUM cana-6220 210 13 ) ) PUNCT cana-6220 210 14 πœ‹βˆ—(πœ†|πœ‰ πœ‹βˆ—(πœ†|πœ‰ PROPN cana-6220 210 15 , , PUNCT cana-6220 210 16 πœƒ πœƒ NOUN cana-6220 210 17 , , PUNCT cana-6220 210 18 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 210 19 ) ) PUNCT cana-6220 210 20 ∝ ∝ PROPN cana-6220 210 21 πœ†π‘Ž2+π‘›βˆ’1πœƒβˆ’π‘›πœ†π‘’βˆ’π‘2πœ† πœ†π‘Ž2+π‘›βˆ’1πœƒβˆ’π‘›πœ†π‘’βˆ’π‘2πœ† VERB cana-6220 210 22 ∏ ∏ PROPN cana-6220 210 23 ( ( PUNCT cana-6220 210 24 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 210 25 𝑖=1 𝑖=1 PUNCT cana-6220 210 26 ∏ ∏ PROPN cana-6220 211 1 [ [ X cana-6220 211 2 ( ( PUNCT cana-6220 211 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 211 4 ] ] PUNCT cana-6220 211 5 2𝑛 2𝑛 PROPN cana-6220 211 6 𝑖=1 𝑖=1 PROPN cana-6220 211 7 ( ( PUNCT cana-6220 211 8 33 33 NUM cana-6220 211 9 ) ) PUNCT cana-6220 211 10 and and CCONJ cana-6220 211 11 communications communication NOUN cana-6220 211 12 on on ADP cana-6220 211 13 applied apply VERB cana-6220 211 14 nonlinear nonlinear ADJ cana-6220 211 15 analysis analysis NOUN cana-6220 211 16 issn issn NOUN cana-6220 211 17 : : PUNCT cana-6220 211 18 1074 1074 NUM cana-6220 211 19 - - PUNCT cana-6220 211 20 133x 133x NUM cana-6220 211 21 vol vol VERB cana-6220 211 22 32 32 NUM cana-6220 211 23 no no NOUN cana-6220 211 24 . . PUNCT cana-6220 212 1 10s 10 NOUN cana-6220 212 2 ( ( PUNCT cana-6220 212 3 2025 2025 NUM cana-6220 212 4 ) ) PUNCT cana-6220 212 5 3556 3556 NUM cana-6220 212 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 212 7 πœ‹βˆ—(πœƒ|πœ‰ πœ‹βˆ—(πœƒ|πœ‰ NOUN cana-6220 212 8 , , PUNCT cana-6220 212 9 πœ† πœ† NOUN cana-6220 212 10 , , PUNCT cana-6220 212 11 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 212 12 ) ) PUNCT cana-6220 212 13 ∝ ∝ PROPN cana-6220 212 14 πœƒπ‘Ž3βˆ’π‘›πœ†βˆ’1π‘’βˆ’π‘3πœƒ πœƒπ‘Ž3βˆ’π‘›πœ†βˆ’1π‘’βˆ’π‘3πœƒ X cana-6220 212 15 ∏ ∏ PROPN cana-6220 212 16 ( ( PUNCT cana-6220 212 17 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 πœƒ+𝑑𝑖)βˆ’(πœ†+1)𝑛 PRON cana-6220 212 18 𝑖=1 𝑖=1 PUNCT cana-6220 212 19 ∏ ∏ PROPN cana-6220 213 1 [ [ X cana-6220 213 2 ( ( PUNCT cana-6220 213 3 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† 1+πœ‰)πœƒβˆ’πœ†βˆ’(πœƒ+𝑑𝑖)βˆ’πœ† NUM cana-6220 213 4 ] ] PUNCT cana-6220 213 5 2𝑛 2𝑛 PROPN cana-6220 213 6 𝑖=1 𝑖=1 PROPN cana-6220 213 7 ( ( PUNCT cana-6220 213 8 34 34 NUM cana-6220 213 9 ) ) PUNCT cana-6220 213 10 the the DET cana-6220 213 11 conditional conditional ADJ cana-6220 213 12 posterior posterior ADJ cana-6220 213 13 distributions distribution NOUN cana-6220 213 14 in in ADP cana-6220 213 15 eq eq ADP cana-6220 213 16 . . PUNCT cana-6220 214 1 ( ( PUNCT cana-6220 214 2 32 32 NUM cana-6220 214 3 ) ) PUNCT cana-6220 214 4 , , PUNCT cana-6220 214 5 ( ( PUNCT cana-6220 214 6 33 33 NUM cana-6220 214 7 ) ) PUNCT cana-6220 214 8 and and CCONJ cana-6220 214 9 ( ( PUNCT cana-6220 214 10 34 34 NUM cana-6220 214 11 ) ) PUNCT cana-6220 214 12 of of ADP cana-6220 214 13 the the DET cana-6220 214 14 parameters parameter NOUN cana-6220 214 15 under under ADP cana-6220 214 16 the the DET cana-6220 214 17 bayesian bayesian NOUN cana-6220 214 18 framework framework NOUN cana-6220 214 19 do do AUX cana-6220 214 20 not not PART cana-6220 214 21 follow follow VERB cana-6220 214 22 any any DET cana-6220 214 23 standard standard ADJ cana-6220 214 24 or or CCONJ cana-6220 214 25 closed closed ADJ cana-6220 214 26 - - PUNCT cana-6220 214 27 form form NOUN cana-6220 214 28 distribution distribution NOUN cana-6220 214 29 . . PUNCT cana-6220 215 1 this this DET cana-6220 215 2 non non ADJ cana-6220 215 3 - - ADJ cana-6220 215 4 standard standard ADJ cana-6220 215 5 nature nature NOUN cana-6220 215 6 arises arise VERB cana-6220 215 7 due due ADP cana-6220 215 8 to to ADP cana-6220 215 9 the the DET cana-6220 215 10 complexity complexity NOUN cana-6220 215 11 of of ADP cana-6220 215 12 our our PRON cana-6220 215 13 likelihood likelihood NOUN cana-6220 215 14 function function NOUN cana-6220 215 15 combined combine VERB cana-6220 215 16 with with ADP cana-6220 215 17 the the DET cana-6220 215 18 gamma gamma NOUN cana-6220 215 19 prior prior ADJ cana-6220 215 20 distributions distribution NOUN cana-6220 215 21 , , PUNCT cana-6220 215 22 which which PRON cana-6220 215 23 prevents prevent VERB cana-6220 215 24 the the DET cana-6220 215 25 use use NOUN cana-6220 215 26 of of ADP cana-6220 215 27 direct direct ADJ cana-6220 215 28 sampling sampling NOUN cana-6220 215 29 methods method NOUN cana-6220 215 30 . . PUNCT cana-6220 216 1 as as ADP cana-6220 216 2 a a DET cana-6220 216 3 result result NOUN cana-6220 216 4 , , PUNCT cana-6220 216 5 conventional conventional ADJ cana-6220 216 6 analytical analytical ADJ cana-6220 216 7 approaches approach NOUN cana-6220 216 8 become become VERB cana-6220 216 9 impractical impractical ADJ cana-6220 216 10 . . PUNCT cana-6220 217 1 to to PART cana-6220 217 2 address address VERB cana-6220 217 3 this this PRON cana-6220 217 4 , , PUNCT cana-6220 217 5 the the DET cana-6220 217 6 metropolis metropolis PROPN cana-6220 217 7 - - PUNCT cana-6220 217 8 hastings hastings PROPN cana-6220 217 9 ( ( PUNCT cana-6220 217 10 mh mh PROPN cana-6220 217 11 ) ) PUNCT cana-6220 217 12 algorithm algorithm NOUN cana-6220 217 13 is be AUX cana-6220 217 14 employed employ VERB cana-6220 217 15 as as ADP cana-6220 217 16 a a DET cana-6220 217 17 flexible flexible ADJ cana-6220 217 18 and and CCONJ cana-6220 217 19 efficient efficient ADJ cana-6220 217 20 markov markov NOUN cana-6220 217 21 chain chain NOUN cana-6220 217 22 monte monte PROPN cana-6220 217 23 carlo carlo PROPN cana-6220 217 24 ( ( PUNCT cana-6220 217 25 mcmc mcmc PROPN cana-6220 217 26 ) ) PUNCT cana-6220 217 27 technique technique NOUN cana-6220 217 28 to to PART cana-6220 217 29 generate generate VERB cana-6220 217 30 samples sample NOUN cana-6220 217 31 from from ADP cana-6220 217 32 the the DET cana-6220 217 33 intractable intractable ADJ cana-6220 217 34 conditional conditional ADJ cana-6220 217 35 distributions distribution NOUN cana-6220 217 36 and and CCONJ cana-6220 217 37 obtain obtain VERB cana-6220 217 38 the the DET cana-6220 217 39 bayesian bayesian NOUN cana-6220 217 40 estimates estimate NOUN cana-6220 217 41 of of ADP cana-6220 217 42 the the DET cana-6220 217 43 parameters parameter NOUN cana-6220 217 44 . . PUNCT cana-6220 218 1 mh mh PROPN cana-6220 218 2 algorithm algorithm PROPN cana-6220 218 3 is be AUX cana-6220 218 4 carried carry VERB cana-6220 218 5 out out ADP cana-6220 218 6 in in ADP cana-6220 218 7 following follow VERB cana-6220 218 8 steps step NOUN cana-6220 218 9 : : PUNCT cana-6220 218 10 1 1 X cana-6220 218 11 . . X cana-6220 218 12 set set VERB cana-6220 218 13 the the DET cana-6220 218 14 starting starting NOUN cana-6220 218 15 value value NOUN cana-6220 218 16 ΞΎ(0 ΞΎ(0 NOUN cana-6220 218 17 ) ) PUNCT cana-6220 218 18 = = SYM cana-6220 218 19 ΞΎΜ‚ ΞΎΜ‚ NOUN cana-6220 218 20 , , PUNCT cana-6220 218 21 Ξ»(0 Ξ»(0 NOUN cana-6220 218 22 ) ) PUNCT cana-6220 218 23 = = SYM cana-6220 218 24 Ξ»Μ‚ Ξ»Μ‚ X cana-6220 218 25 and and CCONJ cana-6220 218 26 ΞΈ(0 ΞΈ(0 PROPN cana-6220 218 27 ) ) PUNCT cana-6220 218 28 = = NOUN cana-6220 219 1 ΞΈΜ‚ ΞΈΜ‚ VERB cana-6220 219 2 through through ADP cana-6220 219 3 mle mle PROPN cana-6220 219 4 . . PROPN cana-6220 219 5 2 2 NUM cana-6220 219 6 . . X cana-6220 219 7 set set VERB cana-6220 219 8 𝑖 𝑖 X cana-6220 220 1 = = NOUN cana-6220 220 2 1 1 NUM cana-6220 220 3 . . NOUN cana-6220 221 1 3 3 X cana-6220 221 2 . . X cana-6220 221 3 create create VERB cana-6220 221 4 xiβˆ— xiβˆ— PROPN cana-6220 221 5 , , PUNCT cana-6220 221 6 Ξ»βˆ— Ξ»βˆ— NOUN cana-6220 221 7 and and CCONJ cana-6220 221 8 ΞΈβˆ— ΞΈβˆ— NOUN cana-6220 221 9 from from ADP cana-6220 221 10 n(ΞΎΜ‚ n(ΞΎΜ‚ PROPN cana-6220 221 11 , , PUNCT cana-6220 221 12 Οƒ2 Οƒ2 NOUN cana-6220 221 13 ΞΎΜ‚ ΞΎΜ‚ NOUN cana-6220 221 14 ) ) PUNCT cana-6220 221 15 , , PUNCT cana-6220 221 16 n(Ξ»Μ‚ n(Ξ»Μ‚ PROPN cana-6220 221 17 , , PUNCT cana-6220 221 18 Οƒ2 Οƒ2 NOUN cana-6220 221 19 Ξ»Μ‚ Ξ»Μ‚ NUM cana-6220 221 20 ) ) PUNCT cana-6220 221 21 and and CCONJ cana-6220 221 22 n(ΞΈΜ‚ n(ΞΈΜ‚ PROPN cana-6220 221 23 , , PUNCT cana-6220 221 24 Οƒ2 Οƒ2 NOUN cana-6220 221 25 ΞΈΜ‚ ΞΈΜ‚ NUM cana-6220 221 26 ) ) PUNCT cana-6220 221 27 , , PUNCT cana-6220 221 28 respectively respectively ADV cana-6220 221 29 . . PUNCT cana-6220 222 1 4 4 X cana-6220 222 2 . . X cana-6220 222 3 find find VERB cana-6220 222 4 π΄πœ‰ π΄πœ‰ ADP cana-6220 222 5 , , PUNCT cana-6220 222 6 aΞ» aΞ» ADP cana-6220 222 7 and and CCONJ cana-6220 222 8 aπœƒ aπœƒ PROPN cana-6220 222 9 as as ADP cana-6220 222 10 𝐴ξ 𝐴ξ PROPN cana-6220 222 11 = = PUNCT cana-6220 222 12 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN cana-6220 222 13 { { PUNCT cana-6220 222 14 1 1 NUM cana-6220 222 15 , , PUNCT cana-6220 222 16 Ο€βˆ—(ΞΎβˆ—|Ξ»(π‘–βˆ’1 Ο€βˆ—(ΞΎβˆ—|Ξ»(π‘–βˆ’1 NOUN cana-6220 222 17 ) ) PUNCT cana-6220 222 18 , , PUNCT cana-6220 222 19 ΞΈ(π‘–βˆ’1 ΞΈ(π‘–βˆ’1 NOUN cana-6220 222 20 ) ) PUNCT cana-6220 222 21 , , PUNCT cana-6220 222 22 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 23 ) ) PUNCT cana-6220 222 24 Ο€βˆ—(ΞΎ(π‘–βˆ’1)|Ξ»(π‘–βˆ’1 Ο€βˆ—(ΞΎ(π‘–βˆ’1)|Ξ»(π‘–βˆ’1 PROPN cana-6220 222 25 ) ) PUNCT cana-6220 222 26 , , PUNCT cana-6220 222 27 ΞΈ(π‘–βˆ’1 ΞΈ(π‘–βˆ’1 NOUN cana-6220 222 28 ) ) PUNCT cana-6220 222 29 , , PUNCT cana-6220 222 30 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 31 ) ) PUNCT cana-6220 222 32 } } PUNCT cana-6220 222 33 , , PUNCT cana-6220 222 34 𝐴λ 𝐴λ PROPN cana-6220 222 35 = = PUNCT cana-6220 222 36 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN cana-6220 222 37 { { PUNCT cana-6220 222 38 1 1 NUM cana-6220 222 39 , , PUNCT cana-6220 222 40 Ο€βˆ—(Ξ»βˆ—|ΞΎ(π‘–βˆ’1 Ο€βˆ—(Ξ»βˆ—|ΞΎ(π‘–βˆ’1 NOUN cana-6220 222 41 ) ) PUNCT cana-6220 222 42 , , PUNCT cana-6220 222 43 ΞΈ(π‘–βˆ’1 ΞΈ(π‘–βˆ’1 NOUN cana-6220 222 44 ) ) PUNCT cana-6220 222 45 , , PUNCT cana-6220 222 46 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 47 ) ) PUNCT cana-6220 222 48 Ο€βˆ—(Ξ»(π‘–βˆ’1)|ΞΎ(π‘–βˆ’1 Ο€βˆ—(Ξ»(π‘–βˆ’1)|ΞΎ(π‘–βˆ’1 PROPN cana-6220 222 49 ) ) PUNCT cana-6220 222 50 , , PUNCT cana-6220 222 51 ΞΈ(π‘–βˆ’1 ΞΈ(π‘–βˆ’1 NOUN cana-6220 222 52 ) ) PUNCT cana-6220 222 53 , , PUNCT cana-6220 222 54 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 55 ) ) PUNCT cana-6220 222 56 } } PUNCT cana-6220 222 57 and and CCONJ cana-6220 222 58 𝐴θ 𝐴θ PROPN cana-6220 222 59 = = PUNCT cana-6220 222 60 π‘šπ‘–π‘› π‘šπ‘–π‘› PROPN cana-6220 222 61 { { PUNCT cana-6220 222 62 1 1 NUM cana-6220 222 63 , , PUNCT cana-6220 222 64 Ο€βˆ—(ΞΈβˆ—|ΞΎ(π‘–βˆ’1 Ο€βˆ—(ΞΈβˆ—|ΞΎ(π‘–βˆ’1 NUM cana-6220 222 65 ) ) PUNCT cana-6220 222 66 , , PUNCT cana-6220 222 67 Ξ»(π‘–βˆ’1 Ξ»(π‘–βˆ’1 NOUN cana-6220 222 68 ) ) PUNCT cana-6220 222 69 , , PUNCT cana-6220 222 70 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 71 ) ) PUNCT cana-6220 222 72 Ο€βˆ—(ΞΈ(π‘–βˆ’1)|ΞΎ(π‘–βˆ’1 Ο€βˆ—(ΞΈ(π‘–βˆ’1)|ΞΎ(π‘–βˆ’1 PROPN cana-6220 222 73 ) ) PUNCT cana-6220 222 74 , , PUNCT cana-6220 222 75 Ξ»(π‘–βˆ’1 Ξ»(π‘–βˆ’1 NOUN cana-6220 222 76 ) ) PUNCT cana-6220 222 77 , , PUNCT cana-6220 222 78 π‘‘π‘Žπ‘‘π‘Ž π‘‘π‘Žπ‘‘π‘Ž NOUN cana-6220 222 79 ) ) PUNCT cana-6220 222 80 } } PUNCT cana-6220 222 81 5 5 X cana-6220 222 82 . . PUNCT cana-6220 222 83 utilizing utilize VERB cana-6220 222 84 the the DET cana-6220 222 85 uniform uniform ADJ cana-6220 222 86 u u PROPN cana-6220 222 87 ( ( PUNCT cana-6220 222 88 0,1 0,1 NOUN cana-6220 222 89 ) ) PUNCT cana-6220 222 90 distribution distribution NOUN cana-6220 222 91 , , PUNCT cana-6220 222 92 generate generate VERB cana-6220 222 93 samples sample NOUN cana-6220 222 94 u1 u1 NOUN cana-6220 222 95 , , PUNCT cana-6220 222 96 u2 u2 NOUN cana-6220 222 97 and and CCONJ cana-6220 222 98 u3 u3 NOUN cana-6220 222 99 respectively respectively ADV cana-6220 222 100 for for ADP cana-6220 222 101 ΞΎ ΞΎ PROPN cana-6220 222 102 , , PUNCT cana-6220 222 103 Ξ» Ξ» PROPN cana-6220 222 104 and and CCONJ cana-6220 222 105 ΞΈ ΞΈ PROPN cana-6220 222 106 . . PROPN cana-6220 222 107 6 6 NUM cana-6220 222 108 . . PUNCT cana-6220 223 1 if if SCONJ cana-6220 223 2 u1 u1 PROPN cana-6220 223 3 , , PUNCT cana-6220 223 4 u2 u2 NOUN cana-6220 223 5 and and CCONJ cana-6220 223 6 u3 u3 NOUN cana-6220 223 7 are be AUX cana-6220 223 8 less less ADJ cana-6220 223 9 than than ADP cana-6220 223 10 aΞΎ aΞΎ PROPN cana-6220 223 11 , , PUNCT cana-6220 223 12 aΞ» aΞ» ADP cana-6220 223 13 and and CCONJ cana-6220 223 14 aΞΈ aΞΈ VERB cana-6220 223 15 , , PUNCT cana-6220 223 16 respectively respectively ADV cana-6220 223 17 than than SCONJ cana-6220 223 18 set set VERB cana-6220 223 19 ΞΎ(i ΞΎ(i NUM cana-6220 223 20 ) ) PUNCT cana-6220 223 21 = = SYM cana-6220 224 1 ΞΎβˆ— ΞΎβˆ— NOUN cana-6220 224 2 , , PUNCT cana-6220 224 3 Ξ»(i Ξ»(i PROPN cana-6220 224 4 ) ) PUNCT cana-6220 224 5 = = SYM cana-6220 224 6 Ξ»βˆ— Ξ»βˆ— NOUN cana-6220 224 7 and and CCONJ cana-6220 224 8 ΞΈ(i ΞΈ(i PROPN cana-6220 224 9 ) ) PUNCT cana-6220 224 10 = = SYM cana-6220 224 11 ΞΈβˆ— ΞΈβˆ— NOUN cana-6220 224 12 , , PUNCT cana-6220 224 13 respectively respectively ADV cana-6220 224 14 . . PUNCT cana-6220 225 1 otherwise otherwise ADV cana-6220 225 2 , , PUNCT cana-6220 225 3 set set VERB cana-6220 225 4 ΞΎ(i ΞΎ(i NUM cana-6220 225 5 ) ) PUNCT cana-6220 226 1 = = SYM cana-6220 226 2 ΞΎiβˆ’1 ΞΎiβˆ’1 PROPN cana-6220 226 3 , , PUNCT cana-6220 226 4 Ξ»(i Ξ»(i PROPN cana-6220 226 5 ) ) PUNCT cana-6220 226 6 = = SYM cana-6220 226 7 Ξ»iβˆ’1 Ξ»iβˆ’1 PROPN cana-6220 226 8 and and CCONJ cana-6220 226 9 ΞΈ(i ΞΈ(i PROPN cana-6220 226 10 ) ) PUNCT cana-6220 226 11 = = SYM cana-6220 226 12 ΞΈiβˆ’1 ΞΈiβˆ’1 PROPN cana-6220 226 13 , , PUNCT cana-6220 226 14 respectively respectively ADV cana-6220 226 15 . . PUNCT cana-6220 227 1 7 7 X cana-6220 227 2 . . X cana-6220 227 3 set set VERB cana-6220 227 4 i i NOUN cana-6220 228 1 = = PUNCT cana-6220 229 1 i i PRON cana-6220 229 2 + + NOUN cana-6220 229 3 1 1 NUM cana-6220 229 4 8 8 NUM cana-6220 229 5 . . PUNCT cana-6220 230 1 redo redo NOUN cana-6220 230 2 steps step NOUN cana-6220 230 3 3 3 NUM cana-6220 230 4 7 7 NUM cana-6220 230 5 , , PUNCT cana-6220 230 6 l l NOUN cana-6220 230 7 times time NOUN cana-6220 230 8 to to PART cana-6220 230 9 get get VERB cana-6220 230 10 ΞΎ(i ΞΎ(i PROPN cana-6220 230 11 ) ) PUNCT cana-6220 230 12 , , PUNCT cana-6220 230 13 Ξ»(i Ξ»(i PROPN cana-6220 230 14 ) ) PUNCT cana-6220 230 15 and and CCONJ cana-6220 230 16 ΞΈ(i)for ΞΈ(i)for ADP cana-6220 230 17 i i PRON cana-6220 230 18 = = NOUN cana-6220 230 19 1,2 1,2 NUM cana-6220 230 20 , , PUNCT cana-6220 230 21 βˆ’ βˆ’ PROPN cana-6220 230 22 βˆ’ βˆ’ PROPN cana-6220 230 23 βˆ’ βˆ’ NOUN cana-6220 230 24 , , PUNCT cana-6220 230 25 l. l. NOUN cana-6220 230 26 9 9 NUM cana-6220 230 27 . . PUNCT cana-6220 231 1 after after ADP cana-6220 231 2 a a DET cana-6220 231 3 suitable suitable ADJ cana-6220 231 4 burn burn NOUN cana-6220 231 5 - - PUNCT cana-6220 231 6 in in ADP cana-6220 231 7 phase phase NOUN cana-6220 231 8 , , PUNCT cana-6220 231 9 say say VERB cana-6220 231 10 d d INTJ cana-6220 231 11 , , PUNCT cana-6220 231 12 obtain obtain VERB cana-6220 231 13 the the DET cana-6220 231 14 bayes bayes NOUN cana-6220 231 15 estimate estimate NOUN cana-6220 231 16 of of ADP cana-6220 231 17 the the DET cana-6220 231 18 parameter parameter NOUN cana-6220 231 19 ΞΎ ΞΎ PROPN cana-6220 231 20 , , PUNCT cana-6220 231 21 Ξ» Ξ» PROPN cana-6220 231 22 and and CCONJ cana-6220 231 23 ΞΈ ΞΈ PROPN cana-6220 231 24 as as ADP cana-6220 231 25 an an DET cana-6220 231 26 example example NOUN cana-6220 231 27 , , PUNCT cana-6220 231 28 as as ADP cana-6220 231 29 ΞΎΜƒ ΞΎΜƒ PROPN cana-6220 231 30 = = SYM cana-6220 231 31 1 1 NUM cana-6220 231 32 𝐿 𝐿 PROPN cana-6220 231 33 βˆ’ βˆ’ PROPN cana-6220 231 34 𝐷 𝐷 PROPN cana-6220 231 35 βˆ‘ βˆ‘ PUNCT cana-6220 231 36 ΞΎ(𝑖 ΞΎ(𝑖 NOUN cana-6220 231 37 ) ) PUNCT cana-6220 231 38 𝐿 𝐿 PROPN cana-6220 231 39 𝑖=𝐷+1 𝑖=𝐷+1 PUNCT cana-6220 231 40 , , PUNCT cana-6220 231 41 Ξ»Μƒ Ξ»Μƒ PROPN cana-6220 231 42 = = SYM cana-6220 231 43 1 1 NUM cana-6220 231 44 𝐿 𝐿 PROPN cana-6220 231 45 βˆ’ βˆ’ PROPN cana-6220 231 46 𝐷 𝐷 PROPN cana-6220 231 47 βˆ‘ βˆ‘ NOUN cana-6220 231 48 Ξ»(𝑖 Ξ»(𝑖 PROPN cana-6220 231 49 ) ) PUNCT cana-6220 231 50 𝐿 𝐿 PROPN cana-6220 231 51 𝑖=𝐷+1 𝑖=𝐷+1 NOUN cana-6220 231 52 , , PUNCT cana-6220 231 53 ΞΈΜƒ ΞΈΜƒ NOUN cana-6220 231 54 = = SYM cana-6220 231 55 1 1 NUM cana-6220 231 56 𝐿 𝐿 PROPN cana-6220 231 57 βˆ’ βˆ’ PROPN cana-6220 231 58 𝐷 𝐷 PROPN cana-6220 231 59 βˆ‘ βˆ‘ ADP cana-6220 231 60 ΞΈ(𝑖 ΞΈ(𝑖 PROPN cana-6220 231 61 ) ) PUNCT cana-6220 231 62 𝐿 𝐿 PROPN cana-6220 231 63 𝑖=𝐷+1 𝑖=𝐷+1 PUNCT cana-6220 231 64 . . PUNCT cana-6220 232 1 communications communication NOUN cana-6220 232 2 on on ADP cana-6220 232 3 applied apply VERB cana-6220 232 4 nonlinear nonlinear ADJ cana-6220 232 5 analysis analysis NOUN cana-6220 232 6 issn issn NOUN cana-6220 232 7 : : PUNCT cana-6220 232 8 1074 1074 NUM cana-6220 232 9 - - PUNCT cana-6220 232 10 133x 133x NUM cana-6220 232 11 vol vol VERB cana-6220 232 12 32 32 NUM cana-6220 232 13 no no NOUN cana-6220 232 14 . . PUNCT cana-6220 233 1 10s 10 NOUN cana-6220 233 2 ( ( PUNCT cana-6220 233 3 2025 2025 NUM cana-6220 233 4 ) ) PUNCT cana-6220 233 5 3557 3557 NUM cana-6220 233 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 233 7 7 7 X cana-6220 233 8 . . PUNCT cana-6220 233 9 simulation simulation NOUN cana-6220 233 10 study study NOUN cana-6220 233 11 in in ADP cana-6220 233 12 this this DET cana-6220 233 13 section section NOUN cana-6220 233 14 , , PUNCT cana-6220 233 15 to to PART cana-6220 233 16 determine determine VERB cana-6220 233 17 the the DET cana-6220 233 18 effectiveness effectiveness NOUN cana-6220 233 19 of of ADP cana-6220 233 20 mold mold NOUN cana-6220 233 21 estimators estimator NOUN cana-6220 233 22 , , PUNCT cana-6220 233 23 we we PRON cana-6220 233 24 conduct conduct VERB cana-6220 233 25 a a DET cana-6220 233 26 monte monte PROPN cana-6220 233 27 carlo carlo PROPN cana-6220 233 28 simulation simulation PROPN cana-6220 233 29 . . PUNCT cana-6220 234 1 using use VERB cana-6220 234 2 specific specific ADJ cana-6220 234 3 selected select VERB cana-6220 234 4 variable variable ADJ cana-6220 234 5 values value NOUN cana-6220 234 6 and and CCONJ cana-6220 234 7 the the DET cana-6220 234 8 mold mold NOUN cana-6220 234 9 distribution distribution NOUN cana-6220 234 10 , , PUNCT cana-6220 234 11 a a DET cana-6220 234 12 number number NOUN cana-6220 234 13 of of ADP cana-6220 234 14 random random ADJ cana-6220 234 15 numbers number NOUN cana-6220 234 16 are be AUX cana-6220 234 17 generated generate VERB cana-6220 234 18 . . PUNCT cana-6220 235 1 the the DET cana-6220 235 2 following follow VERB cana-6220 235 3 procedures procedure NOUN cana-6220 235 4 to to PART cana-6220 235 5 investigate investigate VERB cana-6220 235 6 the the DET cana-6220 235 7 new new ADJ cana-6220 235 8 model model NOUN cana-6220 235 9 are be AUX cana-6220 235 10 now now ADV cana-6220 235 11 presented present VERB cana-6220 235 12 : : PUNCT cana-6220 236 1 [ [ X cana-6220 236 2 step:1 step:1 X cana-6220 236 3 ] ] X cana-6220 236 4 fix fix VERB cana-6220 236 5 the the DET cana-6220 236 6 values value NOUN cana-6220 236 7 of of ADP cana-6220 236 8 mold mold NOUN cana-6220 236 9 ( ( PUNCT cana-6220 236 10 ΞΎ ΞΎ PROPN cana-6220 236 11 , , PUNCT cana-6220 236 12 Ξ» Ξ» PROPN cana-6220 236 13 , , PUNCT cana-6220 236 14 ΞΈ ΞΈ NOUN cana-6220 236 15 ) ) PUNCT cana-6220 236 16 as as ADP cana-6220 236 17 set-1 set-1 PUNCT cana-6220 236 18 mold mold NOUN cana-6220 236 19 ( ( PUNCT cana-6220 236 20 9 9 NUM cana-6220 236 21 , , PUNCT cana-6220 236 22 5 5 NUM cana-6220 236 23 , , PUNCT cana-6220 236 24 0.25 0.25 NUM cana-6220 236 25 ) ) PUNCT cana-6220 236 26 and and CCONJ cana-6220 236 27 set-2 set-2 PUNCT cana-6220 236 28 mold mold NOUN cana-6220 236 29 ( ( PUNCT cana-6220 236 30 0.02 0.02 NUM cana-6220 236 31 , , PUNCT cana-6220 236 32 0.05 0.05 NUM cana-6220 236 33 , , PUNCT cana-6220 236 34 10 10 NUM cana-6220 236 35 ) ) PUNCT cana-6220 236 36 . . PUNCT cana-6220 237 1 [ [ X cana-6220 237 2 step:2 step:2 X cana-6220 237 3 ] ] X cana-6220 237 4 fix fix VERB cana-6220 237 5 the the DET cana-6220 237 6 sample sample NOUN cana-6220 237 7 sizes size NOUN cana-6220 237 8 n n CCONJ cana-6220 237 9 as as ADP cana-6220 237 10 n n NOUN cana-6220 237 11 = = NUM cana-6220 237 12 10 10 NUM cana-6220 237 13 , , PUNCT cana-6220 237 14 30 30 NUM cana-6220 237 15 , , PUNCT cana-6220 237 16 50 50 NUM cana-6220 237 17 , , PUNCT cana-6220 237 18 200 200 NUM cana-6220 237 19 . . PUNCT cana-6220 238 1 [ [ X cana-6220 238 2 step:3 step:3 NOUN cana-6220 238 3 ] ] X cana-6220 238 4 fix fix VERB cana-6220 238 5 the the DET cana-6220 238 6 number number NOUN cana-6220 238 7 of of ADP cana-6220 238 8 replications replication NOUN cana-6220 238 9 as as ADP cana-6220 238 10 1000 1000 NUM cana-6220 238 11 . . PUNCT cana-6220 239 1 [ [ X cana-6220 239 2 step:4 step:4 X cana-6220 239 3 ] ] PUNCT cana-6220 239 4 generate generate VERB cana-6220 239 5 the the DET cana-6220 239 6 random random ADJ cana-6220 239 7 samples sample NOUN cana-6220 239 8 using use VERB cana-6220 239 9 quantile quantile ADJ cana-6220 239 10 function function NOUN cana-6220 239 11 given give VERB cana-6220 239 12 in in ADP cana-6220 239 13 eq eq ADP cana-6220 239 14 . . PUNCT cana-6220 240 1 ( ( PUNCT cana-6220 240 2 13 13 NUM cana-6220 240 3 ) ) PUNCT cana-6220 240 4 . . PUNCT cana-6220 241 1 π‘₯𝑖 π‘₯𝑖 PROPN cana-6220 242 1 = = SYM cana-6220 242 2 ΞΈ ΞΈ PROPN cana-6220 243 1 [ [ X cana-6220 243 2 ( ( PUNCT cana-6220 243 3 1 1 NUM cana-6220 243 4 + + SYM cana-6220 243 5 ΞΎ ΞΎ PROPN cana-6220 243 6 βˆ’ βˆ’ NOUN cana-6220 243 7 𝑒𝑖 𝑒𝑖 NOUN cana-6220 243 8 ( ( PUNCT cana-6220 243 9 1 1 NUM cana-6220 243 10 + + NUM cana-6220 243 11 ΞΎ)(1 ΞΎ)(1 NOUN cana-6220 243 12 βˆ’ βˆ’ NOUN cana-6220 243 13 𝑒𝑖 𝑒𝑖 NOUN cana-6220 243 14 ) ) PUNCT cana-6220 243 15 ) ) PUNCT cana-6220 244 1 1 1 X cana-6220 244 2 / / SYM cana-6220 244 3 Ξ» Ξ» X cana-6220 244 4 βˆ’ βˆ’ NOUN cana-6220 244 5 1 1 NUM cana-6220 244 6 ] ] PUNCT cana-6220 244 7 , , PUNCT cana-6220 244 8 where where SCONJ cana-6220 244 9 𝑒𝑖 𝑒𝑖 ADP cana-6220 244 10 ∼ ∼ NOUN cana-6220 244 11 π‘ˆ(0,1 π‘ˆ(0,1 NOUN cana-6220 244 12 ) ) PUNCT cana-6220 244 13 , , PUNCT cana-6220 244 14 𝑖 𝑖 NOUN cana-6220 244 15 = = SYM cana-6220 244 16 1,2 1,2 NUM cana-6220 244 17 , , PUNCT cana-6220 244 18 … … PUNCT cana-6220 244 19 , , PUNCT cana-6220 244 20 𝑛. 𝑛. NOUN cana-6220 244 21 [ [ X cana-6220 244 22 step:5 step:5 X cana-6220 244 23 ] ] X cana-6220 244 24 the the DET cana-6220 244 25 mle mle NOUN cana-6220 244 26 of of ADP cana-6220 244 27 each each DET cana-6220 244 28 parameter parameter NOUN cana-6220 244 29 are be AUX cana-6220 244 30 obtained obtain VERB cana-6220 244 31 using use VERB cana-6220 244 32 the the DET cana-6220 244 33 optim optim ADJ cana-6220 244 34 function function NOUN cana-6220 244 35 in in ADP cana-6220 244 36 r r NOUN cana-6220 244 37 software software NOUN cana-6220 244 38 using use VERB cana-6220 244 39 the the DET cana-6220 244 40 log log NOUN cana-6220 244 41 - - PUNCT cana-6220 244 42 likelihood likelihood NOUN cana-6220 244 43 function function NOUN cana-6220 244 44 from from ADP cana-6220 244 45 eq eq PROPN cana-6220 244 46 . . PUNCT cana-6220 245 1 ( ( PUNCT cana-6220 245 2 23 23 NUM cana-6220 245 3 ) ) PUNCT cana-6220 245 4 . . PUNCT cana-6220 246 1 [ [ X cana-6220 246 2 step:6 step:6 X cana-6220 246 3 ] ] X cana-6220 246 4 bayes bayes PROPN cana-6220 246 5 estimates estimate NOUN cana-6220 246 6 of of ADP cana-6220 246 7 the the DET cana-6220 246 8 parameters parameter NOUN cana-6220 246 9 are be AUX cana-6220 246 10 obtained obtain VERB cana-6220 246 11 based base VERB cana-6220 246 12 on on ADP cana-6220 246 13 two two NUM cana-6220 246 14 informative informative ADJ cana-6220 246 15 prior prior ADJ cana-6220 246 16 sets set NOUN cana-6220 246 17 as as ADP cana-6220 246 18 prior-1 prior-1 PROPN cana-6220 246 19 ( ( PUNCT cana-6220 246 20 p-1 p-1 NOUN cana-6220 246 21 ) ) PUNCT cana-6220 246 22 ( ( PUNCT cana-6220 246 23 a1 a1 PROPN cana-6220 246 24 , , PUNCT cana-6220 246 25 a2 a2 PROPN cana-6220 246 26 , , PUNCT cana-6220 246 27 a4 a4 NOUN cana-6220 246 28 ) ) PUNCT cana-6220 246 29 = = SYM cana-6220 246 30 ( ( PUNCT cana-6220 246 31 18,10,0.5 18,10,0.5 NUM cana-6220 246 32 ) ) PUNCT cana-6220 246 33 and and CCONJ cana-6220 246 34 bi bi NOUN cana-6220 246 35 = = NOUN cana-6220 246 36 2 2 NUM cana-6220 246 37 for for ADP cana-6220 246 38 i i PRON cana-6220 246 39 = = NOUN cana-6220 246 40 1 1 NUM cana-6220 246 41 , , PUNCT cana-6220 246 42 2 2 NUM cana-6220 246 43 , , PUNCT cana-6220 246 44 3 3 NUM cana-6220 246 45 . . PUNCT cana-6220 247 1 prior-2 prior-2 NUM cana-6220 247 2 ( ( PUNCT cana-6220 247 3 p-2 p-2 NOUN cana-6220 247 4 ) ) PUNCT cana-6220 247 5 ( ( PUNCT cana-6220 247 6 a1 a1 PROPN cana-6220 247 7 , , PUNCT cana-6220 247 8 a2 a2 PROPN cana-6220 247 9 , , PUNCT cana-6220 247 10 a4 a4 NOUN cana-6220 247 11 ) ) PUNCT cana-6220 247 12 = = SYM cana-6220 247 13 ( ( PUNCT cana-6220 247 14 0.08,0.20,40 0.08,0.20,40 NUM cana-6220 247 15 ) ) PUNCT cana-6220 247 16 and and CCONJ cana-6220 247 17 bi bi NOUN cana-6220 247 18 = = NOUN cana-6220 247 19 4 4 NUM cana-6220 247 20 for for ADP cana-6220 247 21 i i PRON cana-6220 247 22 = = NOUN cana-6220 247 23 1 1 NUM cana-6220 247 24 , , PUNCT cana-6220 247 25 2 2 NUM cana-6220 247 26 , , PUNCT cana-6220 247 27 3 3 NUM cana-6220 247 28 . . PUNCT cana-6220 248 1 [ [ X cana-6220 248 2 step:7 step:7 X cana-6220 248 3 ] ] X cana-6220 248 4 the the DET cana-6220 248 5 performance performance NOUN cana-6220 248 6 of of ADP cana-6220 248 7 the the DET cana-6220 248 8 point point NOUN cana-6220 248 9 estimates estimate NOUN cana-6220 248 10 is be AUX cana-6220 248 11 assessed assess VERB cana-6220 248 12 using use VERB cana-6220 248 13 two two NUM cana-6220 248 14 criteria criterion NOUN cana-6220 248 15 : : PUNCT cana-6220 248 16 mean mean VERB cana-6220 248 17 squared square VERB cana-6220 248 18 error error NOUN cana-6220 248 19 ( ( PUNCT cana-6220 248 20 mse mse NOUN cana-6220 248 21 ) ) PUNCT cana-6220 248 22 and and CCONJ cana-6220 248 23 absolute absolute ADJ cana-6220 248 24 bias bias NOUN cana-6220 248 25 ( ( PUNCT cana-6220 248 26 ab ab NOUN cana-6220 248 27 ) ) PUNCT cana-6220 248 28 . . PUNCT cana-6220 249 1 𝑀𝑆𝐸 𝑀𝑆𝐸 NOUN cana-6220 249 2 = = NOUN cana-6220 249 3 1 1 NUM cana-6220 249 4 𝑁 𝑁 PROPN cana-6220 249 5 βˆ‘(ΞΈΜ‚ βˆ‘(ΞΈΜ‚ ADV cana-6220 249 6 βˆ’ βˆ’ NUM cana-6220 249 7 ΞΈ ΞΈ NOUN cana-6220 249 8 ) ) PUNCT cana-6220 249 9 2 2 NUM cana-6220 249 10 𝑁 𝑁 PROPN cana-6220 249 11 𝑖=1 𝑖=1 PUNCT cana-6220 249 12 𝐴𝐡 𝐴𝐡 NOUN cana-6220 249 13 = = SYM cana-6220 250 1 |(πœƒ |(πœƒ PROPN cana-6220 250 2 βˆ’ βˆ’ NOUN cana-6220 250 3 ΞΈ)| ΞΈ)| PROPN cana-6220 250 4 where where SCONJ cana-6220 250 5 , , PUNCT cana-6220 250 6 ΞΈ= ΞΈ= PROPN cana-6220 250 7 parameter parameter PROPN cana-6220 250 8 true true ADJ cana-6220 250 9 value value NOUN cana-6220 250 10 , , PUNCT cana-6220 250 11 ΞΈΜ‚ ΞΈΜ‚ PUNCT cana-6220 250 12 = = SYM cana-6220 250 13 estimated estimate VERB cana-6220 250 14 value value NOUN cana-6220 250 15 of of ADP cana-6220 250 16 the the DET cana-6220 250 17 parameter parameter NOUN cana-6220 250 18 . . PUNCT cana-6220 251 1 table table NOUN cana-6220 251 2 1 1 NUM cana-6220 251 3 : : PUNCT cana-6220 251 4 mean mean ADJ cana-6220 251 5 estimate estimate NOUN cana-6220 251 6 , , PUNCT cana-6220 251 7 absolute absolute ADJ cana-6220 251 8 bias bias NOUN cana-6220 251 9 ( ( PUNCT cana-6220 251 10 ab ab NOUN cana-6220 251 11 ) ) PUNCT cana-6220 251 12 and and CCONJ cana-6220 251 13 mean mean VERB cana-6220 251 14 squared square VERB cana-6220 251 15 error error NOUN cana-6220 251 16 ( ( PUNCT cana-6220 251 17 mse mse NOUN cana-6220 251 18 ) ) PUNCT cana-6220 251 19 of of ADP cana-6220 251 20 the the DET cana-6220 251 21 parameters parameter NOUN cana-6220 251 22 of of ADP cana-6220 251 23 mold mold NOUN cana-6220 251 24 under under ADP cana-6220 251 25 mle mle PROPN cana-6220 251 26 and and CCONJ cana-6220 251 27 bayesian bayesian NOUN cana-6220 251 28 method method NOUN cana-6220 251 29 ( ( PUNCT cana-6220 251 30 bm bm PROPN cana-6220 251 31 ) ) PUNCT cana-6220 251 32 for for ADP cana-6220 251 33 case-1 case-1 NUM cana-6220 251 34 𝑛 𝑛 PRON cana-6220 251 35 properties property NOUN cana-6220 251 36 mle mle PROPN cana-6220 251 37 bm bm PROPN cana-6220 251 38 ΞΎ ΞΎ PROPN cana-6220 251 39 = = SYM cana-6220 251 40 9 9 NUM cana-6220 251 41 Ξ» Ξ» NOUN cana-6220 251 42 = = SYM cana-6220 252 1 5 5 NUM cana-6220 252 2 πœƒ πœƒ NOUN cana-6220 252 3 = = NOUN cana-6220 252 4 0.25 0.25 NUM cana-6220 252 5 ΞΎ ΞΎ X cana-6220 252 6 = = SYM cana-6220 252 7 9 9 NUM cana-6220 252 8 Ξ» Ξ» NOUN cana-6220 252 9 = = SYM cana-6220 252 10 5 5 NUM cana-6220 252 11 πœƒ πœƒ NOUN cana-6220 252 12 = = SYM cana-6220 252 13 0.25 0.25 NUM cana-6220 252 14 mean mean NOUN cana-6220 252 15 estimate estimate VERB cana-6220 252 16 8.35711 8.35711 NUM cana-6220 252 17 7.12690 7.12690 NUM cana-6220 252 18 0.26704 0.26704 NUM cana-6220 252 19 8.96335 8.96335 NUM cana-6220 252 20 4.97687 4.97687 NUM cana-6220 252 21 0.25111 0.25111 NUM cana-6220 252 22 10 10 NUM cana-6220 252 23 ab ab PROPN cana-6220 252 24 0.64289 0.64289 NUM cana-6220 252 25 2.12690 2.12690 NUM cana-6220 252 26 0.01704 0.01704 NUM cana-6220 252 27 0.03665 0.03665 NUM cana-6220 252 28 0.02313 0.02313 NUM cana-6220 252 29 0.00111 0.00111 NUM cana-6220 252 30 mse mse NOUN cana-6220 252 31 10.91290 10.91290 NUM cana-6220 252 32 16.11558 16.11558 NUM cana-6220 252 33 0.01407 0.01407 NUM cana-6220 252 34 0.34820 0.34820 NUM cana-6220 252 35 0.50040 0.50040 NUM cana-6220 252 36 0.00636 0.00636 NUM cana-6220 252 37 mean mean NOUN cana-6220 252 38 estimate estimate VERB cana-6220 252 39 8.33814 8.33814 NUM cana-6220 252 40 7.05030 7.05030 NUM cana-6220 252 41 0.25669 0.25669 NUM cana-6220 252 42 9.08599 9.08599 NUM cana-6220 252 43 4.98748 4.98748 NUM cana-6220 252 44 0.25240 0.25240 NUM cana-6220 252 45 30 30 NUM cana-6220 252 46 ab ab PROPN cana-6220 252 47 0.66187 0.66187 NUM cana-6220 252 48 2.05030 2.05030 NUM cana-6220 252 49 0.00669 0.00669 NUM cana-6220 252 50 0.08599 0.08599 NUM cana-6220 252 51 0.01252 0.01252 NUM cana-6220 252 52 0.00240 0.00240 NUM cana-6220 252 53 communications communication NOUN cana-6220 252 54 on on ADP cana-6220 252 55 applied apply VERB cana-6220 252 56 nonlinear nonlinear ADJ cana-6220 252 57 analysis analysis NOUN cana-6220 252 58 issn issn NOUN cana-6220 252 59 : : PUNCT cana-6220 252 60 1074 1074 NUM cana-6220 252 61 - - PUNCT cana-6220 252 62 133x 133x NUM cana-6220 252 63 vol vol VERB cana-6220 252 64 32 32 NUM cana-6220 252 65 no no NOUN cana-6220 252 66 . . PUNCT cana-6220 253 1 10s 10 NOUN cana-6220 253 2 ( ( PUNCT cana-6220 253 3 2025 2025 NUM cana-6220 253 4 ) ) PUNCT cana-6220 253 5 3558 3558 NUM cana-6220 253 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 253 7 mse mse NOUN cana-6220 253 8 9.48808 9.48808 NUM cana-6220 253 9 12.27414 12.27414 NUM cana-6220 253 10 0.00397 0.00397 NUM cana-6220 253 11 0.55615 0.55615 NUM cana-6220 253 12 0.50785 0.50785 NUM cana-6220 253 13 0.00424 0.00424 NUM cana-6220 253 14 mean mean NOUN cana-6220 253 15 estimate estimate VERB cana-6220 253 16 8.20359 8.20359 NUM cana-6220 253 17 6.85089 6.85089 NUM cana-6220 253 18 0.25723 0.25723 NUM cana-6220 253 19 9.04125 9.04125 NUM cana-6220 254 1 5.11707 5.11707 NUM cana-6220 254 2 0.25892 0.25892 NUM cana-6220 254 3 50 50 NUM cana-6220 254 4 ab ab PROPN cana-6220 254 5 0.79641 0.79641 NUM cana-6220 254 6 1.85089 1.85089 NUM cana-6220 254 7 0.00723 0.00723 NUM cana-6220 254 8 0.04125 0.04125 NUM cana-6220 254 9 0.11707 0.11707 NUM cana-6220 254 10 0.00892 0.00892 NUM cana-6220 254 11 mse mse NOUN cana-6220 255 1 9.52439 9.52439 NUM cana-6220 255 2 9.91493 9.91493 NUM cana-6220 255 3 0.00253 0.00253 NUM cana-6220 255 4 0.42477 0.42477 NUM cana-6220 255 5 0.64209 0.64209 NUM cana-6220 255 6 0.00343 0.00343 NUM cana-6220 255 7 mean mean NOUN cana-6220 255 8 estimate estimate VERB cana-6220 255 9 8.81283 8.81283 NUM cana-6220 255 10 6.18065 6.18065 NUM cana-6220 255 11 0.25527 0.25527 NUM cana-6220 255 12 9.02399 9.02399 NUM cana-6220 255 13 5.00547 5.00547 NUM cana-6220 256 1 0.25215 0.25215 NUM cana-6220 256 2 200 200 NUM cana-6220 256 3 ab ab PROPN cana-6220 256 4 0.18717 0.18717 NUM cana-6220 256 5 1.18065 1.18065 NUM cana-6220 256 6 0.00527 0.00527 NUM cana-6220 256 7 0.02399 0.02399 NUM cana-6220 256 8 0.00547 0.00547 NUM cana-6220 256 9 0.00215 0.00215 NUM cana-6220 256 10 mse mse NOUN cana-6220 256 11 3.23149 3.23149 NUM cana-6220 256 12 3.64873 3.64873 NUM cana-6220 256 13 0.00051 0.00051 NUM cana-6220 256 14 0.74400 0.74400 NUM cana-6220 256 15 0.69949 0.69949 NUM cana-6220 256 16 0.00272 0.00272 NUM cana-6220 256 17 table table NOUN cana-6220 256 18 2 2 NUM cana-6220 256 19 : : PUNCT cana-6220 256 20 mean mean ADJ cana-6220 256 21 estimate estimate NOUN cana-6220 256 22 , , PUNCT cana-6220 256 23 absolute absolute ADJ cana-6220 256 24 bias bias NOUN cana-6220 256 25 ( ( PUNCT cana-6220 256 26 ab ab NOUN cana-6220 256 27 ) ) PUNCT cana-6220 256 28 and and CCONJ cana-6220 256 29 mean mean VERB cana-6220 256 30 squared square VERB cana-6220 256 31 error error NOUN cana-6220 256 32 ( ( PUNCT cana-6220 256 33 mse mse NOUN cana-6220 256 34 ) ) PUNCT cana-6220 256 35 of of ADP cana-6220 256 36 the the DET cana-6220 256 37 parameters parameter NOUN cana-6220 256 38 of of ADP cana-6220 256 39 mold mold NOUN cana-6220 256 40 under under ADP cana-6220 256 41 mle mle PROPN cana-6220 256 42 and and CCONJ cana-6220 256 43 bayesian bayesian NOUN cana-6220 256 44 method method NOUN cana-6220 256 45 ( ( PUNCT cana-6220 256 46 bm bm PROPN cana-6220 256 47 ) ) PUNCT cana-6220 256 48 for for ADP cana-6220 256 49 case-2 case-2 NUM cana-6220 256 50 𝑛 𝑛 DET cana-6220 256 51 properties property NOUN cana-6220 256 52 mle mle PROPN cana-6220 256 53 bm bm PROPN cana-6220 256 54 ΞΎ ΞΎ PROPN cana-6220 256 55 = = SYM cana-6220 256 56 0.02 0.02 NUM cana-6220 256 57 Ξ» Ξ» NOUN cana-6220 256 58 = = NOUN cana-6220 256 59 0.05 0.05 NUM cana-6220 256 60 πœƒ πœƒ NOUN cana-6220 256 61 = = NOUN cana-6220 256 62 10 10 NUM cana-6220 256 63 ΞΎ ΞΎ X cana-6220 256 64 = = SYM cana-6220 256 65 0.02 0.02 NUM cana-6220 256 66 Ξ» Ξ» NOUN cana-6220 256 67 = = NOUN cana-6220 256 68 0.05 0.05 NUM cana-6220 256 69 πœƒ πœƒ NOUN cana-6220 256 70 = = SYM cana-6220 256 71 10 10 NUM cana-6220 256 72 mean mean NOUN cana-6220 256 73 estimate estimate VERB cana-6220 257 1 0.09588 0.09588 NUM cana-6220 257 2 0.02575 0.02575 NUM cana-6220 257 3 9.99064 9.99064 NUM cana-6220 257 4 0.05352 0.05352 NUM cana-6220 257 5 0.09236 0.09236 NUM cana-6220 257 6 10.04951 10.04951 NUM cana-6220 257 7 10 10 NUM cana-6220 257 8 ab ab PROPN cana-6220 257 9 0.07588 0.07588 NUM cana-6220 257 10 0.02425 0.02425 NUM cana-6220 257 11 0.00936 0.00936 NUM cana-6220 257 12 0.03352 0.03352 NUM cana-6220 257 13 0.04236 0.04236 NUM cana-6220 257 14 0.04951 0.04951 NUM cana-6220 257 15 mse mse NOUN cana-6220 257 16 0.01284 0.01284 NUM cana-6220 257 17 0.00188 0.00188 NUM cana-6220 257 18 0.08164 0.08164 NUM cana-6220 257 19 0.00241 0.00241 NUM cana-6220 257 20 0.00580 0.00580 NUM cana-6220 257 21 2.46946 2.46946 NUM cana-6220 257 22 mean mean NOUN cana-6220 257 23 estimate estimate NOUN cana-6220 257 24 0.06400 0.06400 NUM cana-6220 258 1 0.03510 0.03510 NUM cana-6220 258 2 9.99969 9.99969 NUM cana-6220 258 3 0.05335 0.05335 NUM cana-6220 258 4 0.10310 0.10310 NUM cana-6220 258 5 9.92382 9.92382 NUM cana-6220 258 6 30 30 NUM cana-6220 258 7 ab ab NOUN cana-6220 258 8 0.04400 0.04400 NUM cana-6220 258 9 0.01490 0.01490 NUM cana-6220 258 10 0.00031 0.00031 NUM cana-6220 258 11 0.03335 0.03335 NUM cana-6220 258 12 0.05310 0.05310 NUM cana-6220 258 13 0.07618 0.07618 NUM cana-6220 258 14 mse mse VERB cana-6220 258 15 0.00439 0.00439 NUM cana-6220 258 16 0.00141 0.00141 NUM cana-6220 258 17 0.00000 0.00000 NUM cana-6220 258 18 0.00344 0.00344 NUM cana-6220 258 19 0.01054 0.01054 NUM cana-6220 258 20 2.12657 2.12657 NUM cana-6220 258 21 mean mean NOUN cana-6220 258 22 estimate estimate NOUN cana-6220 258 23 0.05590 0.05590 NUM cana-6220 258 24 0.03890 0.03890 NUM cana-6220 258 25 9.99959 9.99959 NUM cana-6220 258 26 0.05349 0.05349 NUM cana-6220 258 27 0.09945 0.09945 NUM cana-6220 258 28 9.82858 9.82858 NUM cana-6220 258 29 50 50 NUM cana-6220 258 30 ab ab PROPN cana-6220 258 31 0.03590 0.03590 NUM cana-6220 258 32 0.01110 0.01110 NUM cana-6220 258 33 0.00041 0.00041 NUM cana-6220 258 34 0.03349 0.03349 NUM cana-6220 258 35 0.04945 0.04945 NUM cana-6220 258 36 0.17142 0.17142 NUM cana-6220 258 37 mse mse NOUN cana-6220 258 38 0.00321 0.00321 NUM cana-6220 258 39 0.00128 0.00128 NUM cana-6220 258 40 0.00001 0.00001 NUM cana-6220 258 41 0.00476 0.00476 NUM cana-6220 258 42 0.01133 0.01133 NUM cana-6220 258 43 1.42323 1.42323 NUM cana-6220 258 44 mean mean NOUN cana-6220 258 45 estimate estimate NOUN cana-6220 259 1 0.02828 0.02828 NUM cana-6220 259 2 0.05120 0.05120 NUM cana-6220 259 3 9.97097 9.97097 NUM cana-6220 259 4 0.02491 0.02491 NUM cana-6220 259 5 0.05684 0.05684 NUM cana-6220 259 6 9.84556 9.84556 NUM cana-6220 259 7 200 200 NUM cana-6220 259 8 ab ab PROPN cana-6220 259 9 0.00828 0.00828 NUM cana-6220 259 10 0.00120 0.00120 NUM cana-6220 259 11 0.02904 0.02904 NUM cana-6220 259 12 0.00491 0.00491 NUM cana-6220 259 13 0.00684 0.00684 NUM cana-6220 259 14 0.15444 0.15444 NUM cana-6220 259 15 mse mse NOUN cana-6220 259 16 0.00063 0.00063 NUM cana-6220 259 17 0.00071 0.00071 NUM cana-6220 259 18 0.10122 0.10122 NUM cana-6220 259 19 0.00038 0.00038 NUM cana-6220 259 20 0.00140 0.00140 NUM cana-6220 259 21 0.43880 0.43880 NUM cana-6220 259 22 tables table NOUN cana-6220 259 23 ( ( PUNCT cana-6220 259 24 1 1 NUM cana-6220 259 25 ) ) PUNCT cana-6220 259 26 and and CCONJ cana-6220 259 27 ( ( PUNCT cana-6220 259 28 2 2 X cana-6220 259 29 ) ) PUNCT cana-6220 259 30 present present NOUN cana-6220 259 31 the the DET cana-6220 259 32 parameter parameter NOUN cana-6220 259 33 estimates estimate NOUN cana-6220 259 34 for for ADP cana-6220 259 35 the the DET cana-6220 259 36 mold mold NOUN cana-6220 259 37 distribution distribution NOUN cana-6220 259 38 obtained obtain VERB cana-6220 259 39 through through ADP cana-6220 259 40 maximum maximum ADJ cana-6220 259 41 likelihood likelihood NOUN cana-6220 259 42 estimation estimation NOUN cana-6220 259 43 and and CCONJ cana-6220 259 44 bayesian bayesian NOUN cana-6220 259 45 methodology methodology NOUN cana-6220 259 46 , , PUNCT cana-6220 259 47 respectively respectively ADV cana-6220 259 48 . . PUNCT cana-6220 260 1 a a DET cana-6220 260 2 comparative comparative ADJ cana-6220 260 3 analysis analysis NOUN cana-6220 260 4 of of ADP cana-6220 260 5 the the DET cana-6220 260 6 results result NOUN cana-6220 260 7 indicates indicate VERB cana-6220 260 8 that that SCONJ cana-6220 260 9 the the DET cana-6220 260 10 bayesian bayesian NOUN cana-6220 260 11 approach approach NOUN cana-6220 260 12 yields yield VERB cana-6220 260 13 superior superior ADJ cana-6220 260 14 parameter parameter NOUN cana-6220 260 15 estimates estimate NOUN cana-6220 260 16 relative relative ADJ cana-6220 260 17 to to ADP cana-6220 260 18 the the DET cana-6220 260 19 maximum maximum ADJ cana-6220 260 20 likelihood likelihood NOUN cana-6220 260 21 method method NOUN cana-6220 260 22 , , PUNCT cana-6220 260 23 consistent consistent ADJ cana-6220 260 24 with with ADP cana-6220 260 25 findings finding NOUN cana-6220 260 26 reported report VERB cana-6220 260 27 in in ADP cana-6220 260 28 the the DET cana-6220 260 29 existing exist VERB cana-6220 260 30 literature literature NOUN cana-6220 260 31 . . PUNCT cana-6220 261 1 8 8 X cana-6220 261 2 . . X cana-6220 261 3 application application NOUN cana-6220 261 4 to to PART cana-6220 261 5 demonstrate demonstrate VERB cana-6220 261 6 the the DET cana-6220 261 7 practical practical ADJ cana-6220 261 8 applicability applicability NOUN cana-6220 261 9 of of ADP cana-6220 261 10 the the DET cana-6220 261 11 proposed propose VERB cana-6220 261 12 mold mold NOUN cana-6220 261 13 distribution distribution NOUN cana-6220 261 14 , , PUNCT cana-6220 261 15 we we PRON cana-6220 261 16 analyse analyse VERB cana-6220 261 17 a a DET cana-6220 261 18 medical medical ADJ cana-6220 261 19 dataset dataset NOUN cana-6220 261 20 comprising comprising NOUN cana-6220 261 21 remission remission NOUN cana-6220 261 22 times time NOUN cana-6220 261 23 ( ( PUNCT cana-6220 261 24 measured measure VERB cana-6220 261 25 in in ADP cana-6220 261 26 months month NOUN cana-6220 261 27 ) ) PUNCT cana-6220 261 28 for for ADP cana-6220 261 29 137 137 NUM cana-6220 261 30 bladder bladder NOUN cana-6220 261 31 cancer cancer NOUN cana-6220 261 32 patients patient NOUN cana-6220 261 33 . . PUNCT cana-6220 262 1 this this DET cana-6220 262 2 dataset dataset NOUN cana-6220 262 3 table table NOUN cana-6220 262 4 ( ( PUNCT cana-6220 262 5 3 3 NUM cana-6220 262 6 ) ) PUNCT cana-6220 262 7 , , PUNCT cana-6220 262 8 originally originally ADV cana-6220 262 9 reported report VERB cana-6220 262 10 by by ADP cana-6220 262 11 ( ( PUNCT cana-6220 262 12 lee lee PROPN cana-6220 262 13 & & CCONJ cana-6220 262 14 wang wang PROPN cana-6220 262 15 , , PUNCT cana-6220 262 16 2003 2003 NUM cana-6220 262 17 ) ) PUNCT cana-6220 262 18 , , PUNCT cana-6220 262 19 provides provide VERB cana-6220 262 20 survival survival NOUN cana-6220 262 21 times time NOUN cana-6220 262 22 that that PRON cana-6220 262 23 exhibit exhibit VERB cana-6220 262 24 the the DET cana-6220 262 25 characteristics characteristic NOUN cana-6220 262 26 commonly commonly ADV cana-6220 262 27 observed observe VERB cana-6220 262 28 in in ADP cana-6220 262 29 oncological oncological ADJ cana-6220 262 30 studies study NOUN cana-6220 262 31 . . PUNCT cana-6220 263 1 the the DET cana-6220 263 2 observed observe VERB cana-6220 263 3 remission remission NOUN cana-6220 263 4 times times PROPN cana-6220 263 5 range range VERB cana-6220 263 6 from from ADP cana-6220 263 7 0.08 0.08 NUM cana-6220 263 8 to to ADP cana-6220 263 9 79.05 79.05 NUM cana-6220 263 10 months month NOUN cana-6220 263 11 , , PUNCT cana-6220 263 12 with with SCONJ cana-6220 263 13 the the DET cana-6220 263 14 complete complete ADJ cana-6220 263 15 dataset dataset NOUN cana-6220 263 16 presented present VERB cana-6220 263 17 as as SCONJ cana-6220 263 18 follows follow VERB cana-6220 263 19 : : PUNCT cana-6220 263 20 table table NOUN cana-6220 263 21 3 3 NUM cana-6220 263 22 : : PUNCT cana-6220 263 23 remission remission NOUN cana-6220 263 24 time time NOUN cana-6220 263 25 ( ( PUNCT cana-6220 263 26 in in ADP cana-6220 263 27 month month NOUN cana-6220 263 28 ) ) PUNCT cana-6220 263 29 of of ADP cana-6220 263 30 137 137 NUM cana-6220 263 31 cancer cancer NOUN cana-6220 263 32 patients patient NOUN cana-6220 263 33 4.5 4.5 NUM cana-6220 263 34 32.15 32.15 NUM cana-6220 264 1 3.88 3.88 NUM cana-6220 264 2 13.8 13.8 NUM cana-6220 264 3 19.13 19.13 NUM cana-6220 264 4 4.87 4.87 NUM cana-6220 264 5 3.02 3.02 NUM cana-6220 264 6 5.85 5.85 NUM cana-6220 264 7 14.24 14.24 NUM cana-6220 264 8 5.71 5.71 NUM cana-6220 264 9 19.36 19.36 NUM cana-6220 264 10 7.09 7.09 NUM cana-6220 264 11 7.87 7.87 NUM cana-6220 264 12 7.59 7.59 NUM cana-6220 264 13 20.28 20.28 NUM cana-6220 264 14 5.32 5.32 NUM cana-6220 264 15 5.49 5.49 NUM cana-6220 264 16 3.02 3.02 NUM cana-6220 264 17 46.12 46.12 NUM cana-6220 264 18 4.33 4.33 NUM cana-6220 264 19 2.02 2.02 NUM cana-6220 264 20 4.51 4.51 NUM cana-6220 264 21 5.17 5.17 NUM cana-6220 264 22 2.83 2.83 NUM cana-6220 264 23 9.22 9.22 NUM cana-6220 264 24 1.05 1.05 NUM cana-6220 264 25 0.2 0.2 NUM cana-6220 264 26 8.37 8.37 NUM cana-6220 264 27 3.82 3.82 NUM cana-6220 264 28 9.47 9.47 NUM cana-6220 264 29 36.66 36.66 NUM cana-6220 264 30 14.77 14.77 NUM cana-6220 264 31 26.31 26.31 NUM cana-6220 264 32 79.05 79.05 NUM cana-6220 264 33 10.06 10.06 NUM cana-6220 264 34 8.53 8.53 NUM cana-6220 264 35 4.65 4.65 NUM cana-6220 264 36 2.02 2.02 NUM cana-6220 264 37 4.98 4.98 NUM cana-6220 264 38 11.98 11.98 NUM cana-6220 264 39 2.62 2.62 NUM cana-6220 264 40 4.26 4.26 NUM cana-6220 264 41 5.06 5.06 NUM cana-6220 264 42 1.76 1.76 NUM cana-6220 264 43 0.9 0.9 NUM cana-6220 264 44 11.25 11.25 NUM cana-6220 264 45 16.62 16.62 NUM cana-6220 264 46 4.4 4.4 NUM cana-6220 264 47 21.73 21.73 NUM cana-6220 264 48 10.34 10.34 NUM cana-6220 264 49 12.07 12.07 NUM cana-6220 264 50 34.26 34.26 NUM cana-6220 264 51 0.87 0.87 NUM cana-6220 264 52 10.66 10.66 NUM cana-6220 264 53 6.97 6.97 NUM cana-6220 264 54 2.07 2.07 NUM cana-6220 264 55 0.51 0.51 NUM cana-6220 264 56 12.03 12.03 NUM cana-6220 264 57 0.08 0.08 NUM cana-6220 264 58 17.12 17.12 NUM cana-6220 264 59 communications communication NOUN cana-6220 264 60 on on ADP cana-6220 264 61 applied apply VERB cana-6220 264 62 nonlinear nonlinear ADJ cana-6220 264 63 analysis analysis NOUN cana-6220 264 64 issn issn NOUN cana-6220 264 65 : : PUNCT cana-6220 264 66 1074 1074 NUM cana-6220 264 67 - - PUNCT cana-6220 264 68 133x 133x NUM cana-6220 264 69 vol vol VERB cana-6220 264 70 32 32 NUM cana-6220 264 71 no no NOUN cana-6220 264 72 . . PUNCT cana-6220 265 1 10s 10 NOUN cana-6220 265 2 ( ( PUNCT cana-6220 265 3 2025 2025 NUM cana-6220 265 4 ) ) PUNCT cana-6220 265 5 3559 3559 NUM cana-6220 265 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 265 7 3.36 3.36 NUM cana-6220 265 8 2.64 2.64 NUM cana-6220 265 9 1.4 1.4 NUM cana-6220 265 10 12.63 12.63 NUM cana-6220 265 11 43.01 43.01 NUM cana-6220 265 12 14.76 14.76 NUM cana-6220 265 13 2.75 2.75 NUM cana-6220 265 14 7.66 7.66 NUM cana-6220 265 15 0.81 0.81 NUM cana-6220 265 16 1.19 1.19 NUM cana-6220 265 17 7.32 7.32 NUM cana-6220 265 18 4.18 4.18 NUM cana-6220 265 19 3.36 3.36 NUM cana-6220 265 20 8.66 8.66 NUM cana-6220 265 21 1.26 1.26 NUM cana-6220 265 22 13.29 13.29 NUM cana-6220 265 23 1.46 1.46 NUM cana-6220 265 24 14.83 14.83 NUM cana-6220 265 25 6.76 6.76 NUM cana-6220 265 26 23.63 23.63 NUM cana-6220 265 27 24.8 24.8 NUM cana-6220 265 28 5.62 5.62 NUM cana-6220 265 29 8.6 8.6 NUM cana-6220 265 30 3.25 3.25 NUM cana-6220 265 31 10.86 10.86 NUM cana-6220 265 32 18.1 18.1 NUM cana-6220 265 33 7.62 7.62 NUM cana-6220 265 34 7.63 7.63 NUM cana-6220 265 35 17.14 17.14 NUM cana-6220 265 36 25.74 25.74 NUM cana-6220 265 37 3.52 3.52 NUM cana-6220 265 38 2.87 2.87 NUM cana-6220 265 39 15.96 15.96 NUM cana-6220 265 40 17.36 17.36 NUM cana-6220 265 41 9.74 9.74 NUM cana-6220 265 42 3.31 3.31 NUM cana-6220 265 43 7.28 7.28 NUM cana-6220 265 44 1.35 1.35 NUM cana-6220 265 45 0.4 0.4 NUM cana-6220 265 46 2.26 2.26 NUM cana-6220 265 47 4.33 4.33 NUM cana-6220 265 48 9.02 9.02 NUM cana-6220 265 49 5.41 5.41 NUM cana-6220 265 50 2.69 2.69 NUM cana-6220 265 51 22.69 22.69 NUM cana-6220 265 52 6.94 6.94 NUM cana-6220 265 53 2.54 2.54 NUM cana-6220 265 54 11.79 11.79 NUM cana-6220 265 55 2.46 2.46 NUM cana-6220 265 56 7.26 7.26 NUM cana-6220 265 57 2.69 2.69 NUM cana-6220 265 58 5.34 5.34 NUM cana-6220 265 59 3.48 3.48 NUM cana-6220 265 60 4.7 4.7 NUM cana-6220 265 61 8.26 8.26 NUM cana-6220 265 62 6.93 6.93 NUM cana-6220 265 63 4.23 4.23 NUM cana-6220 265 64 3.7 3.7 NUM cana-6220 265 65 0.5 0.5 NUM cana-6220 265 66 10.75 10.75 NUM cana-6220 265 67 6.54 6.54 NUM cana-6220 265 68 3.64 3.64 NUM cana-6220 265 69 5.32 5.32 NUM cana-6220 265 70 13.11 13.11 NUM cana-6220 265 71 8.65 8.65 NUM cana-6220 265 72 3.57 3.57 NUM cana-6220 265 73 5.09 5.09 NUM cana-6220 265 74 7.39 7.39 NUM cana-6220 265 75 5.41 5.41 NUM cana-6220 265 76 11.64 11.64 NUM cana-6220 265 77 2.09 2.09 NUM cana-6220 265 78 2.23 2.23 NUM cana-6220 265 79 6.25 6.25 NUM cana-6220 265 80 7.93 7.93 NUM cana-6220 265 81 4.34 4.34 NUM cana-6220 265 82 25.82 25.82 NUM cana-6220 265 83 12.02 12.02 NUM cana-6220 265 84 we we PRON cana-6220 265 85 applied apply VERB cana-6220 265 86 mle mle NOUN cana-6220 265 87 and and CCONJ cana-6220 265 88 bayesian bayesian NOUN cana-6220 265 89 method method NOUN cana-6220 265 90 to to PART cana-6220 265 91 fit fit VERB cana-6220 265 92 the the DET cana-6220 265 93 mold mold NOUN cana-6220 265 94 parameters parameter NOUN cana-6220 265 95 and and CCONJ cana-6220 265 96 conducted conduct VERB cana-6220 265 97 a a DET cana-6220 265 98 comparative comparative ADJ cana-6220 265 99 study study NOUN cana-6220 265 100 against against ADP cana-6220 265 101 seven seven NUM cana-6220 265 102 competing compete VERB cana-6220 265 103 distributions distribution NOUN cana-6220 265 104 from from ADP cana-6220 265 105 the the DET cana-6220 265 106 lomax lomax PROPN cana-6220 265 107 family family NOUN cana-6220 265 108 . . PUNCT cana-6220 266 1 the the DET cana-6220 266 2 comparative comparative ADJ cana-6220 266 3 models model NOUN cana-6220 266 4 included include VERB cana-6220 266 5 log log NOUN cana-6220 266 6 - - PUNCT cana-6220 266 7 lomax lomax PROPN cana-6220 266 8 ( ( PUNCT cana-6220 266 9 lol lol PROPN cana-6220 266 10 ) ) PUNCT cana-6220 266 11 by by ADP cana-6220 266 12 ( ( PUNCT cana-6220 266 13 ishaq ishaq PROPN cana-6220 266 14 et et PROPN cana-6220 266 15 al al PROPN cana-6220 266 16 . . PROPN cana-6220 266 17 , , PUNCT cana-6220 266 18 2025 2025 NUM cana-6220 266 19 ) ) PUNCT cana-6220 266 20 , , PUNCT cana-6220 266 21 power power NOUN cana-6220 266 22 lomax lomax PROPN cana-6220 266 23 ( ( PUNCT cana-6220 266 24 pol pol PROPN cana-6220 266 25 ) ) PUNCT cana-6220 266 26 by by ADP cana-6220 266 27 ( ( PUNCT cana-6220 266 28 rady rady PROPN cana-6220 266 29 et et PROPN cana-6220 266 30 al al PROPN cana-6220 266 31 . . PROPN cana-6220 266 32 , , PUNCT cana-6220 266 33 2016 2016 NUM cana-6220 266 34 ) ) PUNCT cana-6220 266 35 , , PUNCT cana-6220 266 36 rayleigh rayleigh PROPN cana-6220 266 37 lomax lomax PROPN cana-6220 266 38 ( ( PUNCT cana-6220 266 39 ral ral PROPN cana-6220 266 40 ) ) PUNCT cana-6220 266 41 by by ADP cana-6220 266 42 ( ( PUNCT cana-6220 266 43 shabbir shabbir PROPN cana-6220 266 44 et et PROPN cana-6220 266 45 al al PROPN cana-6220 266 46 . . PROPN cana-6220 266 47 , , PUNCT cana-6220 266 48 2018 2018 NUM cana-6220 266 49 ) ) PUNCT cana-6220 266 50 , , PUNCT cana-6220 266 51 power power NOUN cana-6220 266 52 x x PROPN cana-6220 266 53 - - NOUN cana-6220 266 54 lindey lindey PROPN cana-6220 266 55 ( ( PUNCT cana-6220 266 56 pxlin pxlin PROPN cana-6220 266 57 ) ) PUNCT cana-6220 266 58 by by ADP cana-6220 266 59 ( ( PUNCT cana-6220 266 60 elgarhy elgarhy PROPN cana-6220 266 61 et et PROPN cana-6220 266 62 al al PROPN cana-6220 266 63 . . PROPN cana-6220 266 64 , , PUNCT cana-6220 266 65 2025 2025 NUM cana-6220 266 66 ) ) PUNCT cana-6220 266 67 , , PUNCT cana-6220 266 68 poisson poisson PROPN cana-6220 266 69 inverted invert VERB cana-6220 266 70 lomax lomax PROPN cana-6220 266 71 ( ( PUNCT cana-6220 266 72 poil poil PROPN cana-6220 266 73 ) ) PUNCT cana-6220 266 74 by by ADP cana-6220 266 75 ( ( PUNCT cana-6220 266 76 joshi joshi PROPN cana-6220 266 77 & & CCONJ cana-6220 266 78 kumar kumar PROPN cana-6220 266 79 , , PUNCT cana-6220 266 80 2021 2021 NUM cana-6220 266 81 ) ) PUNCT cana-6220 266 82 , , PUNCT cana-6220 266 83 exponentiated exponentiate VERB cana-6220 266 84 odd odd ADJ cana-6220 266 85 lomax lomax PROPN cana-6220 266 86 exponential exponential ADJ cana-6220 266 87 distribution distribution NOUN cana-6220 266 88 ( ( PUNCT cana-6220 266 89 eole eole NOUN cana-6220 266 90 ) ) PUNCT cana-6220 266 91 by by ADP cana-6220 266 92 ( ( PUNCT cana-6220 266 93 dhungana dhungana PROPN cana-6220 266 94 & & CCONJ cana-6220 266 95 kumar kumar PROPN cana-6220 266 96 , , PUNCT cana-6220 266 97 2022 2022 NUM cana-6220 266 98 ) ) PUNCT cana-6220 266 99 and and CCONJ cana-6220 266 100 transmuted transmute VERB cana-6220 266 101 exponential exponential ADJ cana-6220 266 102 lomax lomax NOUN cana-6220 266 103 ( ( PUNCT cana-6220 266 104 tel tel PROPN cana-6220 266 105 ) ) PUNCT cana-6220 266 106 by by ADP cana-6220 266 107 ( ( PUNCT cana-6220 266 108 ashour ashour PROPN cana-6220 266 109 & & CCONJ cana-6220 266 110 eltehiwy eltehiwy PROPN cana-6220 266 111 , , PUNCT cana-6220 266 112 2013 2013 NUM cana-6220 266 113 ) ) PUNCT cana-6220 266 114 . . PUNCT cana-6220 267 1 distribution distribution NOUN cana-6220 267 2 comparison comparison NOUN cana-6220 267 3 is be AUX cana-6220 267 4 performed perform VERB cana-6220 267 5 using use VERB cana-6220 267 6 a a DET cana-6220 267 7 comprehensive comprehensive ADJ cana-6220 267 8 set set NOUN cana-6220 267 9 of of ADP cana-6220 267 10 information information NOUN cana-6220 267 11 criteria criterion NOUN cana-6220 267 12 , , PUNCT cana-6220 267 13 specifically specifically ADV cana-6220 267 14 aic aic PROPN cana-6220 267 15 , , PUNCT cana-6220 267 16 bic bic PROPN cana-6220 267 17 , , PUNCT cana-6220 267 18 caic caic PROPN cana-6220 267 19 , , PUNCT cana-6220 267 20 and and CCONJ cana-6220 267 21 hqic hqic NOUN cana-6220 267 22 , , PUNCT cana-6220 267 23 representing represent VERB cana-6220 267 24 the the DET cana-6220 267 25 akaike akaike ADJ cana-6220 267 26 , , PUNCT cana-6220 267 27 bayesian bayesian NOUN cana-6220 267 28 , , PUNCT cana-6220 267 29 consistent consistent ADJ cana-6220 267 30 akaike akaike ADJ cana-6220 267 31 , , PUNCT cana-6220 267 32 and and CCONJ cana-6220 267 33 hannan hannan PROPN cana-6220 267 34 - - PUNCT cana-6220 267 35 quinn quinn PROPN cana-6220 267 36 information information NOUN cana-6220 267 37 criteria criterion NOUN cana-6220 267 38 , , PUNCT cana-6220 267 39 respectively respectively ADV cana-6220 267 40 . . PUNCT cana-6220 268 1 we we PRON cana-6220 268 2 also also ADV cana-6220 268 3 used use VERB cana-6220 268 4 the the DET cana-6220 268 5 kolmogorov kolmogorov ADJ cana-6220 268 6 - - PUNCT cana-6220 268 7 smirnov smirnov NOUN cana-6220 268 8 ( ( PUNCT cana-6220 268 9 k k NOUN cana-6220 268 10 - - PUNCT cana-6220 268 11 s s NOUN cana-6220 268 12 ) ) PUNCT cana-6220 268 13 test test NOUN cana-6220 268 14 to to PART cana-6220 268 15 better well ADV cana-6220 268 16 check check VERB cana-6220 268 17 how how SCONJ cana-6220 268 18 well well ADV cana-6220 268 19 each each DET cana-6220 268 20 distribution distribution NOUN cana-6220 268 21 worked work VERB cana-6220 268 22 . . PUNCT cana-6220 269 1 we we PRON cana-6220 269 2 picked pick VERB cana-6220 269 3 the the DET cana-6220 269 4 best good ADJ cana-6220 269 5 distribution distribution NOUN cana-6220 269 6 by by ADP cana-6220 269 7 looking look VERB cana-6220 269 8 for for ADP cana-6220 269 9 the the DET cana-6220 269 10 one one NOUN cana-6220 269 11 with with ADP cana-6220 269 12 the the DET cana-6220 269 13 highest high ADJ cana-6220 269 14 log log NOUN cana-6220 269 15 - - PUNCT cana-6220 269 16 likelihood likelihood NOUN cana-6220 269 17 value value NOUN cana-6220 269 18 , , PUNCT cana-6220 269 19 the the DET cana-6220 269 20 best good ADJ cana-6220 269 21 p p NOUN cana-6220 269 22 - - PUNCT cana-6220 269 23 value value NOUN cana-6220 269 24 from from ADP cana-6220 269 25 the the DET cana-6220 269 26 k k PROPN cana-6220 269 27 - - PUNCT cana-6220 269 28 s s PART cana-6220 269 29 test test NOUN cana-6220 269 30 , , PUNCT cana-6220 269 31 and and CCONJ cana-6220 269 32 the the DET cana-6220 269 33 lowest low ADJ cana-6220 269 34 aic aic PROPN cana-6220 269 35 , , PUNCT cana-6220 269 36 bic bic PROPN cana-6220 269 37 , , PUNCT cana-6220 269 38 and and CCONJ cana-6220 269 39 caic caic PROPN cana-6220 269 40 scores score NOUN cana-6220 269 41 . . PUNCT cana-6220 270 1 table table NOUN cana-6220 270 2 4 4 NUM cana-6220 270 3 : : PUNCT cana-6220 270 4 goodness goodness NOUN cana-6220 270 5 of of ADP cana-6220 270 6 fit fit ADJ cana-6220 270 7 tests test NOUN cana-6220 270 8 for for ADP cana-6220 270 9 cancer cancer NOUN cana-6220 270 10 patient patient NOUN cana-6220 270 11 dataset dataset NOUN cana-6220 270 12 distributions distribution NOUN cana-6220 270 13 -2logl -2logl ADP cana-6220 270 14 aic aic PROPN cana-6220 270 15 bic bic PROPN cana-6220 270 16 hqic hqic PROPN cana-6220 270 17 caic caic PROPN cana-6220 270 18 k k PROPN cana-6220 270 19 - - PUNCT cana-6220 270 20 s s PART cana-6220 270 21 p p ADJ cana-6220 270 22 - - PUNCT cana-6220 270 23 value value NOUN cana-6220 270 24 moldx moldx NOUN cana-6220 270 25 885.4448 885.4448 NUM cana-6220 270 26 891.4448 891.4448 NUM cana-6220 270 27 900.2047 900.2047 NUM cana-6220 270 28 895.0046 895.0046 NUM cana-6220 270 29 891.6253 891.6253 NUM cana-6220 270 30 0.17 0.17 NUM cana-6220 270 31 0.000726 0.000726 NUM cana-6220 270 32 ral ral ADJ cana-6220 270 33 885.8124 885.8124 NUM cana-6220 270 34 891.8124 891.8124 NUM cana-6220 270 35 900.5723 900.5723 NUM cana-6220 270 36 895.3722 895.3722 NUM cana-6220 270 37 891.9929 891.9929 NUM cana-6220 270 38 0.1961 0.1961 NUM cana-6220 270 39 5.33e-05 5.33e-05 NUM cana-6220 270 40 lol lol ADJ cana-6220 270 41 888.3446 888.3446 NUM cana-6220 270 42 894.3446 894.3446 NUM cana-6220 270 43 903.1045 903.1045 NUM cana-6220 270 44 897.9044 897.9044 NUM cana-6220 270 45 894.5251 894.5251 NUM cana-6220 270 46 0.2103 0.2103 NUM cana-6220 270 47 1.09e-05 1.09e-05 NUM cana-6220 270 48 pxlin pxlin NOUN cana-6220 270 49 912.2588 912.2588 NUM cana-6220 270 50 918.2588 918.2588 NUM cana-6220 270 51 927.0187 927.0187 NUM cana-6220 270 52 921.8186 921.8186 NUM cana-6220 270 53 918.4393 918.4393 NUM cana-6220 270 54 0.2052 0.2052 NUM cana-6220 270 55 1.94e-05 1.94e-05 NUM cana-6220 270 56 poil poil NOUN cana-6220 270 57 989.5734 989.5734 NUM cana-6220 270 58 995.5734 995.5734 NUM cana-6220 270 59 1004.333 1004.333 NUM cana-6220 270 60 999.1332 999.1332 NUM cana-6220 270 61 995.7539 995.7539 NUM cana-6220 270 62 0.3391 0.3391 NUM cana-6220 270 63 4.18e-14 4.18e-14 NUM cana-6220 270 64 eole eole NOUN cana-6220 270 65 997.8764 997.8764 NUM cana-6220 270 66 997.5734 997.5734 NUM cana-6220 270 67 997.5734 997.5734 NUM cana-6220 270 68 1009.253 1009.253 NUM cana-6220 270 69 1002.32 1002.32 NUM cana-6220 270 70 0.1955 0.1955 NUM cana-6220 270 71 5.64e-05 5.64e-05 NUM cana-6220 270 72 tel tel ADP cana-6220 270 73 1017.408 1017.408 NUM cana-6220 270 74 1025.408 1025.408 NUM cana-6220 270 75 1037.087 1037.087 NUM cana-6220 270 76 1030.154 1030.154 NUM cana-6220 270 77 1025.711 1025.711 NUM cana-6220 270 78 0.3384 0.3384 NUM cana-6220 270 79 4.72e-14 4.72e-14 NUM cana-6220 270 80 pol pol NOUN cana-6220 270 81 1111.972 1111.972 PROPN cana-6220 270 82 1117.972 1117.972 PROPN cana-6220 270 83 1126.732 1126.732 NUM cana-6220 270 84 1121.531 1121.531 NUM cana-6220 270 85 1118.152 1118.152 NUM cana-6220 270 86 0.2587 0.2587 NUM cana-6220 270 87 2.17e-08 2.17e-08 NUM cana-6220 270 88 table table NOUN cana-6220 270 89 ( ( PUNCT cana-6220 270 90 4 4 NUM cana-6220 270 91 ) ) PUNCT cana-6220 270 92 presents present VERB cana-6220 270 93 a a DET cana-6220 270 94 comparative comparative ADJ cana-6220 270 95 analysis analysis NOUN cana-6220 270 96 of of ADP cana-6220 270 97 the the DET cana-6220 270 98 mold mold NOUN cana-6220 270 99 against against ADP cana-6220 270 100 seven seven NUM cana-6220 270 101 alternative alternative ADJ cana-6220 270 102 distribution distribution NOUN cana-6220 270 103 functions function NOUN cana-6220 270 104 using use VERB cana-6220 270 105 goodness goodness NOUN cana-6220 270 106 - - PUNCT cana-6220 270 107 of of ADP cana-6220 270 108 - - PUNCT cana-6220 270 109 fit fit ADJ cana-6220 270 110 measures measure NOUN cana-6220 270 111 . . PUNCT cana-6220 271 1 the the DET cana-6220 271 2 results result NOUN cana-6220 271 3 demonstrate demonstrate VERB cana-6220 271 4 that that SCONJ cana-6220 271 5 mold mold NOUN cana-6220 271 6 exhibits exhibit VERB cana-6220 271 7 superior superior ADJ cana-6220 271 8 performance performance NOUN cana-6220 271 9 , , PUNCT cana-6220 271 10 achieving achieve VERB cana-6220 271 11 the the DET cana-6220 271 12 minimum minimum ADJ cana-6220 271 13 values value NOUN cana-6220 271 14 for for ADP cana-6220 271 15 aic aic PROPN cana-6220 271 16 , , PUNCT cana-6220 271 17 bic bic PROPN cana-6220 271 18 , , PUNCT cana-6220 271 19 hqic hqic NOUN cana-6220 271 20 , , PUNCT cana-6220 271 21 and and CCONJ cana-6220 271 22 caic caic PROPN cana-6220 271 23 relative relative ADJ cana-6220 271 24 to to ADP cana-6220 271 25 the the DET cana-6220 271 26 seven seven NUM cana-6220 271 27 competing compete VERB cana-6220 271 28 distributions distribution NOUN cana-6220 271 29 . . PUNCT cana-6220 272 1 additionally additionally ADV cana-6220 272 2 , , PUNCT cana-6220 272 3 we we PRON cana-6220 272 4 computed compute VERB cana-6220 272 5 the the DET cana-6220 272 6 kolmogorov kolmogorov ADJ cana-6220 272 7 smirnov smirnov PROPN cana-6220 272 8 test test NOUN cana-6220 272 9 statistic statistic NOUN cana-6220 272 10 alongside alongside ADP cana-6220 272 11 its its PRON cana-6220 272 12 associated associated ADJ cana-6220 272 13 p p NOUN cana-6220 272 14 - - PUNCT cana-6220 272 15 value value NOUN cana-6220 272 16 . . PUNCT cana-6220 273 1 optimal optimal ADJ cana-6220 273 2 model model NOUN cana-6220 273 3 fit fit NOUN cana-6220 273 4 is be AUX cana-6220 273 5 characterized characterize VERB cana-6220 273 6 by by ADP cana-6220 273 7 minimal minimal ADJ cana-6220 273 8 k k PROPN cana-6220 273 9 - - PUNCT cana-6220 273 10 s s PART cana-6220 273 11 values value NOUN cana-6220 273 12 and and CCONJ cana-6220 273 13 maximal maximal ADJ cana-6220 273 14 p p NOUN cana-6220 273 15 - - PUNCT cana-6220 273 16 values value NOUN cana-6220 273 17 . . PUNCT cana-6220 274 1 the the DET cana-6220 274 2 mold mold NOUN cana-6220 274 3 yielded yield VERB cana-6220 274 4 a a DET cana-6220 274 5 k k PROPN cana-6220 274 6 - - PUNCT cana-6220 274 7 s s NOUN cana-6220 274 8 statistic statistic NOUN cana-6220 274 9 of of ADP cana-6220 274 10 0.17 0.17 NUM cana-6220 274 11 with with ADP cana-6220 274 12 a a DET cana-6220 274 13 corresponding corresponding ADJ cana-6220 274 14 p p NOUN cana-6220 274 15 - - PUNCT cana-6220 274 16 value value NOUN cana-6220 274 17 of of ADP cana-6220 274 18 0.000726 0.000726 NUM cana-6220 274 19 , , PUNCT cana-6220 274 20 representing represent VERB cana-6220 274 21 the the DET cana-6220 274 22 most most ADV cana-6220 274 23 favourable favourable ADJ cana-6220 274 24 performance performance NOUN cana-6220 274 25 among among ADP cana-6220 274 26 all all DET cana-6220 274 27 competing compete VERB cana-6220 274 28 models model NOUN cana-6220 274 29 , , PUNCT cana-6220 274 30 thereby thereby ADV cana-6220 274 31 establishing establish VERB cana-6220 274 32 mold mold NOUN cana-6220 274 33 as as ADP cana-6220 274 34 the the DET cana-6220 274 35 most most ADV cana-6220 274 36 appropriate appropriate ADJ cana-6220 274 37 distribution distribution NOUN cana-6220 274 38 for for ADP cana-6220 274 39 practical practical ADJ cana-6220 274 40 applications application NOUN cana-6220 274 41 , , PUNCT cana-6220 274 42 particularly particularly ADV cana-6220 274 43 in in ADP cana-6220 274 44 modelling model VERB cana-6220 274 45 cancer cancer NOUN cana-6220 274 46 patient patient PROPN cana-6220 274 47 remission remission PROPN cana-6220 274 48 times time NOUN cana-6220 274 49 . . PUNCT cana-6220 275 1 communications communication NOUN cana-6220 275 2 on on ADP cana-6220 275 3 applied apply VERB cana-6220 275 4 nonlinear nonlinear ADJ cana-6220 275 5 analysis analysis NOUN cana-6220 275 6 issn issn NOUN cana-6220 275 7 : : PUNCT cana-6220 275 8 1074 1074 NUM cana-6220 275 9 - - PUNCT cana-6220 275 10 133x 133x NUM cana-6220 275 11 vol vol VERB cana-6220 275 12 32 32 NUM cana-6220 275 13 no no NOUN cana-6220 275 14 . . PUNCT cana-6220 276 1 10s 10 NOUN cana-6220 276 2 ( ( PUNCT cana-6220 276 3 2025 2025 NUM cana-6220 276 4 ) ) PUNCT cana-6220 276 5 3560 3560 NUM cana-6220 276 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 276 7 figure figure NOUN cana-6220 276 8 5 5 NUM cana-6220 276 9 . . PUNCT cana-6220 276 10 plots plot NOUN cana-6220 276 11 for for ADP cana-6220 276 12 the the DET cana-6220 276 13 cancer cancer NOUN cana-6220 276 14 patient patient NOUN cana-6220 276 15 ’s ’s PART cana-6220 276 16 dataset dataset ADJ cana-6220 276 17 figure figure NOUN cana-6220 276 18 ( ( PUNCT cana-6220 276 19 5 5 NUM cana-6220 276 20 ) ) PUNCT cana-6220 276 21 displays display VERB cana-6220 276 22 three three NUM cana-6220 276 23 visual visual ADJ cana-6220 276 24 diagnostic diagnostic ADJ cana-6220 276 25 tools tool NOUN cana-6220 276 26 β€” β€” PUNCT cana-6220 276 27 probability probability NOUN cana-6220 276 28 density density NOUN cana-6220 276 29 function function NOUN cana-6220 276 30 histogram histogram NOUN cana-6220 276 31 , , PUNCT cana-6220 276 32 empirical empirical ADJ cana-6220 276 33 cumulative cumulative ADJ cana-6220 276 34 distribution distribution NOUN cana-6220 276 35 function function NOUN cana-6220 276 36 ( ( PUNCT cana-6220 276 37 ecdf ecdf ADJ cana-6220 276 38 ) ) PUNCT cana-6220 276 39 , , PUNCT cana-6220 276 40 and and CCONJ cana-6220 276 41 probability probability NOUN cana-6220 276 42 - - PUNCT cana-6220 276 43 probability probability NOUN cana-6220 276 44 plot plot NOUN cana-6220 276 45 utilized utilize VERB cana-6220 276 46 to to PART cana-6220 276 47 assess assess VERB cana-6220 276 48 model model NOUN cana-6220 276 49 adequacy adequacy NOUN cana-6220 276 50 across across ADP cana-6220 276 51 various various ADJ cana-6220 276 52 distributions distribution NOUN cana-6220 276 53 for for ADP cana-6220 276 54 the the DET cana-6220 276 55 given give VERB cana-6220 276 56 dataset dataset NOUN cana-6220 276 57 . . PUNCT cana-6220 277 1 throughout throughout ADP cana-6220 277 2 all all DET cana-6220 277 3 three three NUM cana-6220 277 4 evaluation evaluation NOUN cana-6220 277 5 methods method NOUN cana-6220 277 6 , , PUNCT cana-6220 277 7 mold mold NOUN cana-6220 277 8 exhibits exhibit VERB cana-6220 277 9 optimal optimal ADJ cana-6220 277 10 fitting fitting ADJ cana-6220 277 11 characteristics characteristic NOUN cana-6220 277 12 , , PUNCT cana-6220 277 13 as as SCONJ cana-6220 277 14 evidenced evidence VERB cana-6220 277 15 by by ADP cana-6220 277 16 its its PRON cana-6220 277 17 curves curve NOUN cana-6220 277 18 closely closely ADV cana-6220 277 19 following follow VERB cana-6220 277 20 the the DET cana-6220 277 21 observed observe VERB cana-6220 277 22 data data NOUN cana-6220 277 23 patterns pattern NOUN cana-6220 277 24 . . PUNCT cana-6220 278 1 the the DET cana-6220 278 2 newly newly ADV cana-6220 278 3 developed develop VERB cana-6220 278 4 mold mold NOUN cana-6220 278 5 distribution distribution NOUN cana-6220 278 6 achieved achieve VERB cana-6220 278 7 superior superior ADJ cana-6220 278 8 performance performance NOUN cana-6220 278 9 when when SCONJ cana-6220 278 10 compared compare VERB cana-6220 278 11 to to ADP cana-6220 278 12 existing exist VERB cana-6220 278 13 competitive competitive ADJ cana-6220 278 14 models model NOUN cana-6220 278 15 , , PUNCT cana-6220 278 16 showing show VERB cana-6220 278 17 better well ADJ cana-6220 278 18 goodness goodness NOUN cana-6220 278 19 - - PUNCT cana-6220 278 20 of of ADP cana-6220 278 21 - - PUNCT cana-6220 278 22 fit fit NOUN cana-6220 278 23 measures measure NOUN cana-6220 278 24 and and CCONJ cana-6220 278 25 diminished diminish VERB cana-6220 278 26 information information NOUN cana-6220 278 27 criteria criterion NOUN cana-6220 278 28 scores score NOUN cana-6220 278 29 . . PUNCT cana-6220 279 1 these these DET cana-6220 279 2 empirical empirical ADJ cana-6220 279 3 outcomes outcome NOUN cana-6220 279 4 emphasize emphasize VERB cana-6220 279 5 its its PRON cana-6220 279 6 capability capability NOUN cana-6220 279 7 in in ADP cana-6220 279 8 modelling model VERB cana-6220 279 9 non non ADJ cana-6220 279 10 - - ADJ cana-6220 279 11 symmetric symmetric ADJ cana-6220 279 12 and and CCONJ cana-6220 279 13 sophisticated sophisticated ADJ cana-6220 279 14 data datum NOUN cana-6220 279 15 configurations configuration NOUN cana-6220 279 16 . . PUNCT cana-6220 280 1 the the DET cana-6220 280 2 findings finding NOUN cana-6220 280 3 of of ADP cana-6220 280 4 this this DET cana-6220 280 5 investigation investigation NOUN cana-6220 280 6 present present VERB cana-6220 280 7 the the DET cana-6220 280 8 mold mold NOUN cana-6220 280 9 as as ADP cana-6220 280 10 a a DET cana-6220 280 11 significant significant ADJ cana-6220 280 12 analytical analytical ADJ cana-6220 280 13 resource resource NOUN cana-6220 280 14 for for ADP cana-6220 280 15 reliability reliability NOUN cana-6220 280 16 engineering engineering NOUN cana-6220 280 17 , , PUNCT cana-6220 280 18 survival survival NOUN cana-6220 280 19 research research NOUN cana-6220 280 20 , , PUNCT cana-6220 280 21 and and CCONJ cana-6220 280 22 risk risk NOUN cana-6220 280 23 management management NOUN cana-6220 280 24 applications application NOUN cana-6220 280 25 . . PUNCT cana-6220 281 1 9 9 X cana-6220 281 2 . . X cana-6220 281 3 conclusion conclusion NOUN cana-6220 281 4 this this DET cana-6220 281 5 research research NOUN cana-6220 281 6 introduces introduce VERB cana-6220 281 7 the the DET cana-6220 281 8 mold mold NOUN cana-6220 281 9 , , PUNCT cana-6220 281 10 a a DET cana-6220 281 11 new new ADJ cana-6220 281 12 three three NUM cana-6220 281 13 - - PUNCT cana-6220 281 14 parameter parameter NOUN cana-6220 281 15 extension extension NOUN cana-6220 281 16 of of ADP cana-6220 281 17 the the DET cana-6220 281 18 standard standard ADJ cana-6220 281 19 lomax lomax PROPN cana-6220 281 20 distribution distribution NOUN cana-6220 281 21 , , PUNCT cana-6220 281 22 created create VERB cana-6220 281 23 to to PART cana-6220 281 24 overcome overcome VERB cana-6220 281 25 challenges challenge NOUN cana-6220 281 26 in in ADP cana-6220 281 27 studying study VERB cana-6220 281 28 complex complex ADJ cana-6220 281 29 survival survival NOUN cana-6220 281 30 and and CCONJ cana-6220 281 31 reliability reliability NOUN cana-6220 281 32 data datum NOUN cana-6220 281 33 . . PUNCT cana-6220 282 1 the the DET cana-6220 282 2 distribution distribution NOUN cana-6220 282 3 features feature VERB cana-6220 282 4 heavy heavy ADJ cana-6220 282 5 tails tail NOUN cana-6220 282 6 and and CCONJ cana-6220 282 7 a a DET cana-6220 282 8 decreasing decrease VERB cana-6220 282 9 hazard hazard NOUN cana-6220 282 10 rate rate NOUN cana-6220 282 11 , , PUNCT cana-6220 282 12 making make VERB cana-6220 282 13 it it PRON cana-6220 282 14 suitable suitable ADJ cana-6220 282 15 for for ADP cana-6220 282 16 long long ADJ cana-6220 282 17 - - PUNCT cana-6220 282 18 term term NOUN cana-6220 282 19 survival survival NOUN cana-6220 282 20 analysis analysis NOUN cana-6220 282 21 . . PUNCT cana-6220 283 1 by by ADP cana-6220 283 2 combining combine VERB cana-6220 283 3 the the DET cana-6220 283 4 flexible flexible ADJ cana-6220 283 5 properties property NOUN cana-6220 283 6 of of ADP cana-6220 283 7 the the DET cana-6220 283 8 modi modi PROPN cana-6220 283 9 family family PROPN cana-6220 283 10 with with ADP cana-6220 283 11 the the DET cana-6220 283 12 basic basic ADJ cana-6220 283 13 structure structure NOUN cana-6220 283 14 of of ADP cana-6220 283 15 the the DET cana-6220 283 16 lomax lomax PROPN cana-6220 283 17 distribution distribution NOUN cana-6220 283 18 , , PUNCT cana-6220 283 19 the the DET cana-6220 283 20 mold mold NOUN cana-6220 283 21 shows show VERB cana-6220 283 22 improved improve VERB cana-6220 283 23 adaptability adaptability NOUN cana-6220 283 24 through through ADP cana-6220 283 25 its its PRON cana-6220 283 26 hazard hazard NOUN cana-6220 283 27 function function NOUN cana-6220 283 28 behaviour behaviour NOUN cana-6220 283 29 , , PUNCT cana-6220 283 30 quantile quantile NOUN cana-6220 283 31 features feature NOUN cana-6220 283 32 , , PUNCT cana-6220 283 33 and and CCONJ cana-6220 283 34 tail tail NOUN cana-6220 283 35 properties property NOUN cana-6220 283 36 . . PUNCT cana-6220 284 1 we we PRON cana-6220 284 2 developed develop VERB cana-6220 284 3 a a DET cana-6220 284 4 complete complete ADJ cana-6220 284 5 mathematical mathematical ADJ cana-6220 284 6 framework framework NOUN cana-6220 284 7 for for ADP cana-6220 284 8 the the DET cana-6220 284 9 distribution distribution NOUN cana-6220 284 10 , , PUNCT cana-6220 284 11 including include VERB cana-6220 284 12 moments moment NOUN cana-6220 284 13 , , PUNCT cana-6220 284 14 survival survival NOUN cana-6220 284 15 functions function NOUN cana-6220 284 16 , , PUNCT cana-6220 284 17 and and CCONJ cana-6220 284 18 entropy entropy NOUN cana-6220 284 19 measures measure NOUN cana-6220 284 20 , , PUNCT cana-6220 284 21 which which PRON cana-6220 284 22 confirms confirm VERB cana-6220 284 23 its its PRON cana-6220 284 24 theoretical theoretical ADJ cana-6220 284 25 strength strength NOUN cana-6220 284 26 . . PUNCT cana-6220 285 1 for for ADP cana-6220 285 2 parameter parameter NOUN cana-6220 285 3 estimation estimation NOUN cana-6220 285 4 , , PUNCT cana-6220 285 5 we we PRON cana-6220 285 6 applied apply VERB cana-6220 285 7 both both CCONJ cana-6220 285 8 classical classical ADJ cana-6220 285 9 maximum maximum ADJ cana-6220 285 10 likelihood likelihood NOUN cana-6220 285 11 estimation estimation NOUN cana-6220 285 12 ( ( PUNCT cana-6220 285 13 mle mle PROPN cana-6220 285 14 ) ) PUNCT cana-6220 285 15 and and CCONJ cana-6220 285 16 bayesian bayesian NOUN cana-6220 285 17 methods method NOUN cana-6220 285 18 using use VERB cana-6220 285 19 gamma gamma NOUN cana-6220 285 20 priors prior NOUN cana-6220 285 21 . . PUNCT cana-6220 286 1 monte monte PROPN cana-6220 286 2 carlo carlo PROPN cana-6220 286 3 simulations simulation NOUN cana-6220 286 4 validated validate VERB cana-6220 286 5 that that SCONJ cana-6220 286 6 the the DET cana-6220 286 7 mle mle PROPN cana-6220 286 8 estimators estimator NOUN cana-6220 286 9 are be AUX cana-6220 286 10 consistent consistent ADJ cana-6220 286 11 and and CCONJ cana-6220 286 12 asymptotically asymptotically ADV cana-6220 286 13 efficient efficient ADJ cana-6220 286 14 . . PUNCT cana-6220 287 1 our our PRON cana-6220 287 2 simulation simulation NOUN cana-6220 287 3 studies study NOUN cana-6220 287 4 examined examine VERB cana-6220 287 5 estimator estimator NOUN cana-6220 287 6 performance performance NOUN cana-6220 287 7 using use VERB cana-6220 287 8 mean mean NOUN cana-6220 287 9 squared square VERB cana-6220 287 10 error error NOUN cana-6220 287 11 , , PUNCT cana-6220 287 12 showing show VERB cana-6220 287 13 that that SCONJ cana-6220 287 14 estimation estimation NOUN cana-6220 287 15 accuracy accuracy NOUN cana-6220 287 16 improves improve VERB cana-6220 287 17 as as SCONJ cana-6220 287 18 sample sample NOUN cana-6220 287 19 sizes size NOUN cana-6220 287 20 increase increase VERB cana-6220 287 21 . . PUNCT cana-6220 288 1 to to PART cana-6220 288 2 test test VERB cana-6220 288 3 practical practical ADJ cana-6220 288 4 usefulness usefulness NOUN cana-6220 288 5 , , PUNCT cana-6220 288 6 we we PRON cana-6220 288 7 applied apply VERB cana-6220 288 8 the the DET cana-6220 288 9 mold mold NOUN cana-6220 288 10 to to ADP cana-6220 288 11 a a DET cana-6220 288 12 bladder bladder NOUN cana-6220 288 13 cancer cancer NOUN cana-6220 288 14 patient patient NOUN cana-6220 288 15 dataset dataset VERB cana-6220 288 16 and and CCONJ cana-6220 288 17 compared compare VERB cana-6220 288 18 it it PRON cana-6220 288 19 with with ADP cana-6220 288 20 existing exist VERB cana-6220 288 21 distributions distribution NOUN cana-6220 288 22 using use VERB cana-6220 288 23 standard standard ADJ cana-6220 288 24 measures measure NOUN cana-6220 288 25 like like ADP cana-6220 288 26 aic aic PROPN cana-6220 288 27 , , PUNCT cana-6220 288 28 bic bic PROPN cana-6220 288 29 , , PUNCT cana-6220 288 30 caic caic PROPN cana-6220 288 31 , , PUNCT cana-6220 288 32 log log NOUN cana-6220 288 33 - - PUNCT cana-6220 288 34 likelihood likelihood NOUN cana-6220 288 35 , , PUNCT cana-6220 288 36 and and CCONJ cana-6220 288 37 the the DET cana-6220 288 38 kolmogorov kolmogorov ADJ cana-6220 288 39 - - PUNCT cana-6220 288 40 smirnov smirnov ADJ cana-6220 288 41 test test NOUN cana-6220 288 42 . . PUNCT cana-6220 289 1 the the DET cana-6220 289 2 mold mold NOUN cana-6220 289 3 consistently consistently ADV cana-6220 289 4 performed perform VERB cana-6220 289 5 better well ADV cana-6220 289 6 than than ADP cana-6220 289 7 competing compete VERB cana-6220 289 8 models model NOUN cana-6220 289 9 , , PUNCT cana-6220 289 10 showing show VERB cana-6220 289 11 superior superior ADJ cana-6220 289 12 fit fit ADJ cana-6220 289 13 quality quality NOUN cana-6220 289 14 and and CCONJ cana-6220 289 15 lower low ADJ cana-6220 289 16 information information NOUN cana-6220 289 17 criteria criterion NOUN cana-6220 289 18 values value NOUN cana-6220 289 19 . . PUNCT cana-6220 290 1 these these DET cana-6220 290 2 results result NOUN cana-6220 290 3 demonstrate demonstrate VERB cana-6220 290 4 its its PRON cana-6220 290 5 effectiveness effectiveness NOUN cana-6220 290 6 in in ADP cana-6220 290 7 modelling model VERB cana-6220 290 8 skewed skewed ADJ cana-6220 290 9 and and CCONJ cana-6220 290 10 complex complex ADJ cana-6220 290 11 data datum NOUN cana-6220 290 12 patterns pattern NOUN cana-6220 290 13 . . PUNCT cana-6220 291 1 communications communication NOUN cana-6220 291 2 on on ADP cana-6220 291 3 applied apply VERB cana-6220 291 4 nonlinear nonlinear ADJ cana-6220 291 5 analysis analysis NOUN cana-6220 291 6 issn issn NOUN cana-6220 291 7 : : PUNCT cana-6220 291 8 1074 1074 NUM cana-6220 291 9 - - PUNCT cana-6220 291 10 133x 133x NUM cana-6220 291 11 vol vol VERB cana-6220 291 12 32 32 NUM cana-6220 291 13 no no NOUN cana-6220 291 14 . . PUNCT cana-6220 292 1 10s 10 NOUN cana-6220 292 2 ( ( PUNCT cana-6220 292 3 2025 2025 NUM cana-6220 292 4 ) ) PUNCT cana-6220 292 5 3561 3561 NUM cana-6220 292 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 293 1 the the DET cana-6220 293 2 study study NOUN cana-6220 293 3 establishes establish VERB cana-6220 293 4 the the DET cana-6220 293 5 mold mold NOUN cana-6220 293 6 as as ADP cana-6220 293 7 a a DET cana-6220 293 8 useful useful ADJ cana-6220 293 9 tool tool NOUN cana-6220 293 10 for for ADP cana-6220 293 11 reliability reliability NOUN cana-6220 293 12 analysis analysis NOUN cana-6220 293 13 , , PUNCT cana-6220 293 14 survival survival NOUN cana-6220 293 15 studies study NOUN cana-6220 293 16 , , PUNCT cana-6220 293 17 and and CCONJ cana-6220 293 18 risk risk NOUN cana-6220 293 19 assessment assessment NOUN cana-6220 293 20 , , PUNCT cana-6220 293 21 particularly particularly ADV cana-6220 293 22 when when SCONJ cana-6220 293 23 dealing deal VERB cana-6220 293 24 with with ADP cana-6220 293 25 heavy heavy ADJ cana-6220 293 26 - - PUNCT cana-6220 293 27 tailed tail VERB cana-6220 293 28 data datum NOUN cana-6220 293 29 that that PRON cana-6220 293 30 exhibits exhibit VERB cana-6220 293 31 decreasing decrease VERB cana-6220 293 32 failure failure NOUN cana-6220 293 33 rates rate NOUN cana-6220 293 34 over over ADP cana-6220 293 35 time time NOUN cana-6220 293 36 . . PUNCT cana-6220 294 1 10 10 NUM cana-6220 294 2 . . PUNCT cana-6220 295 1 future future ADJ cana-6220 295 2 scope scope NOUN cana-6220 295 3 future future ADJ cana-6220 295 4 work work NOUN cana-6220 295 5 could could AUX cana-6220 295 6 develop develop VERB cana-6220 295 7 the the DET cana-6220 295 8 mold mold NOUN cana-6220 295 9 for for ADP cana-6220 295 10 multiple multiple ADJ cana-6220 295 11 variables variable NOUN cana-6220 295 12 and and CCONJ cana-6220 295 13 use use VERB cana-6220 295 14 bayesian bayesian NOUN cana-6220 295 15 approaches approach NOUN cana-6220 295 16 for for ADP cana-6220 295 17 complicated complicated ADJ cana-6220 295 18 data datum NOUN cana-6220 295 19 analysis analysis NOUN cana-6220 295 20 . . PUNCT cana-6220 296 1 researchers researcher NOUN cana-6220 296 2 could could AUX cana-6220 296 3 also also ADV cana-6220 296 4 improve improve VERB cana-6220 296 5 how how SCONJ cana-6220 296 6 it it PRON cana-6220 296 7 handles handle VERB cana-6220 296 8 incomplete incomplete ADJ cana-6220 296 9 data datum NOUN cana-6220 296 10 and and CCONJ cana-6220 296 11 combine combine VERB cana-6220 296 12 it it PRON cana-6220 296 13 with with ADP cana-6220 296 14 artificial artificial ADJ cana-6220 296 15 intelligence intelligence NOUN cana-6220 296 16 for for ADP cana-6220 296 17 better well ADJ cana-6220 296 18 predictions prediction NOUN cana-6220 296 19 . . PUNCT cana-6220 297 1 testing test VERB cana-6220 297 2 the the DET cana-6220 297 3 mold mold NOUN cana-6220 297 4 against against ADP cana-6220 297 5 newer new ADJ cana-6220 297 6 statistical statistical ADJ cana-6220 297 7 models model NOUN cana-6220 297 8 and and CCONJ cana-6220 297 9 adapting adapt VERB cana-6220 297 10 it it PRON cana-6220 297 11 for for ADP cana-6220 297 12 specific specific ADJ cana-6220 297 13 fields field NOUN cana-6220 297 14 like like ADP cana-6220 297 15 weather weather NOUN cana-6220 297 16 studies study NOUN cana-6220 297 17 or or CCONJ cana-6220 297 18 smart smart ADJ cana-6220 297 19 device device NOUN cana-6220 297 20 networks network NOUN cana-6220 297 21 would would AUX cana-6220 297 22 show show VERB cana-6220 297 23 how how SCONJ cana-6220 297 24 widely widely ADV cana-6220 297 25 it it PRON cana-6220 297 26 can can AUX cana-6220 297 27 be be AUX cana-6220 297 28 used use VERB cana-6220 297 29 and and CCONJ cana-6220 297 30 help help VERB cana-6220 297 31 advance advance VERB cana-6220 297 32 survival survival NOUN cana-6220 297 33 analysis analysis NOUN cana-6220 297 34 and and CCONJ cana-6220 297 35 risk risk NOUN cana-6220 297 36 assessment assessment NOUN cana-6220 297 37 . . PUNCT cana-6220 298 1 references reference NOUN cana-6220 298 2 [ [ X cana-6220 298 3 1 1 NUM cana-6220 298 4 ] ] PUNCT cana-6220 298 5 ahsanullah ahsanullah NOUN cana-6220 298 6 , , PUNCT cana-6220 298 7 m. m. NOUN cana-6220 298 8 ( ( PUNCT cana-6220 298 9 1991 1991 NUM cana-6220 298 10 ) ) PUNCT cana-6220 298 11 . . PUNCT cana-6220 299 1 β€œ " PUNCT cana-6220 299 2 record record ADJ cana-6220 299 3 values value NOUN cana-6220 299 4 of of ADP cana-6220 299 5 the the DET cana-6220 299 6 lomax lomax PROPN cana-6220 299 7 distribution distribution NOUN cana-6220 299 8 ” " PUNCT cana-6220 299 9 . . PUNCT cana-6220 300 1 statistica statistica PROPN cana-6220 300 2 neerlandica neerlandica PROPN cana-6220 300 3 , , PUNCT cana-6220 300 4 45(1 45(1 NOUN cana-6220 300 5 ) ) PUNCT cana-6220 300 6 , , PUNCT cana-6220 300 7 21–29 21–29 NUM cana-6220 300 8 . . PUNCT cana-6220 301 1 [ [ X cana-6220 301 2 2 2 NUM cana-6220 301 3 ] ] X cana-6220 301 4 arnold arnold PROPN cana-6220 301 5 , , PUNCT cana-6220 301 6 b. b. PROPN cana-6220 301 7 c. c. PROPN cana-6220 301 8 ( ( PUNCT cana-6220 301 9 1983 1983 NUM cana-6220 301 10 ) ) PUNCT cana-6220 301 11 . . PUNCT cana-6220 302 1 pareto pareto ADJ cana-6220 302 2 distribution distribution NOUN cana-6220 302 3 . . PUNCT cana-6220 303 1 john john PROPN cana-6220 303 2 wiley wiley PROPN cana-6220 303 3 & & CCONJ cana-6220 303 4 sons sons PROPN cana-6220 303 5 , , PUNCT cana-6220 303 6 ltd ltd PROPN cana-6220 303 7 . . PUNCT cana-6220 304 1 [ [ X cana-6220 304 2 3 3 NUM cana-6220 304 3 ] ] SYM cana-6220 304 4 ashour ashour NOUN cana-6220 304 5 , , PUNCT cana-6220 304 6 s. s. PROPN cana-6220 304 7 k. k. PROPN cana-6220 304 8 , , PUNCT cana-6220 304 9 & & CCONJ cana-6220 304 10 eltehiwy eltehiwy PROPN cana-6220 304 11 , , PUNCT cana-6220 304 12 m. m. NOUN cana-6220 304 13 a. a. PROPN cana-6220 304 14 ( ( PUNCT cana-6220 304 15 2013 2013 NUM cana-6220 304 16 ) ) PUNCT cana-6220 304 17 . . PUNCT cana-6220 305 1 β€œ " PUNCT cana-6220 305 2 transmuted transmute VERB cana-6220 305 3 exponentiated exponentiated ADJ cana-6220 305 4 lomax lomax PROPN cana-6220 305 5 distribution distribution NOUN cana-6220 305 6 ” " PUNCT cana-6220 305 7 . . PUNCT cana-6220 306 1 australian australian ADJ cana-6220 306 2 journal journal NOUN cana-6220 306 3 of of ADP cana-6220 306 4 basic basic ADJ cana-6220 306 5 and and CCONJ cana-6220 306 6 applied applied ADJ cana-6220 306 7 sciences science NOUN cana-6220 306 8 , , PUNCT cana-6220 306 9 7(7 7(7 NUM cana-6220 306 10 ) ) PUNCT cana-6220 306 11 , , PUNCT cana-6220 306 12 658–667 658–667 NUM cana-6220 306 13 . . PUNCT cana-6220 307 1 [ [ X cana-6220 307 2 4 4 NUM cana-6220 307 3 ] ] X cana-6220 307 4 atkinson atkinson PROPN cana-6220 307 5 , , PUNCT cana-6220 307 6 a. a. PROPN cana-6220 307 7 b. b. PROPN cana-6220 307 8 , , PUNCT cana-6220 307 9 & & CCONJ cana-6220 307 10 harrison harrison PROPN cana-6220 307 11 , , PUNCT cana-6220 307 12 a. a. PROPN cana-6220 307 13 j. j. PROPN cana-6220 307 14 ( ( PUNCT cana-6220 307 15 1978 1978 NUM cana-6220 307 16 ) ) PUNCT cana-6220 307 17 . . PUNCT cana-6220 308 1 distribution distribution NOUN cana-6220 308 2 of of ADP cana-6220 308 3 personal personal ADJ cana-6220 308 4 wealth wealth NOUN cana-6220 308 5 in in ADP cana-6220 308 6 britain britain PROPN cana-6220 308 7 . . PUNCT cana-6220 309 1 cambridge cambridge PROPN cana-6220 309 2 , , PUNCT cana-6220 309 3 uk uk PROPN cana-6220 309 4 : : PUNCT cana-6220 309 5 cambridge cambridge PROPN cana-6220 309 6 university university PROPN cana-6220 309 7 press press NOUN cana-6220 309 8 . . PUNCT cana-6220 310 1 [ [ X cana-6220 310 2 5 5 NUM cana-6220 310 3 ] ] X cana-6220 310 4 balakrishnan balakrishnan PROPN cana-6220 310 5 , , PUNCT cana-6220 310 6 n. n. NOUN cana-6220 310 7 , , PUNCT cana-6220 310 8 & & CCONJ cana-6220 310 9 ahsanullah ahsanullah PROPN cana-6220 310 10 , , PUNCT cana-6220 310 11 m. m. NOUN cana-6220 310 12 ( ( PUNCT cana-6220 310 13 1994 1994 NUM cana-6220 310 14 ) ) PUNCT cana-6220 310 15 . . PUNCT cana-6220 311 1 β€œ " PUNCT cana-6220 311 2 relations relation NOUN cana-6220 311 3 for for ADP cana-6220 311 4 single single ADJ cana-6220 311 5 and and CCONJ cana-6220 311 6 product product NOUN cana-6220 311 7 moments moment NOUN cana-6220 311 8 of of ADP cana-6220 311 9 record record NOUN cana-6220 311 10 values value NOUN cana-6220 311 11 from from ADP cana-6220 311 12 lomax lomax PROPN cana-6220 311 13 distribution distribution NOUN cana-6220 311 14 ” " PUNCT cana-6220 311 15 . . PUNCT cana-6220 312 1 sankhyā sankhyā NOUN cana-6220 312 2 : : PUNCT cana-6220 312 3 the the DET cana-6220 312 4 indian indian PROPN cana-6220 312 5 journal journal PROPN cana-6220 312 6 of of ADP cana-6220 312 7 statistics statistic NOUN cana-6220 312 8 , , PUNCT cana-6220 312 9 series series PROPN cana-6220 312 10 b b PROPN cana-6220 312 11 , , PUNCT cana-6220 312 12 140–146 140–146 NUM cana-6220 312 13 . . PUNCT cana-6220 313 1 [ [ X cana-6220 313 2 6 6 NUM cana-6220 313 3 ] ] SYM cana-6220 313 4 balkema balkema NOUN cana-6220 313 5 , , PUNCT cana-6220 313 6 a. a. NOUN cana-6220 313 7 a. a. PROPN cana-6220 313 8 , , PUNCT cana-6220 313 9 & & CCONJ cana-6220 313 10 de de PROPN cana-6220 313 11 haan haan PROPN cana-6220 313 12 , , PUNCT cana-6220 313 13 l. l. PROPN cana-6220 313 14 ( ( PUNCT cana-6220 313 15 1974 1974 NUM cana-6220 313 16 ) ) PUNCT cana-6220 313 17 . . PUNCT cana-6220 314 1 β€œ " PUNCT cana-6220 314 2 residual residual ADJ cana-6220 314 3 life life NOUN cana-6220 314 4 time time NOUN cana-6220 314 5 at at ADP cana-6220 314 6 great great ADJ cana-6220 314 7 age age NOUN cana-6220 314 8 ” " PUNCT cana-6220 314 9 . . PUNCT cana-6220 315 1 the the DET cana-6220 315 2 annals annal NOUN cana-6220 315 3 of of ADP cana-6220 315 4 probability probability NOUN cana-6220 315 5 , , PUNCT cana-6220 315 6 2(5 2(5 NUM cana-6220 315 7 ) ) PUNCT cana-6220 315 8 , , PUNCT cana-6220 315 9 792–804 792–804 NUM cana-6220 315 10 . . PUNCT cana-6220 316 1 [ [ X cana-6220 316 2 7 7 NUM cana-6220 316 3 ] ] X cana-6220 316 4 bryson bryson PROPN cana-6220 316 5 , , PUNCT cana-6220 316 6 m. m. PROPN cana-6220 316 7 c. c. PROPN cana-6220 316 8 ( ( PUNCT cana-6220 316 9 1974 1974 NUM cana-6220 316 10 ) ) PUNCT cana-6220 316 11 . . PUNCT cana-6220 317 1 β€œ " PUNCT cana-6220 317 2 heavy heavy ADJ cana-6220 317 3 - - PUNCT cana-6220 317 4 tailed tail VERB cana-6220 317 5 distributions distribution NOUN cana-6220 317 6 : : PUNCT cana-6220 317 7 properties property NOUN cana-6220 317 8 and and CCONJ cana-6220 317 9 tests test NOUN cana-6220 317 10 ” " PUNCT cana-6220 317 11 . . PUNCT cana-6220 318 1 technometrics technometric NOUN cana-6220 318 2 , , PUNCT cana-6220 318 3 16(1 16(1 NUM cana-6220 318 4 ) ) PUNCT cana-6220 318 5 , , PUNCT cana-6220 318 6 61–68 61–68 NUM cana-6220 318 7 . . PUNCT cana-6220 319 1 [ [ X cana-6220 319 2 8 8 NUM cana-6220 319 3 ] ] X cana-6220 319 4 chahkandi chahkandi NOUN cana-6220 319 5 , , PUNCT cana-6220 319 6 m. m. NOUN cana-6220 319 7 , , PUNCT cana-6220 319 8 farsi farsi NOUN cana-6220 319 9 , , PUNCT cana-6220 319 10 m. m. NOUN cana-6220 319 11 , , PUNCT cana-6220 319 12 & & CCONJ cana-6220 319 13 ganjali ganjali PROPN cana-6220 319 14 , , PUNCT cana-6220 319 15 m. m. NOUN cana-6220 319 16 ( ( PUNCT cana-6220 319 17 2009 2009 NUM cana-6220 319 18 ) ) PUNCT cana-6220 319 19 . . PUNCT cana-6220 320 1 β€œ " PUNCT cana-6220 320 2 on on ADP cana-6220 320 3 the the DET cana-6220 320 4 renewal renewal NOUN cana-6220 320 5 function function NOUN cana-6220 320 6 of of ADP cana-6220 320 7 poisson poisson NOUN cana-6220 320 8 shock shock NOUN cana-6220 320 9 models model NOUN cana-6220 320 10 with with ADP cana-6220 320 11 lomax lomax PROPN cana-6220 320 12 distribution distribution NOUN cana-6220 320 13 as as ADP cana-6220 320 14 the the DET cana-6220 320 15 time time NOUN cana-6220 320 16 between between ADP cana-6220 320 17 the the DET cana-6220 320 18 shocks shock NOUN cana-6220 320 19 ” " PUNCT cana-6220 320 20 . . PUNCT cana-6220 321 1 journal journal PROPN cana-6220 321 2 of of ADP cana-6220 321 3 the the DET cana-6220 321 4 iranian iranian ADJ cana-6220 321 5 statistical statistical ADJ cana-6220 321 6 society society NOUN cana-6220 321 7 , , PUNCT cana-6220 321 8 8(1–2 8(1–2 PROPN cana-6220 321 9 ) ) PUNCT cana-6220 321 10 , , PUNCT cana-6220 321 11 63 63 NUM cana-6220 321 12 – – PUNCT cana-6220 321 13 75 75 NUM cana-6220 321 14 . . PUNCT cana-6220 322 1 [ [ X cana-6220 322 2 9 9 NUM cana-6220 322 3 ] ] PUNCT cana-6220 322 4 dhungana dhungana NOUN cana-6220 322 5 , , PUNCT cana-6220 322 6 g. g. PROPN cana-6220 322 7 p. p. PROPN cana-6220 322 8 , , PUNCT cana-6220 322 9 & & CCONJ cana-6220 322 10 kumar kumar PROPN cana-6220 322 11 , , PUNCT cana-6220 322 12 v. v. PROPN cana-6220 322 13 ( ( PUNCT cana-6220 322 14 2022 2022 NUM cana-6220 322 15 ) ) PUNCT cana-6220 322 16 . . PUNCT cana-6220 323 1 β€œ " PUNCT cana-6220 323 2 exponentiated exponentiate VERB cana-6220 323 3 odd odd ADJ cana-6220 323 4 lomax lomax PROPN cana-6220 323 5 exponential exponential ADJ cana-6220 323 6 distribution distribution NOUN cana-6220 323 7 with with ADP cana-6220 323 8 application application NOUN cana-6220 323 9 to to ADP cana-6220 323 10 covid-19 covid-19 PROPN cana-6220 323 11 death death NOUN cana-6220 323 12 cases case NOUN cana-6220 323 13 of of ADP cana-6220 323 14 nepal nepal NOUN cana-6220 323 15 ” " PUNCT cana-6220 323 16 . . PUNCT cana-6220 324 1 plos plos PROPN cana-6220 324 2 one one NUM cana-6220 324 3 , , PUNCT cana-6220 324 4 17(6 17(6 NUM cana-6220 324 5 ) ) PUNCT cana-6220 324 6 , , PUNCT cana-6220 324 7 e0269450 e0269450 NOUN cana-6220 324 8 . . PUNCT cana-6220 325 1 [ [ X cana-6220 325 2 10 10 NUM cana-6220 325 3 ] ] X cana-6220 325 4 elgarhy elgarhy ADJ cana-6220 325 5 , , PUNCT cana-6220 325 6 m. m. NOUN cana-6220 325 7 , , PUNCT cana-6220 325 8 hassan hassan PROPN cana-6220 325 9 , , PUNCT cana-6220 325 10 a. a. PROPN cana-6220 325 11 s. s. PROPN cana-6220 325 12 , , PUNCT cana-6220 325 13 alsadat alsadat NOUN cana-6220 325 14 , , PUNCT cana-6220 325 15 n. n. NOUN cana-6220 325 16 , , PUNCT cana-6220 325 17 balogun balogun VERB cana-6220 325 18 , , PUNCT cana-6220 325 19 o. o. PROPN cana-6220 325 20 s. s. PROPN cana-6220 325 21 , , PUNCT cana-6220 325 22 shawki shawki NOUN cana-6220 325 23 , , PUNCT cana-6220 325 24 a. a. PROPN cana-6220 325 25 w. w. PROPN cana-6220 325 26 , , PUNCT cana-6220 325 27 & & CCONJ cana-6220 325 28 ragab ragab PROPN cana-6220 325 29 , , PUNCT cana-6220 325 30 i. i. PROPN cana-6220 325 31 e. e. PROPN cana-6220 325 32 ( ( PUNCT cana-6220 325 33 2025 2025 NUM cana-6220 325 34 ) ) PUNCT cana-6220 325 35 . . PUNCT cana-6220 326 1 β€œ " PUNCT cana-6220 326 2 a a DET cana-6220 326 3 heavy heavy ADJ cana-6220 326 4 tailed tail VERB cana-6220 326 5 model model NOUN cana-6220 326 6 based base VERB cana-6220 326 7 on on ADP cana-6220 326 8 power power NOUN cana-6220 326 9 xlindley xlindley ADJ cana-6220 326 10 distribution distribution NOUN cana-6220 326 11 with with ADP cana-6220 326 12 actuarial actuarial ADJ cana-6220 326 13 data datum NOUN cana-6220 326 14 applications application NOUN cana-6220 326 15 ” " PUNCT cana-6220 326 16 . . PUNCT cana-6220 327 1 computer computer NOUN cana-6220 327 2 modeling modeling NOUN cana-6220 327 3 in in ADP cana-6220 327 4 engineering engineering PROPN cana-6220 327 5 & & CCONJ cana-6220 327 6 sciences sciences PROPN cana-6220 327 7 ( ( PUNCT cana-6220 327 8 cmes cme NOUN cana-6220 327 9 ) ) PUNCT cana-6220 327 10 , , PUNCT cana-6220 327 11 142(3 142(3 NUM cana-6220 327 12 ) ) PUNCT cana-6220 327 13 . . PUNCT cana-6220 328 1 [ [ X cana-6220 328 2 11 11 NUM cana-6220 328 3 ] ] X cana-6220 328 4 harris harris PROPN cana-6220 328 5 , , PUNCT cana-6220 328 6 c. c. PROPN cana-6220 328 7 m. m. NOUN cana-6220 328 8 ( ( PUNCT cana-6220 328 9 1968 1968 NUM cana-6220 328 10 ) ) PUNCT cana-6220 328 11 . . PUNCT cana-6220 329 1 β€œ " PUNCT cana-6220 329 2 the the DET cana-6220 329 3 pareto pareto ADJ cana-6220 329 4 distribution distribution NOUN cana-6220 329 5 as as ADP cana-6220 329 6 a a DET cana-6220 329 7 queue queue NOUN cana-6220 329 8 service service NOUN cana-6220 329 9 discipline discipline NOUN cana-6220 329 10 ” " PUNCT cana-6220 329 11 . . PUNCT cana-6220 330 1 operations operation NOUN cana-6220 330 2 research research NOUN cana-6220 330 3 , , PUNCT cana-6220 330 4 16(2 16(2 NUM cana-6220 330 5 ) ) PUNCT cana-6220 330 6 , , PUNCT cana-6220 330 7 307–313 307–313 NUM cana-6220 330 8 . . PUNCT cana-6220 331 1 [ [ X cana-6220 331 2 12 12 NUM cana-6220 331 3 ] ] X cana-6220 331 4 ishaq ishaq PROPN cana-6220 331 5 , , PUNCT cana-6220 331 6 a. a. NOUN cana-6220 331 7 i. i. PROPN cana-6220 331 8 , , PUNCT cana-6220 331 9 usman usman PROPN cana-6220 331 10 , , PUNCT cana-6220 331 11 a. a. NOUN cana-6220 331 12 u. u. PROPN cana-6220 331 13 , , PUNCT cana-6220 331 14 alqifari alqifari PROPN cana-6220 331 15 , , PUNCT cana-6220 331 16 h. h. PROPN cana-6220 331 17 n. n. PROPN cana-6220 331 18 , , PUNCT cana-6220 331 19 almohaimeed almohaimeed ADJ cana-6220 331 20 , , PUNCT cana-6220 331 21 a. a. NOUN cana-6220 331 22 , , PUNCT cana-6220 331 23 daud daud PROPN cana-6220 331 24 , , PUNCT cana-6220 331 25 h. h. PROPN cana-6220 331 26 , , PUNCT cana-6220 331 27 abba abba PROPN cana-6220 331 28 , , PUNCT cana-6220 331 29 s. s. PROPN cana-6220 331 30 i. i. PROPN cana-6220 331 31 , , PUNCT cana-6220 331 32 & & CCONJ cana-6220 331 33 suleiman suleiman PROPN cana-6220 331 34 , , PUNCT cana-6220 331 35 a. a. NOUN cana-6220 331 36 a. a. NOUN cana-6220 331 37 ( ( PUNCT cana-6220 331 38 2025 2025 NUM cana-6220 331 39 ) ) PUNCT cana-6220 331 40 . . PUNCT cana-6220 332 1 β€œ " PUNCT cana-6220 332 2 a a DET cana-6220 332 3 new new ADJ cana-6220 332 4 log log NOUN cana-6220 332 5 - - PUNCT cana-6220 332 6 lomax lomax NOUN cana-6220 332 7 distribution distribution NOUN cana-6220 332 8 , , PUNCT cana-6220 332 9 properties property NOUN cana-6220 332 10 , , PUNCT cana-6220 332 11 stock stock NOUN cana-6220 332 12 price price NOUN cana-6220 332 13 , , PUNCT cana-6220 332 14 and and CCONJ cana-6220 332 15 heart heart NOUN cana-6220 332 16 attack attack NOUN cana-6220 332 17 predictions prediction NOUN cana-6220 332 18 using use VERB cana-6220 332 19 machine machine NOUN cana-6220 332 20 learning learn VERB cana-6220 332 21 techniques technique NOUN cana-6220 332 22 ” " PUNCT cana-6220 332 23 . . PUNCT cana-6220 333 1 aims aim VERB cana-6220 333 2 mathematics mathematic NOUN cana-6220 333 3 , , PUNCT cana-6220 333 4 10(5 10(5 NUM cana-6220 333 5 ) ) PUNCT cana-6220 333 6 , , PUNCT cana-6220 333 7 12761–12807 12761–12807 NUM cana-6220 333 8 . . PUNCT cana-6220 334 1 [ [ X cana-6220 334 2 13 13 NUM cana-6220 334 3 ] ] X cana-6220 334 4 johnson johnson PROPN cana-6220 334 5 , , PUNCT cana-6220 334 6 n. n. PROPN cana-6220 334 7 l. l. PROPN cana-6220 334 8 , , PUNCT cana-6220 334 9 kotz kotz PROPN cana-6220 334 10 , , PUNCT cana-6220 334 11 s. s. PROPN cana-6220 334 12 , , PUNCT cana-6220 334 13 & & CCONJ cana-6220 334 14 balakrishnan balakrishnan PROPN cana-6220 334 15 , , PUNCT cana-6220 334 16 n. n. PROPN cana-6220 334 17 ( ( PUNCT cana-6220 334 18 1994 1994 NUM cana-6220 334 19 ) ) PUNCT cana-6220 334 20 . . PUNCT cana-6220 335 1 continuous continuous ADJ cana-6220 335 2 univariate univariate ADJ cana-6220 335 3 distributions distribution NOUN cana-6220 335 4 , , PUNCT cana-6220 335 5 volume volume NOUN cana-6220 335 6 2 2 NUM cana-6220 335 7 ( ( PUNCT cana-6220 335 8 vol vol NOUN cana-6220 335 9 . . NOUN cana-6220 335 10 2 2 NUM cana-6220 335 11 ) ) PUNCT cana-6220 335 12 . . PUNCT cana-6220 336 1 john john PROPN cana-6220 336 2 wiley wiley PROPN cana-6220 336 3 & & CCONJ cana-6220 336 4 sons son NOUN cana-6220 336 5 . . PUNCT cana-6220 337 1 [ [ X cana-6220 337 2 14 14 NUM cana-6220 337 3 ] ] X cana-6220 337 4 joshi joshi PROPN cana-6220 337 5 , , PUNCT cana-6220 337 6 r. r. PROPN cana-6220 337 7 k. k. PROPN cana-6220 337 8 , , PUNCT cana-6220 337 9 & & CCONJ cana-6220 337 10 kumar kumar PROPN cana-6220 337 11 , , PUNCT cana-6220 337 12 v. v. PROPN cana-6220 337 13 ( ( PUNCT cana-6220 337 14 2021 2021 NUM cana-6220 337 15 ) ) PUNCT cana-6220 337 16 . . PUNCT cana-6220 338 1 β€œ " PUNCT cana-6220 338 2 poisson poisson PROPN cana-6220 338 3 inverted invert VERB cana-6220 338 4 lomax lomax PROPN cana-6220 338 5 distribution distribution NOUN cana-6220 338 6 : : PUNCT cana-6220 338 7 properties property NOUN cana-6220 338 8 and and CCONJ cana-6220 338 9 applications application NOUN cana-6220 338 10 ” " PUNCT cana-6220 338 11 . . PUNCT cana-6220 339 1 international international ADJ cana-6220 339 2 journal journal PROPN cana-6220 339 3 of of ADP cana-6220 339 4 research research NOUN cana-6220 339 5 in in ADP cana-6220 339 6 engineering engineering NOUN cana-6220 339 7 and and CCONJ cana-6220 339 8 science science NOUN cana-6220 339 9 ( ( PUNCT cana-6220 339 10 ijres ijre NOUN cana-6220 339 11 ) ) PUNCT cana-6220 339 12 , , PUNCT cana-6220 339 13 9(1 9(1 NUM cana-6220 339 14 ) ) PUNCT cana-6220 339 15 , , PUNCT cana-6220 339 16 48–57 48–57 NUM cana-6220 339 17 . . PUNCT cana-6220 340 1 communications communication NOUN cana-6220 340 2 on on ADP cana-6220 340 3 applied apply VERB cana-6220 340 4 nonlinear nonlinear ADJ cana-6220 340 5 analysis analysis NOUN cana-6220 340 6 issn issn NOUN cana-6220 340 7 : : PUNCT cana-6220 340 8 1074 1074 NUM cana-6220 340 9 - - PUNCT cana-6220 340 10 133x 133x NUM cana-6220 340 11 vol vol VERB cana-6220 340 12 32 32 NUM cana-6220 340 13 no no NOUN cana-6220 340 14 . . PUNCT cana-6220 341 1 10s 10 NOUN cana-6220 341 2 ( ( PUNCT cana-6220 341 3 2025 2025 NUM cana-6220 341 4 ) ) PUNCT cana-6220 341 5 3562 3562 NUM cana-6220 341 6 https://internationalpubls.com https://internationalpubls.com X cana-6220 342 1 [ [ X cana-6220 342 2 15 15 NUM cana-6220 342 3 ] ] X cana-6220 342 4 kumar kumar PROPN cana-6220 342 5 , , PUNCT cana-6220 342 6 s. s. PROPN cana-6220 342 7 , , PUNCT cana-6220 342 8 meena meena PROPN cana-6220 342 9 , , PUNCT cana-6220 342 10 b. b. PROPN cana-6220 342 11 , , PUNCT cana-6220 342 12 shukla shukla PROPN cana-6220 342 13 , , PUNCT cana-6220 342 14 r. r. PROPN cana-6220 342 15 , , PUNCT cana-6220 342 16 & & CCONJ cana-6220 342 17 singh singh PROPN cana-6220 342 18 , , PUNCT cana-6220 342 19 s. s. PROPN cana-6220 342 20 p. p. PROPN cana-6220 342 21 ( ( PUNCT cana-6220 342 22 2025 2025 NUM cana-6220 342 23 ) ) PUNCT cana-6220 342 24 . . PUNCT cana-6220 343 1 β€œ " PUNCT cana-6220 343 2 modi modi PROPN cana-6220 343 3 rayleigh rayleigh PROPN cana-6220 343 4 distribution distribution NOUN cana-6220 343 5 and and CCONJ cana-6220 343 6 its its PRON cana-6220 343 7 application application NOUN cana-6220 343 8 to to ADP cana-6220 343 9 survival survival NOUN cana-6220 343 10 time time NOUN cana-6220 343 11 data data PROPN cana-6220 343 12 sets set NOUN cana-6220 343 13 ” " PUNCT cana-6220 343 14 . . PUNCT cana-6220 344 1 life life NOUN cana-6220 344 2 cycle cycle NOUN cana-6220 344 3 reliability reliability NOUN cana-6220 344 4 and and CCONJ cana-6220 344 5 safety safety NOUN cana-6220 344 6 engineering engineering NOUN cana-6220 344 7 , , PUNCT cana-6220 344 8 1–10 1–10 NOUN cana-6220 344 9 . . PUNCT cana-6220 345 1 [ [ X cana-6220 345 2 16 16 NUM cana-6220 345 3 ] ] X cana-6220 345 4 kumawat kumawat PROPN cana-6220 345 5 , , PUNCT cana-6220 345 6 h. h. PROPN cana-6220 345 7 , , PUNCT cana-6220 345 8 modi modi PROPN cana-6220 345 9 , , PUNCT cana-6220 345 10 k. k. PROPN cana-6220 345 11 , , PUNCT cana-6220 345 12 & & CCONJ cana-6220 345 13 nagar nagar PROPN cana-6220 345 14 , , PUNCT cana-6220 345 15 p. p. NOUN cana-6220 345 16 ( ( PUNCT cana-6220 345 17 2024 2024 NUM cana-6220 345 18 ) ) PUNCT cana-6220 345 19 . . PUNCT cana-6220 346 1 β€œ " PUNCT cana-6220 346 2 modi modi PROPN cana-6220 346 3 - - PUNCT cana-6220 346 4 weibull weibull PROPN cana-6220 346 5 distribution distribution NOUN cana-6220 346 6 : : PUNCT cana-6220 346 7 inferential inferential ADJ cana-6220 346 8 and and CCONJ cana-6220 346 9 simulation simulation NOUN cana-6220 346 10 study study NOUN cana-6220 346 11 ” " PUNCT cana-6220 346 12 . . PUNCT cana-6220 347 1 journal journal PROPN cana-6220 347 2 annals annal NOUN cana-6220 347 3 of of ADP cana-6220 347 4 data data NOUN cana-6220 347 5 science science NOUN cana-6220 347 6 , , PUNCT cana-6220 347 7 11(06 11(06 NUM cana-6220 347 8 ) ) PUNCT cana-6220 347 9 , , PUNCT cana-6220 347 10 1975–1999 1975–1999 NUM cana-6220 347 11 . . PUNCT cana-6220 348 1 [ [ X cana-6220 348 2 17 17 NUM cana-6220 348 3 ] ] X cana-6220 348 4 lee lee PROPN cana-6220 348 5 , , PUNCT cana-6220 348 6 e. e. PROPN cana-6220 348 7 t. t. PROPN cana-6220 348 8 , , PUNCT cana-6220 348 9 & & CCONJ cana-6220 348 10 wang wang PROPN cana-6220 348 11 , , PUNCT cana-6220 348 12 j. j. PROPN cana-6220 348 13 ( ( PUNCT cana-6220 348 14 2003 2003 NUM cana-6220 348 15 ) ) PUNCT cana-6220 348 16 . . PUNCT cana-6220 349 1 statistical statistical ADJ cana-6220 349 2 methods method NOUN cana-6220 349 3 for for ADP cana-6220 349 4 survival survival NOUN cana-6220 349 5 data datum NOUN cana-6220 349 6 analysis analysis NOUN cana-6220 349 7 ( ( PUNCT cana-6220 349 8 vol vol NOUN cana-6220 349 9 . . PUNCT cana-6220 349 10 476 476 NUM cana-6220 349 11 ) ) PUNCT cana-6220 349 12 . . PUNCT cana-6220 350 1 john john PROPN cana-6220 350 2 wiley wiley PROPN cana-6220 350 3 & & CCONJ cana-6220 350 4 sons son NOUN cana-6220 350 5 . . PUNCT cana-6220 351 1 [ [ X cana-6220 351 2 18 18 NUM cana-6220 351 3 ] ] X cana-6220 351 4 modi modi PROPN cana-6220 351 5 , , PUNCT cana-6220 351 6 k. k. PROPN cana-6220 351 7 , , PUNCT cana-6220 351 8 kumar kumar PROPN cana-6220 351 9 , , PUNCT cana-6220 351 10 d. d. PROPN cana-6220 351 11 , , PUNCT cana-6220 351 12 & & CCONJ cana-6220 351 13 singh singh PROPN cana-6220 351 14 , , PUNCT cana-6220 351 15 y. y. PROPN cana-6220 351 16 ( ( PUNCT cana-6220 351 17 2020 2020 NUM cana-6220 351 18 ) ) PUNCT cana-6220 351 19 . . PUNCT cana-6220 352 1 β€œ " PUNCT cana-6220 352 2 a a DET cana-6220 352 3 new new ADJ cana-6220 352 4 family family NOUN cana-6220 352 5 of of ADP cana-6220 352 6 distribution distribution NOUN cana-6220 352 7 with with ADP cana-6220 352 8 application application NOUN cana-6220 352 9 on on ADP cana-6220 352 10 two two NUM cana-6220 352 11 real real ADJ cana-6220 352 12 datasets dataset NOUN cana-6220 352 13 on on ADP cana-6220 352 14 survival survival NOUN cana-6220 352 15 problem problem NOUN cana-6220 352 16 ” " PUNCT cana-6220 352 17 . . PUNCT cana-6220 353 1 journal journal PROPN cana-6220 353 2 science science PROPN cana-6220 353 3 & & CCONJ cana-6220 353 4 technology technology PROPN cana-6220 353 5 asia asia PROPN cana-6220 353 6 , , PUNCT cana-6220 353 7 1–10 1–10 NOUN cana-6220 353 8 . . PUNCT cana-6220 354 1 [ [ X cana-6220 354 2 19 19 NUM cana-6220 354 3 ] ] X cana-6220 354 4 ndayisaba ndayisaba PROPN cana-6220 354 5 , , PUNCT cana-6220 354 6 a. a. PROPN cana-6220 354 7 d. d. PROPN cana-6220 354 8 , , PUNCT cana-6220 354 9 odongo odongo PROPN cana-6220 354 10 , , PUNCT cana-6220 354 11 l. l. PROPN cana-6220 354 12 o. o. PROPN cana-6220 354 13 , , PUNCT cana-6220 354 14 & & CCONJ cana-6220 354 15 ngunyi ngunyi PROPN cana-6220 354 16 , , PUNCT cana-6220 354 17 a. a. NOUN cana-6220 354 18 ( ( PUNCT cana-6220 354 19 2023 2023 NUM cana-6220 354 20 ) ) PUNCT cana-6220 354 21 . . PUNCT cana-6220 355 1 β€œ " PUNCT cana-6220 355 2 the the DET cana-6220 355 3 modi modi PROPN cana-6220 355 4 exponentiated exponentiate VERB cana-6220 355 5 exponential exponential ADJ cana-6220 355 6 distribution distribution NOUN cana-6220 355 7 ” " PUNCT cana-6220 355 8 . . PUNCT cana-6220 356 1 j j PROPN cana-6220 356 2 mod mod PROPN cana-6220 356 3 appl appl PROPN cana-6220 356 4 stat stat PROPN cana-6220 356 5 methods method NOUN cana-6220 356 6 , , PUNCT cana-6220 356 7 11 11 NUM cana-6220 356 8 , , PUNCT cana-6220 356 9 341–-359 341–-359 ADJ cana-6220 356 10 . . PUNCT cana-6220 357 1 [ [ X cana-6220 357 2 20 20 NUM cana-6220 357 3 ] ] X cana-6220 357 4 rady rady PROPN cana-6220 357 5 , , PUNCT cana-6220 357 6 e.-h e.-h PROPN cana-6220 357 7 . . PUNCT cana-6220 358 1 a. a. PROPN cana-6220 358 2 , , PUNCT cana-6220 358 3 hassanein hassanein PROPN cana-6220 358 4 , , PUNCT cana-6220 358 5 w. w. PROPN cana-6220 358 6 a. a. PROPN cana-6220 358 7 , , PUNCT cana-6220 358 8 & & CCONJ cana-6220 358 9 elhaddad elhaddad PROPN cana-6220 358 10 , , PUNCT cana-6220 358 11 t. t. NOUN cana-6220 358 12 a. a. NOUN cana-6220 358 13 ( ( PUNCT cana-6220 358 14 2016 2016 NUM cana-6220 358 15 ) ) PUNCT cana-6220 358 16 . . PUNCT cana-6220 359 1 β€œ " PUNCT cana-6220 359 2 the the DET cana-6220 359 3 power power NOUN cana-6220 359 4 lomax lomax PROPN cana-6220 359 5 distribution distribution NOUN cana-6220 359 6 with with ADP cana-6220 359 7 an an DET cana-6220 359 8 application application NOUN cana-6220 359 9 to to ADP cana-6220 359 10 bladder bladder NOUN cana-6220 359 11 cancer cancer NOUN cana-6220 359 12 data datum NOUN cana-6220 359 13 ” " PUNCT cana-6220 359 14 . . PUNCT cana-6220 360 1 springerplus springerplus PROPN cana-6220 360 2 , , PUNCT cana-6220 360 3 5(1 5(1 NUM cana-6220 360 4 ) ) PUNCT cana-6220 360 5 , , PUNCT cana-6220 360 6 1838 1838 NUM cana-6220 360 7 . . PUNCT cana-6220 361 1 [ [ X cana-6220 361 2 21 21 NUM cana-6220 361 3 ] ] X cana-6220 361 4 shabbir shabbir PROPN cana-6220 361 5 , , PUNCT cana-6220 361 6 m. m. NOUN cana-6220 361 7 , , PUNCT cana-6220 361 8 riaz riaz PROPN cana-6220 361 9 , , PUNCT cana-6220 361 10 a. a. PROPN cana-6220 361 11 , , PUNCT cana-6220 361 12 & & CCONJ cana-6220 361 13 gull gull NOUN cana-6220 361 14 , , PUNCT cana-6220 361 15 h. h. PROPN cana-6220 361 16 ( ( PUNCT cana-6220 361 17 2018 2018 NUM cana-6220 361 18 ) ) PUNCT cana-6220 361 19 . . PUNCT cana-6220 362 1 β€œ " PUNCT cana-6220 362 2 rayleigh rayleigh PROPN cana-6220 362 3 lomax lomax PROPN cana-6220 362 4 distribution distribution NOUN cana-6220 362 5 ” " PUNCT cana-6220 362 6 . . PUNCT cana-6220 363 1 the the DET cana-6220 363 2 journal journal NOUN cana-6220 363 3 of of ADP cana-6220 363 4 middle middle PROPN cana-6220 363 5 east east PROPN cana-6220 363 6 and and CCONJ cana-6220 363 7 north north PROPN cana-6220 363 8 africa africa PROPN cana-6220 363 9 sciences sciences PROPN cana-6220 363 10 , , PUNCT cana-6220 363 11 4(12 4(12 NUM cana-6220 363 12 ) ) PUNCT cana-6220 363 13 , , PUNCT cana-6220 363 14 1–4 1–4 PROPN cana-6220 363 15 . . PUNCT cana-6220 364 1 [ [ X cana-6220 364 2 22 22 NUM cana-6220 364 3 ] ] PUNCT cana-6220 364 4 tadikamalla tadikamalla NOUN cana-6220 364 5 , , PUNCT cana-6220 364 6 p. p. PROPN cana-6220 364 7 r. r. PROPN cana-6220 364 8 ( ( PUNCT cana-6220 364 9 1980 1980 NUM cana-6220 364 10 ) ) PUNCT cana-6220 364 11 . . PUNCT cana-6220 365 1 β€œ " PUNCT cana-6220 365 2 a a DET cana-6220 365 3 look look NOUN cana-6220 365 4 at at ADP cana-6220 365 5 the the DET cana-6220 365 6 burr burr NOUN cana-6220 365 7 and and CCONJ cana-6220 365 8 related related ADJ cana-6220 365 9 distributions distribution NOUN cana-6220 365 10 ” " PUNCT cana-6220 365 11 . . PUNCT cana-6220 366 1 international international ADJ cana-6220 366 2 statistical statistical ADJ cana-6220 366 3 review review NOUN cana-6220 366 4 / / SYM cana-6220 366 5 revue revue NOUN cana-6220 366 6 internationale internationale PROPN cana-6220 366 7 de de X cana-6220 366 8 statistique statistique NOUN cana-6220 366 9 , , PUNCT cana-6220 366 10 337–344 337–344 NUM cana-6220 366 11 . . PUNCT