id sid tid token lemma pos iajs-1811 1 1 microsoft microsoft PROPN iajs-1811 1 2 word word NOUN iajs-1811 1 3 378 378 NUM iajs-1811 1 4 - - SYM iajs-1811 1 5 391 391 NUM iajs-1811 1 6 ihsciconf ihsciconf NOUN iajs-1811 1 7 2017 2017 NUM iajs-1811 1 8 special special ADJ iajs-1811 1 9 issue issue NOUN iajs-1811 1 10 ibn ibn PROPN iajs-1811 1 11 al al PROPN iajs-1811 1 12 - - PUNCT iajs-1811 1 13 haitham haitham PROPN iajs-1811 1 14 journal journal PROPN iajs-1811 1 15 for for ADP iajs-1811 1 16 pure pure ADJ iajs-1811 1 17 and and CCONJ iajs-1811 1 18 applied apply VERB iajs-1811 1 19 science science NOUN iajs-1811 1 20 https://doi.org/ https://doi.org/ NOUN iajs-1811 1 21 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 1 22 for for ADP iajs-1811 1 23 more more ADJ iajs-1811 1 24 information information NOUN iajs-1811 1 25 about about ADP iajs-1811 1 26 the the DET iajs-1811 1 27 conference conference NOUN iajs-1811 1 28 please please INTJ iajs-1811 1 29 visit visit VERB iajs-1811 1 30 the the DET iajs-1811 1 31 websites website NOUN iajs-1811 1 32 : : PUNCT iajs-1811 1 33 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 1 34         SPACE iajs-1811 1 35 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 1 36       SPACE iajs-1811 1 37 mathematics|378 mathematics|378 NOUN iajs-1811 1 38         SPACE iajs-1811 1 39 using use VERB iajs-1811 1 40 approximation approximation NOUN iajs-1811 1 41 non non ADJ iajs-1811 1 42 - - ADJ iajs-1811 1 43 bayesian bayesian ADJ iajs-1811 1 44 computation computation NOUN iajs-1811 1 45 with with ADP iajs-1811 1 46 fuzzy fuzzy ADJ iajs-1811 1 47 data datum NOUN iajs-1811 1 48 to to ADP iajs-1811 1 49 estimation estimation NOUN iajs-1811 1 50 inverse inverse NOUN iajs-1811 1 51 weibull weibull PROPN iajs-1811 1 52 parameters parameter NOUN iajs-1811 1 53 and and CCONJ iajs-1811 1 54 reliability reliability NOUN iajs-1811 1 55 function function NOUN iajs-1811 1 56 nadia nadia PROPN iajs-1811 1 57 hashim hashim PROPN iajs-1811 1 58 al al PROPN iajs-1811 1 59 - - PUNCT iajs-1811 1 60 noor noor PROPN iajs-1811 1 61 nadialnoor@uomustansiriyah.edu.iq nadialnoor@uomustansiriyah.edu.iq PROPN iajs-1811 1 62 shurooq shurooq PROPN iajs-1811 1 63 a.k.al a.k.al PROPN iajs-1811 1 64 - - PUNCT iajs-1811 1 65 sultany sultany ADJ iajs-1811 1 66 drnadialnoor@gmail.com drnadialnoor@gmail.com PROPN iajs-1811 1 67 dept dept PROPN iajs-1811 1 68 . . PROPN iajs-1811 2 1 of of ADP iajs-1811 2 2 mathematics/ mathematics/ NUM iajs-1811 2 3 college college NOUN iajs-1811 2 4 of of ADP iajs-1811 2 5 science/ science/ NUM iajs-1811 2 6 mustansiriyah mustansiriyah NOUN iajs-1811 2 7 university university NOUN iajs-1811 2 8 abstract abstract NOUN iajs-1811 2 9 in in ADP iajs-1811 2 10 real real ADJ iajs-1811 2 11 situations situation NOUN iajs-1811 2 12 all all DET iajs-1811 2 13 observations observation NOUN iajs-1811 2 14 and and CCONJ iajs-1811 2 15 measurements measurement NOUN iajs-1811 2 16 are be AUX iajs-1811 2 17 not not PART iajs-1811 2 18 exact exact ADJ iajs-1811 2 19 numbers number NOUN iajs-1811 2 20 but but CCONJ iajs-1811 2 21 more more ADJ iajs-1811 2 22 or or CCONJ iajs-1811 2 23 less less ADJ iajs-1811 2 24 non non ADJ iajs-1811 2 25 - - ADJ iajs-1811 2 26 exact exact ADJ iajs-1811 2 27 , , PUNCT iajs-1811 2 28 also also ADV iajs-1811 2 29 called call VERB iajs-1811 2 30 fuzzy fuzzy ADJ iajs-1811 2 31 . . PUNCT iajs-1811 3 1 so so ADV iajs-1811 3 2 , , PUNCT iajs-1811 3 3 in in ADP iajs-1811 3 4 this this DET iajs-1811 3 5 paper paper NOUN iajs-1811 3 6 , , PUNCT iajs-1811 3 7 we we PRON iajs-1811 3 8 use use VERB iajs-1811 3 9 approximate approximate ADJ iajs-1811 3 10 non non ADJ iajs-1811 3 11 - - ADJ iajs-1811 3 12 bayesian bayesian ADJ iajs-1811 3 13 computational computational ADJ iajs-1811 3 14 methods method NOUN iajs-1811 3 15 to to PART iajs-1811 3 16 estimate estimate VERB iajs-1811 3 17 inverse inverse ADJ iajs-1811 3 18 weibull weibull PROPN iajs-1811 3 19 parameters parameter NOUN iajs-1811 3 20 and and CCONJ iajs-1811 3 21 reliability reliability NOUN iajs-1811 3 22 function function NOUN iajs-1811 3 23 with with ADP iajs-1811 3 24 fuzzy fuzzy ADJ iajs-1811 3 25 data datum NOUN iajs-1811 3 26 . . PUNCT iajs-1811 4 1 the the DET iajs-1811 4 2 maximum maximum ADJ iajs-1811 4 3 likelihood likelihood NOUN iajs-1811 4 4 and and CCONJ iajs-1811 4 5 moment moment NOUN iajs-1811 4 6 estimations estimation NOUN iajs-1811 4 7 are be AUX iajs-1811 4 8 obtained obtain VERB iajs-1811 4 9 as as ADP iajs-1811 4 10 nonbayesian nonbayesian ADJ iajs-1811 4 11 estimation estimation NOUN iajs-1811 4 12 . . PUNCT iajs-1811 5 1 the the DET iajs-1811 5 2 maximum maximum ADJ iajs-1811 5 3 likelihood likelihood NOUN iajs-1811 5 4 estimators estimator NOUN iajs-1811 5 5 have have AUX iajs-1811 5 6 been be AUX iajs-1811 5 7 derived derive VERB iajs-1811 5 8 numerically numerically ADV iajs-1811 5 9 based base VERB iajs-1811 5 10 on on ADP iajs-1811 5 11 two two NUM iajs-1811 5 12 iterative iterative NOUN iajs-1811 5 13 techniques technique NOUN iajs-1811 5 14 namely namely ADV iajs-1811 5 15 “ " PUNCT iajs-1811 5 16 newton newton PROPN iajs-1811 5 17 - - PUNCT iajs-1811 5 18 raphson raphson NOUN iajs-1811 5 19 ” " PUNCT iajs-1811 5 20 and and CCONJ iajs-1811 5 21 the the DET iajs-1811 5 22 “ " PUNCT iajs-1811 5 23 expectationmaximization expectationmaximization NOUN iajs-1811 5 24 ” " PUNCT iajs-1811 5 25 techniques technique NOUN iajs-1811 5 26 . . PUNCT iajs-1811 6 1 in in ADP iajs-1811 6 2 addition addition NOUN iajs-1811 6 3 , , PUNCT iajs-1811 6 4 we we PRON iajs-1811 6 5 provide provide VERB iajs-1811 6 6 compared compare VERB iajs-1811 6 7 numerically numerically ADV iajs-1811 6 8 through through ADP iajs-1811 6 9 montecarlo montecarlo PROPN iajs-1811 6 10 simulation simulation NOUN iajs-1811 6 11 study study NOUN iajs-1811 6 12 to to PART iajs-1811 6 13 obtained obtain VERB iajs-1811 6 14 estimates estimate NOUN iajs-1811 6 15 of of ADP iajs-1811 6 16 the the DET iajs-1811 6 17 parameters parameter NOUN iajs-1811 6 18 and and CCONJ iajs-1811 6 19 reliability reliability NOUN iajs-1811 6 20 function function NOUN iajs-1811 6 21 in in ADP iajs-1811 6 22 terms term NOUN iajs-1811 6 23 of of ADP iajs-1811 6 24 their their PRON iajs-1811 6 25 mean mean ADJ iajs-1811 6 26 squared square VERB iajs-1811 6 27 error error NOUN iajs-1811 6 28 values value NOUN iajs-1811 6 29 and and CCONJ iajs-1811 6 30 integrated integrate VERB iajs-1811 6 31 mean mean NOUN iajs-1811 6 32 squared square VERB iajs-1811 6 33 error error NOUN iajs-1811 6 34 values value NOUN iajs-1811 6 35 respectively respectively ADV iajs-1811 6 36 . . PUNCT iajs-1811 7 1 keywords keyword NOUN iajs-1811 7 2 : : PUNCT iajs-1811 7 3 non non ADJ iajs-1811 7 4 - - ADJ iajs-1811 7 5 bayesian bayesian ADJ iajs-1811 7 6 methods method NOUN iajs-1811 7 7 ; ; PUNCT iajs-1811 7 8 inverse inverse ADJ iajs-1811 7 9 weibull weibull NOUN iajs-1811 7 10 distribution distribution NOUN iajs-1811 7 11 ; ; PUNCT iajs-1811 7 12 expectation expectation NOUN iajs-1811 7 13 maximization maximization NOUN iajs-1811 7 14 algorithm algorithm NOUN iajs-1811 7 15 ; ; PUNCT iajs-1811 7 16 newton newton PROPN iajs-1811 7 17 - - PUNCT iajs-1811 7 18 raphson raphson NOUN iajs-1811 7 19 algorithm algorithm NOUN iajs-1811 7 20 ; ; PUNCT iajs-1811 7 21 moment moment NOUN iajs-1811 7 22 method method NOUN iajs-1811 7 23 ; ; PUNCT iajs-1811 7 24 fuzzy fuzzy ADJ iajs-1811 7 25 data datum NOUN iajs-1811 7 26 . . PUNCT iajs-1811 8 1 ihsciconf ihsciconf PROPN iajs-1811 8 2 2017 2017 NUM iajs-1811 8 3 special special ADJ iajs-1811 8 4 issue issue NOUN iajs-1811 8 5 ibn ibn PROPN iajs-1811 8 6 al al PROPN iajs-1811 8 7 - - PUNCT iajs-1811 8 8 haitham haitham PROPN iajs-1811 8 9 journal journal PROPN iajs-1811 8 10 for for ADP iajs-1811 8 11 pure pure ADJ iajs-1811 8 12 and and CCONJ iajs-1811 8 13 applied apply VERB iajs-1811 8 14 science science NOUN iajs-1811 8 15 https://doi.org/ https://doi.org/ NOUN iajs-1811 8 16 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 8 17 for for ADP iajs-1811 8 18 more more ADJ iajs-1811 8 19 information information NOUN iajs-1811 8 20 about about ADP iajs-1811 8 21 the the DET iajs-1811 8 22 conference conference NOUN iajs-1811 8 23 please please INTJ iajs-1811 8 24 visit visit VERB iajs-1811 8 25 the the DET iajs-1811 8 26 websites website NOUN iajs-1811 8 27 : : PUNCT iajs-1811 8 28 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 8 29         SPACE iajs-1811 8 30 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 8 31       SPACE iajs-1811 8 32 mathematics|379 mathematics|379 VERB iajs-1811 8 33         SPACE iajs-1811 8 34 1.introduction 1.introduction NUM iajs-1811 8 35 statistical statistical ADJ iajs-1811 8 36 analysis analysis NOUN iajs-1811 8 37 of of ADP iajs-1811 8 38 inverse inverse ADJ iajs-1811 8 39 weibull weibull NOUN iajs-1811 8 40 distribution distribution NOUN iajs-1811 8 41 is be AUX iajs-1811 8 42 based base VERB iajs-1811 8 43 on on ADP iajs-1811 8 44 exact exact ADJ iajs-1811 8 45 data datum NOUN iajs-1811 8 46 . . PUNCT iajs-1811 9 1 however however ADV iajs-1811 9 2 , , PUNCT iajs-1811 9 3 in in ADP iajs-1811 9 4 real real ADJ iajs-1811 9 5 situations situation NOUN iajs-1811 9 6 all all DET iajs-1811 9 7 observations observation NOUN iajs-1811 9 8 and and CCONJ iajs-1811 9 9 measurements measurement NOUN iajs-1811 9 10 are be AUX iajs-1811 9 11 not not PART iajs-1811 9 12 exact exact ADJ iajs-1811 9 13 numbers number NOUN iajs-1811 9 14 but but CCONJ iajs-1811 9 15 more more ADJ iajs-1811 9 16 or or CCONJ iajs-1811 9 17 less less ADJ iajs-1811 9 18 nonexact nonexact NOUN iajs-1811 9 19 , , PUNCT iajs-1811 9 20 also also ADV iajs-1811 9 21 called call VERB iajs-1811 9 22 fuzzy fuzzy ADJ iajs-1811 9 23 . . PUNCT iajs-1811 10 1 thus thus ADV iajs-1811 10 2 , , PUNCT iajs-1811 10 3 in in ADP iajs-1811 10 4 this this DET iajs-1811 10 5 paper paper NOUN iajs-1811 10 6 we we PRON iajs-1811 10 7 present present VERB iajs-1811 10 8 a a DET iajs-1811 10 9 non non ADJ iajs-1811 10 10 - - ADJ iajs-1811 10 11 bayesian bayesian ADJ iajs-1811 10 12 approach approach NOUN iajs-1811 10 13 to to PART iajs-1811 10 14 estimate estimate VERB iajs-1811 10 15 the the DET iajs-1811 10 16 parameters parameter NOUN iajs-1811 10 17 and and CCONJ iajs-1811 10 18 reliability reliability NOUN iajs-1811 10 19 function function NOUN iajs-1811 10 20 of of ADP iajs-1811 10 21 inverse inverse ADJ iajs-1811 10 22 weibull weibull NOUN iajs-1811 10 23 distribution distribution NOUN iajs-1811 10 24 with with ADP iajs-1811 10 25 fuzzy fuzzy ADJ iajs-1811 10 26 data datum NOUN iajs-1811 10 27 . . PUNCT iajs-1811 11 1 keller keller PROPN iajs-1811 11 2 et et PROPN iajs-1811 11 3 al al PROPN iajs-1811 11 4 . . PROPN iajs-1811 12 1 ( ( PUNCT iajs-1811 12 2 1985 1985 NUM iajs-1811 12 3 ) ) PUNCT iajs-1811 13 1 [ [ X iajs-1811 13 2 4 4 X iajs-1811 13 3 ] ] PUNCT iajs-1811 13 4 introduced introduce VERB iajs-1811 13 5 inverse inverse ADJ iajs-1811 13 6 weibull weibull NOUN iajs-1811 13 7 distribution distribution NOUN iajs-1811 13 8 as as ADP iajs-1811 13 9 a a DET iajs-1811 13 10 suitable suitable ADJ iajs-1811 13 11 model model NOUN iajs-1811 13 12 to to PART iajs-1811 13 13 describe describe VERB iajs-1811 13 14 degradation degradation NOUN iajs-1811 13 15 phenomena phenomenon NOUN iajs-1811 13 16 of of ADP iajs-1811 13 17 mechanical mechanical ADJ iajs-1811 13 18 components component NOUN iajs-1811 13 19 of of ADP iajs-1811 13 20 diesel diesel NOUN iajs-1811 13 21 engines engine NOUN iajs-1811 13 22 . . PUNCT iajs-1811 14 1 other other ADJ iajs-1811 14 2 names name NOUN iajs-1811 14 3 for for ADP iajs-1811 14 4 this this DET iajs-1811 14 5 distribution distribution NOUN iajs-1811 14 6 are be AUX iajs-1811 14 7 complementary complementary ADJ iajs-1811 14 8 weibull weibull NOUN iajs-1811 14 9 distribution distribution NOUN iajs-1811 14 10 , , PUNCT iajs-1811 14 11 reciprocal reciprocal ADJ iajs-1811 14 12 weibull weibull NOUN iajs-1811 14 13 distribution distribution NOUN iajs-1811 14 14 and and CCONJ iajs-1811 14 15 reverse reverse VERB iajs-1811 14 16 weibull weibull NOUN iajs-1811 14 17 distribution distribution NOUN iajs-1811 14 18 [ [ X iajs-1811 14 19 7 7 NUM iajs-1811 14 20 ] ] PUNCT iajs-1811 14 21 . . PUNCT iajs-1811 15 1 a a DET iajs-1811 15 2 random random ADJ iajs-1811 15 3 variable variable NOUN iajs-1811 15 4 x x PUNCT iajs-1811 15 5 is be AUX iajs-1811 15 6 said say VERB iajs-1811 15 7 to to PART iajs-1811 15 8 have have VERB iajs-1811 15 9 a a DET iajs-1811 15 10 two two NUM iajs-1811 15 11 - - PUNCT iajs-1811 15 12 parameter parameter NOUN iajs-1811 15 13 inverse inverse NOUN iajs-1811 15 14 weibull weibull NOUN iajs-1811 15 15 distribution distribution NOUN iajs-1811 15 16 if if SCONJ iajs-1811 15 17 it it PRON iajs-1811 15 18 has have VERB iajs-1811 15 19 the the DET iajs-1811 15 20 following follow VERB iajs-1811 15 21 probability probability NOUN iajs-1811 15 22 density density NOUN iajs-1811 15 23 function function NOUN iajs-1811 15 24 ( ( PUNCT iajs-1811 15 25 pdf)[8 pdf)[8 PROPN iajs-1811 15 26 ] ] PUNCT iajs-1811 15 27 , , PUNCT iajs-1811 15 28 𝑓 𝑓 PRON iajs-1811 15 29 𝑥 𝑥 NOUN iajs-1811 15 30 ; ; PUNCT iajs-1811 15 31 𝛽 𝛽 NOUN iajs-1811 15 32 , , PUNCT iajs-1811 15 33 𝜆 𝜆 ADV iajs-1811 15 34 𝛽𝜆𝑥 𝛽𝜆𝑥 ADV iajs-1811 15 35 𝑒 𝑒 ADV iajs-1811 15 36 ; ; PUNCT iajs-1811 15 37 𝑥 𝑥 PROPN iajs-1811 15 38 0 0 NUM iajs-1811 15 39 , , PUNCT iajs-1811 15 40 𝛽 𝛽 NOUN iajs-1811 15 41 , , PUNCT iajs-1811 15 42 𝜆 𝜆 PRON iajs-1811 15 43 0 0 NUM iajs-1811 15 44 … … SYM iajs-1811 15 45 1 1 NUM iajs-1811 15 46 the the DET iajs-1811 15 47 cumulative cumulative ADJ iajs-1811 15 48 distribution distribution NOUN iajs-1811 15 49 function(cdf function(cdf NOUN iajs-1811 15 50 ) ) PUNCT iajs-1811 15 51 , , PUNCT iajs-1811 15 52 reliability reliability NOUN iajs-1811 15 53 function function NOUN iajs-1811 15 54 is be AUX iajs-1811 15 55 given give VERB iajs-1811 15 56 respectively respectively ADV iajs-1811 15 57 by by ADP iajs-1811 15 58 : : PUNCT iajs-1811 15 59 𝐹 𝐹 PROPN iajs-1811 15 60 𝑥 𝑥 NOUN iajs-1811 15 61 ; ; PUNCT iajs-1811 15 62 𝛽 𝛽 NOUN iajs-1811 15 63 , , PUNCT iajs-1811 15 64 𝜆 𝜆 PRON iajs-1811 15 65 𝑒 𝑒 ADV iajs-1811 15 66 ; ; PUNCT iajs-1811 15 67 𝑥 𝑥 PROPN iajs-1811 15 68 0 0 NUM iajs-1811 15 69 , , PUNCT iajs-1811 15 70 𝛽 𝛽 NOUN iajs-1811 15 71 , , PUNCT iajs-1811 15 72 𝜆 𝜆 PRON iajs-1811 15 73 0 0 NUM iajs-1811 15 74 … … SYM iajs-1811 15 75 2 2 NUM iajs-1811 15 76 𝑅 𝑅 NOUN iajs-1811 15 77 𝑥 𝑥 PROPN iajs-1811 15 78 1 1 NUM iajs-1811 15 79 𝑒 𝑒 ADV iajs-1811 15 80 ; ; PUNCT iajs-1811 15 81 𝑥 𝑥 PROPN iajs-1811 15 82 0 0 NUM iajs-1811 15 83 , , PUNCT iajs-1811 15 84 𝛽 𝛽 NOUN iajs-1811 15 85 , , PUNCT iajs-1811 15 86 𝜆 𝜆 DET iajs-1811 15 87 0 0 NUM iajs-1811 15 88 … … SYM iajs-1811 15 89 3 3 NUM iajs-1811 15 90 where where SCONJ iajs-1811 15 91 𝛽 𝛽 NOUN iajs-1811 15 92 is be AUX iajs-1811 15 93 the the DET iajs-1811 15 94 shape shape NOUN iajs-1811 15 95 parameter parameter NOUN iajs-1811 15 96 and and CCONJ iajs-1811 15 97 𝜆 𝜆 NOUN iajs-1811 15 98 is be AUX iajs-1811 15 99 the the DET iajs-1811 15 100 scale scale NOUN iajs-1811 15 101 parameter parameter NOUN iajs-1811 15 102 . . PUNCT iajs-1811 16 1 definition definition NOUN iajs-1811 17 1 [ [ X iajs-1811 17 2 9 9 NUM iajs-1811 17 3 ] ] PUNCT iajs-1811 17 4 : : PUNCT iajs-1811 17 5 let let VERB iajs-1811 17 6 ℝ ℝ PROPN iajs-1811 17 7 , , PUNCT iajs-1811 17 8 𝒜 𝒜 NOUN iajs-1811 17 9 , , PUNCT iajs-1811 17 10 p p NOUN iajs-1811 17 11 be be VERB iajs-1811 17 12 a a DET iajs-1811 17 13 probability probability NOUN iajs-1811 17 14 space space NOUN iajs-1811 17 15 in in ADP iajs-1811 17 16 which which PRON iajs-1811 17 17 𝒜 𝒜 NOUN iajs-1811 17 18 is be AUX iajs-1811 17 19 the the DET iajs-1811 17 20 σ σ NUM iajs-1811 17 21 field field NOUN iajs-1811 17 22 of of ADP iajs-1811 17 23 borel borel NOUN iajs-1811 17 24 sets set NOUN iajs-1811 17 25 in in ADP iajs-1811 17 26 ℝ ℝ PROPN iajs-1811 17 27 and and CCONJ iajs-1811 17 28 p p NOUN iajs-1811 17 29 is be AUX iajs-1811 17 30 a a DET iajs-1811 17 31 probability probability NOUN iajs-1811 17 32 measure measure NOUN iajs-1811 17 33 over over ADP iajs-1811 17 34 ℝ ℝ PROPN iajs-1811 17 35 . . PUNCT iajs-1811 18 1 then then ADV iajs-1811 18 2 , , PUNCT iajs-1811 18 3 the the DET iajs-1811 18 4 probability probability NOUN iajs-1811 18 5 of of ADP iajs-1811 18 6 a a DET iajs-1811 18 7 fuzzy fuzzy ADJ iajs-1811 18 8 event event NOUN iajs-1811 18 9 a a PRON iajs-1811 18 10 in in ADP iajs-1811 18 11 ℝ ℝ PROPN iajs-1811 18 12 is be AUX iajs-1811 18 13 defined define VERB iajs-1811 18 14 by by ADP iajs-1811 18 15 : : PUNCT iajs-1811 18 16 𝑃 𝑃 NOUN iajs-1811 18 17 𝐴 𝐴 PROPN iajs-1811 18 18 𝜇 𝜇 ADP iajs-1811 18 19 𝑥 𝑥 DET iajs-1811 18 20 𝑑𝑃 𝑑𝑃 NOUN iajs-1811 18 21 ; ; PUNCT iajs-1811 18 22 𝑓𝑜𝑟 𝑓𝑜𝑟 ADV iajs-1811 18 23 𝑎𝑙𝑙 𝑎𝑙𝑙 VERB iajs-1811 18 24 𝑥 𝑥 X iajs-1811 18 25 ∈ ∈ PROPN iajs-1811 18 26 ℝ ℝ PROPN iajs-1811 18 27 … … PUNCT iajs-1811 18 28 4 4 NUM iajs-1811 18 29 in in ADP iajs-1811 18 30 particular particular ADJ iajs-1811 18 31 , , PUNCT iajs-1811 18 32 suppose suppose VERB iajs-1811 18 33 that that SCONJ iajs-1811 18 34 p p PROPN iajs-1811 18 35 be be VERB iajs-1811 18 36 the the DET iajs-1811 18 37 probability probability NOUN iajs-1811 18 38 distribution distribution NOUN iajs-1811 18 39 of of ADP iajs-1811 18 40 a a DET iajs-1811 18 41 continuous continuous ADJ iajs-1811 18 42 random random ADJ iajs-1811 18 43 variable variable NOUN iajs-1811 18 44 𝑋 𝑋 NOUN iajs-1811 18 45 with with ADP iajs-1811 18 46 pdf pdf NOUN iajs-1811 18 47 𝑔 𝑔 PROPN iajs-1811 18 48 𝑥 𝑥 PROPN iajs-1811 18 49 .the .the DET iajs-1811 18 50 conditional conditional ADJ iajs-1811 18 51 density density NOUN iajs-1811 18 52 of of ADP iajs-1811 18 53 𝑋 𝑋 PROPN iajs-1811 18 54 given give VERB iajs-1811 18 55 𝐴 𝐴 PROPN iajs-1811 18 56 is be AUX iajs-1811 18 57 given give VERB iajs-1811 18 58 by by ADP iajs-1811 18 59 : : PUNCT iajs-1811 18 60 𝑔 𝑔 PROPN iajs-1811 18 61 𝑥|𝐴 𝑥|𝐴 NOUN iajs-1811 18 62 𝜇 𝜇 ADP iajs-1811 18 63 𝑥 𝑥 X iajs-1811 18 64 𝑔 𝑔 PROPN iajs-1811 18 65 𝑥 𝑥 X iajs-1811 18 66 𝜇 𝜇 X iajs-1811 18 67 𝑢 𝑢 X iajs-1811 18 68 𝑔 𝑔 PROPN iajs-1811 18 69 𝑢 𝑢 X iajs-1811 18 70 𝑑𝑢 𝑑𝑢 X iajs-1811 18 71 … … PUNCT iajs-1811 18 72 5 5 NUM iajs-1811 18 73 fuzzy fuzzy ADJ iajs-1811 18 74 data datum NOUN iajs-1811 18 75 and and CCONJ iajs-1811 18 76 the the DET iajs-1811 18 77 likelihood likelihood NOUN iajs-1811 18 78 function function NOUN iajs-1811 18 79 let let VERB iajs-1811 18 80 x x X iajs-1811 18 81 x x SYM iajs-1811 18 82 , , PUNCT iajs-1811 18 83 x x X iajs-1811 18 84 , , PUNCT iajs-1811 18 85 … … PUNCT iajs-1811 18 86 , , PUNCT iajs-1811 18 87 x x PRON iajs-1811 18 88 be be AUX iajs-1811 18 89 an an DET iajs-1811 18 90 ( ( PUNCT iajs-1811 18 91 i.i.d i.i.d NOUN iajs-1811 18 92 . . PUNCT iajs-1811 18 93 ) ) PUNCT iajs-1811 19 1 random random ADJ iajs-1811 19 2 vector vector NOUN iajs-1811 19 3 of of ADP iajs-1811 19 4 a a DET iajs-1811 19 5 random random ADJ iajs-1811 19 6 sample sample NOUN iajs-1811 19 7 of of ADP iajs-1811 19 8 size size NOUN iajs-1811 19 9 𝑛 𝑛 ADP iajs-1811 19 10 from from ADP iajs-1811 19 11 inverse inverse NOUN iajs-1811 19 12 weibull weibull NOUN iajs-1811 19 13 distribution distribution NOUN iajs-1811 19 14 with with ADP iajs-1811 19 15 pdf pdf NOUN iajs-1811 19 16 given give VERB iajs-1811 19 17 by by ADP iajs-1811 19 18 ( ( PUNCT iajs-1811 19 19 1 1 NUM iajs-1811 19 20 ) ) PUNCT iajs-1811 19 21 . . PUNCT iajs-1811 20 1 if if SCONJ iajs-1811 20 2 an an DET iajs-1811 20 3 observations observation NOUN iajs-1811 20 4 of of ADP iajs-1811 20 5 𝑥 𝑥 PROPN iajs-1811 20 6 was be AUX iajs-1811 20 7 known know VERB iajs-1811 20 8 exactly exactly ADV iajs-1811 20 9 , , PUNCT iajs-1811 20 10 then then ADV iajs-1811 20 11 the the DET iajs-1811 20 12 complete complete ADJ iajs-1811 20 13 - - PUNCT iajs-1811 20 14 data data NOUN iajs-1811 20 15 likelihood likelihood NOUN iajs-1811 20 16 function function NOUN iajs-1811 20 17 is be AUX iajs-1811 20 18 : : PUNCT iajs-1811 20 19 𝐿 𝐿 PROPN iajs-1811 20 20 𝛽 𝛽 PROPN iajs-1811 20 21 , , PUNCT iajs-1811 20 22 𝜆 𝜆 NOUN iajs-1811 20 23 ; ; PUNCT iajs-1811 20 24 𝑥 𝑥 PRON iajs-1811 20 25 𝑓 𝑓 PRON iajs-1811 20 26 𝑥 𝑥 X iajs-1811 20 27 , , PUNCT iajs-1811 20 28 𝛽 𝛽 PROPN iajs-1811 20 29 , , PUNCT iajs-1811 20 30 𝜆 𝜆 PROPN iajs-1811 20 31 𝛽 𝛽 NOUN iajs-1811 20 32 𝜆 𝜆 PRON iajs-1811 20 33 𝑥 𝑥 X iajs-1811 20 34 𝑒𝑥𝑝 𝑒𝑥𝑝 INTJ iajs-1811 20 35 𝜆𝑥 𝜆𝑥 NOUN iajs-1811 20 36 ihsciconf ihsciconf NOUN iajs-1811 20 37 2017 2017 NUM iajs-1811 20 38 special special ADJ iajs-1811 20 39 issue issue NOUN iajs-1811 20 40 ibn ibn PROPN iajs-1811 20 41 al al PROPN iajs-1811 20 42 - - PUNCT iajs-1811 20 43 haitham haitham PROPN iajs-1811 20 44 journal journal PROPN iajs-1811 20 45 for for ADP iajs-1811 20 46 pure pure ADJ iajs-1811 20 47 and and CCONJ iajs-1811 20 48 applied apply VERB iajs-1811 20 49 science science NOUN iajs-1811 20 50 https://doi.org/ https://doi.org/ NOUN iajs-1811 20 51 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 20 52 for for ADP iajs-1811 20 53 more more ADJ iajs-1811 20 54 information information NOUN iajs-1811 20 55 about about ADP iajs-1811 20 56 the the DET iajs-1811 20 57 conference conference NOUN iajs-1811 20 58 please please INTJ iajs-1811 20 59 visit visit VERB iajs-1811 20 60 the the DET iajs-1811 20 61 websites website NOUN iajs-1811 20 62 : : PUNCT iajs-1811 20 63 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 20 64         SPACE iajs-1811 20 65 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 20 66       SPACE iajs-1811 20 67 mathematics|380 mathematics|380 NOUN iajs-1811 20 68         SPACE iajs-1811 20 69 ⇒ ⇒ PROPN iajs-1811 20 70 𝐿 𝐿 PROPN iajs-1811 20 71 𝛽 𝛽 PROPN iajs-1811 20 72 , , PUNCT iajs-1811 20 73 𝜆 𝜆 NOUN iajs-1811 20 74 ; ; PUNCT iajs-1811 20 75 𝑥 𝑥 PRON iajs-1811 20 76 𝛽 𝛽 NOUN iajs-1811 20 77 𝜆 𝜆 PRON iajs-1811 20 78 𝑥 𝑥 X iajs-1811 20 79 𝑒𝑥𝑝 𝑒𝑥𝑝 INTJ iajs-1811 20 80 𝜆 𝜆 PROPN iajs-1811 20 81 𝑥 𝑥 X iajs-1811 20 82 … … PUNCT iajs-1811 20 83 6 6 NUM iajs-1811 20 84 now now ADV iajs-1811 20 85 consider consider VERB iajs-1811 20 86 the the DET iajs-1811 20 87 problem problem NOUN iajs-1811 20 88 where where SCONJ iajs-1811 20 89 x x PRON iajs-1811 20 90 is be AUX iajs-1811 20 91 not not PART iajs-1811 20 92 observed observe VERB iajs-1811 20 93 precisely precisely ADV iajs-1811 20 94 and and CCONJ iajs-1811 20 95 only only ADV iajs-1811 20 96 partial partial ADJ iajs-1811 20 97 information information NOUN iajs-1811 20 98 about about ADP iajs-1811 20 99 x x VERB iajs-1811 20 100 is be AUX iajs-1811 20 101 available available ADJ iajs-1811 20 102 in in ADP iajs-1811 20 103 the the DET iajs-1811 20 104 form form NOUN iajs-1811 20 105 of of ADP iajs-1811 20 106 a a DET iajs-1811 20 107 fuzzy fuzzy ADJ iajs-1811 20 108 subset subset NOUN iajs-1811 20 109 x x PUNCT iajs-1811 20 110 with with ADP iajs-1811 20 111 the the DET iajs-1811 20 112 borel borel PROPN iajs-1811 20 113 measurable measurable ADJ iajs-1811 20 114 membership membership NOUN iajs-1811 20 115 function function NOUN iajs-1811 20 116 𝜇 𝜇 ADP iajs-1811 20 117 𝑥 𝑥 PROPN iajs-1811 20 118 . . PUNCT iajs-1811 21 1 the the DET iajs-1811 21 2 observed observe VERB iajs-1811 21 3 - - PUNCT iajs-1811 21 4 data data NOUN iajs-1811 21 5 natural natural ADJ iajs-1811 21 6 log log NOUN iajs-1811 21 7 - - PUNCT iajs-1811 21 8 likelihood likelihood NOUN iajs-1811 21 9 function function NOUN iajs-1811 21 10 can can AUX iajs-1811 21 11 be be AUX iajs-1811 21 12 obtained obtain VERB iajs-1811 21 13 , , PUNCT iajs-1811 21 14 using use VERB iajs-1811 21 15 zadeh zadeh PROPN iajs-1811 21 16 's 's PART iajs-1811 21 17 definition definition NOUN iajs-1811 21 18 of of ADP iajs-1811 21 19 the the DET iajs-1811 21 20 probability probability NOUN iajs-1811 21 21 of of ADP iajs-1811 21 22 a a DET iajs-1811 21 23 fuzzy fuzzy ADJ iajs-1811 21 24 event event NOUN iajs-1811 21 25 in in ADP iajs-1811 21 26 the the DET iajs-1811 21 27 expression expression NOUN iajs-1811 21 28 ( ( PUNCT iajs-1811 21 29 5 5 NUM iajs-1811 21 30 ) ) PUNCT iajs-1811 21 31 as as ADP iajs-1811 21 32 : : PUNCT iajs-1811 21 33 ℓ ℓ PROPN iajs-1811 21 34 𝛽 𝛽 PROPN iajs-1811 21 35 , , PUNCT iajs-1811 21 36 𝜆 𝜆 NOUN iajs-1811 21 37 ; ; PUNCT iajs-1811 21 38 𝑥 𝑥 DET iajs-1811 21 39 𝑙𝑛 𝑙𝑛 X iajs-1811 21 40 𝐿 𝐿 PROPN iajs-1811 21 41 𝛽 𝛽 PROPN iajs-1811 21 42 , , PUNCT iajs-1811 21 43 𝜆 𝜆 NOUN iajs-1811 21 44 ; ; PUNCT iajs-1811 21 45 𝑥 𝑥 PRON iajs-1811 21 46 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 21 47 𝛽𝜆 𝛽𝜆 ADP iajs-1811 21 48 𝑥 𝑥 INTJ iajs-1811 21 49 𝑒𝑥𝑝 𝑒𝑥𝑝 INTJ iajs-1811 21 50 𝜆𝑥 𝜆𝑥 NOUN iajs-1811 21 51 𝜇 𝜇 ADP iajs-1811 21 52 𝑥 𝑥 NOUN iajs-1811 21 53 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 21 54 ⇒ ⇒ PROPN iajs-1811 21 55 ℓ ℓ PROPN iajs-1811 21 56 𝛽 𝛽 PROPN iajs-1811 21 57 , , PUNCT iajs-1811 21 58 𝜆 𝜆 NOUN iajs-1811 21 59 ; ; PUNCT iajs-1811 21 60 𝑥 𝑥 PART iajs-1811 21 61 𝑛 𝑛 PROPN iajs-1811 21 62 𝑙𝑛 𝑙𝑛 X iajs-1811 21 63 𝛽 𝛽 NOUN iajs-1811 21 64 𝑛 𝑛 PROPN iajs-1811 21 65 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 21 66 𝜆 𝜆 ADP iajs-1811 21 67 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 22 1 𝑥 𝑥 INTJ iajs-1811 22 2 𝑒𝑥𝑝 𝑒𝑥𝑝 INTJ iajs-1811 22 3 𝜆𝑥 𝜆𝑥 NOUN iajs-1811 22 4 𝜇 𝜇 ADP iajs-1811 22 5 𝑥 𝑥 NOUN iajs-1811 22 6 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 22 7 . . PUNCT iajs-1811 22 8 . . PUNCT iajs-1811 22 9 . . PUNCT iajs-1811 23 1 7 7 NUM iajs-1811 23 2 maximum maximum ADJ iajs-1811 23 3 likelihood likelihood NOUN iajs-1811 23 4 estimations estimation NOUN iajs-1811 23 5 differentiating differentiate VERB iajs-1811 23 6 the the DET iajs-1811 23 7 natural natural ADJ iajs-1811 23 8 log log NOUN iajs-1811 23 9 - - PUNCT iajs-1811 23 10 likelihood likelihood NOUN iajs-1811 23 11 function function NOUN iajs-1811 23 12 ℓ ℓ PROPN iajs-1811 23 13 β β PROPN iajs-1811 23 14 , , PUNCT iajs-1811 23 15 λ λ X iajs-1811 23 16 ; ; PUNCT iajs-1811 23 17 x x SYM iajs-1811 23 18 , , PUNCT iajs-1811 23 19 given give VERB iajs-1811 23 20 by by ADP iajs-1811 23 21 ( ( PUNCT iajs-1811 23 22 7 7 NUM iajs-1811 23 23 ) ) PUNCT iajs-1811 23 24 , , PUNCT iajs-1811 23 25 partially partially ADV iajs-1811 23 26 with with ADP iajs-1811 23 27 respect respect NOUN iajs-1811 23 28 to to ADP iajs-1811 23 29 β β PROPN iajs-1811 23 30 and and CCONJ iajs-1811 23 31 λ λ PROPN iajs-1811 23 32 and and CCONJ iajs-1811 23 33 then then ADV iajs-1811 23 34 equating equate VERB iajs-1811 23 35 to to ADP iajs-1811 23 36 zero zero NUM iajs-1811 23 37 we we PRON iajs-1811 23 38 have have VERB iajs-1811 23 39 : : PUNCT iajs-1811 23 40 𝜕ℓ 𝜕ℓ PROPN iajs-1811 23 41 𝛽 𝛽 PROPN iajs-1811 23 42 , , PUNCT iajs-1811 23 43 𝜆 𝜆 NOUN iajs-1811 23 44 ; ; PUNCT iajs-1811 23 45 𝑥 𝑥 PRON iajs-1811 23 46 𝜕𝛽 𝜕𝛽 VERB iajs-1811 23 47 𝑛 𝑛 PRON iajs-1811 23 48 𝛽 𝛽 NOUN iajs-1811 23 49 𝜆 𝜆 NOUN iajs-1811 23 50 𝑥 𝑥 PROPN iajs-1811 23 51 1 1 NUM iajs-1811 23 52 𝑥 𝑥 NOUN iajs-1811 23 53 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 24 1 𝑥 𝑥 X iajs-1811 24 2 𝑒 𝑒 NOUN iajs-1811 24 3 𝜇 𝜇 ADP iajs-1811 24 4 𝑥 𝑥 NOUN iajs-1811 24 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 24 6 1 1 NUM iajs-1811 24 7 𝑥 𝑥 NOUN iajs-1811 24 8 𝑒 𝑒 NOUN iajs-1811 24 9 𝜇 𝜇 ADP iajs-1811 24 10 𝑥 𝑥 NOUN iajs-1811 24 11 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 24 12 0 0 NUM iajs-1811 24 13 … … SYM iajs-1811 24 14 8 8 NUM iajs-1811 24 15 𝜕ℓ 𝜕ℓ NOUN iajs-1811 24 16 𝛽 𝛽 NOUN iajs-1811 24 17 , , PUNCT iajs-1811 24 18 𝜆 𝜆 NOUN iajs-1811 24 19 ; ; PUNCT iajs-1811 24 20 𝑥 𝑥 DET iajs-1811 24 21 𝜕𝜆 𝜕𝜆 NOUN iajs-1811 24 22 𝑛 𝑛 PRON iajs-1811 24 23 𝜆 𝜆 ADP iajs-1811 24 24 1 1 NUM iajs-1811 24 25 𝑥 𝑥 NOUN iajs-1811 24 26 𝑒 𝑒 ADV iajs-1811 24 27 𝜇 𝜇 ADP iajs-1811 24 28 𝑥 𝑥 NOUN iajs-1811 24 29 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 24 30 1 1 NUM iajs-1811 24 31 𝑥 𝑥 NOUN iajs-1811 24 32 𝑒 𝑒 NOUN iajs-1811 24 33 𝜇 𝜇 ADP iajs-1811 24 34 𝑥 𝑥 NOUN iajs-1811 24 35 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 24 36 0 0 NUM iajs-1811 24 37 … … PUNCT iajs-1811 24 38 9 9 NUM iajs-1811 24 39 the the DET iajs-1811 24 40 maximum maximum ADJ iajs-1811 24 41 likelihood likelihood NOUN iajs-1811 24 42 estimates estimate NOUN iajs-1811 24 43 ( ( PUNCT iajs-1811 24 44 mles mle NOUN iajs-1811 24 45 ) ) PUNCT iajs-1811 24 46 of of ADP iajs-1811 24 47 𝛽 𝛽 NOUN iajs-1811 24 48 and and CCONJ iajs-1811 24 49 𝜆 𝜆 NOUN iajs-1811 24 50 are be AUX iajs-1811 24 51 the the DET iajs-1811 24 52 solution solution NOUN iajs-1811 24 53 of of ADP iajs-1811 24 54 the the DET iajs-1811 24 55 likelihood likelihood NOUN iajs-1811 24 56 equations equation NOUN iajs-1811 24 57 ( ( PUNCT iajs-1811 24 58 8) 8) NUM iajs-1811 24 59 and and CCONJ iajs-1811 24 60 ( ( PUNCT iajs-1811 24 61 9 9 NUM iajs-1811 24 62 ) ) PUNCT iajs-1811 24 63 . . PUNCT iajs-1811 25 1 since since SCONJ iajs-1811 25 2 there there PRON iajs-1811 25 3 is be VERB iajs-1811 25 4 no no DET iajs-1811 25 5 closed closed ADJ iajs-1811 25 6 form form NOUN iajs-1811 25 7 of of ADP iajs-1811 25 8 the the DET iajs-1811 25 9 solutions solution NOUN iajs-1811 25 10 , , PUNCT iajs-1811 25 11 an an DET iajs-1811 25 12 iterative iterative NOUN iajs-1811 25 13 approximation approximation NOUN iajs-1811 25 14 technique technique NOUN iajs-1811 25 15 can can AUX iajs-1811 25 16 be be AUX iajs-1811 25 17 used use VERB iajs-1811 25 18 to to PART iajs-1811 25 19 obtain obtain VERB iajs-1811 25 20 the the DET iajs-1811 25 21 mles mle NOUN iajs-1811 25 22 . . PUNCT iajs-1811 26 1 in in ADP iajs-1811 26 2 the the DET iajs-1811 26 3 following following NOUN iajs-1811 26 4 , , PUNCT iajs-1811 26 5 we we PRON iajs-1811 26 6 consider consider VERB iajs-1811 26 7 two two NUM iajs-1811 26 8 iterative iterative NOUN iajs-1811 26 9 approximation approximation NOUN iajs-1811 26 10 techniques technique NOUN iajs-1811 26 11 namely namely ADV iajs-1811 26 12 the the DET iajs-1811 26 13 expectation expectation NOUN iajs-1811 26 14 - - PUNCT iajs-1811 26 15 maximization maximization NOUN iajs-1811 26 16 ( ( PUNCT iajs-1811 26 17 em em NOUN iajs-1811 26 18 ) ) PUNCT iajs-1811 26 19 algorithm algorithm PROPN iajs-1811 26 20 and and CCONJ iajs-1811 26 21 newton newton PROPN iajs-1811 26 22 raphson raphson PROPN iajs-1811 26 23 ( ( PUNCT iajs-1811 26 24 nr nr NOUN iajs-1811 26 25 ) ) PUNCT iajs-1811 26 26 algorithm algorithm NOUN iajs-1811 26 27 . . PUNCT iajs-1811 27 1 expectation expectation NOUN iajs-1811 27 2 - - PUNCT iajs-1811 27 3 maximization maximization NOUN iajs-1811 27 4 algorithm algorithm NOUN iajs-1811 27 5 dempster dempster PROPN iajs-1811 27 6 et et PROPN iajs-1811 27 7 al al PROPN iajs-1811 27 8 . . PROPN iajs-1811 28 1 ( ( PUNCT iajs-1811 28 2 1977 1977 NUM iajs-1811 28 3 ) ) PUNCT iajs-1811 29 1 [ [ X iajs-1811 29 2 2 2 X iajs-1811 29 3 ] ] PUNCT iajs-1811 29 4 presented present VERB iajs-1811 29 5 a a DET iajs-1811 29 6 general general ADJ iajs-1811 29 7 approach approach NOUN iajs-1811 29 8 to to ADP iajs-1811 29 9 iterative iterative ADJ iajs-1811 29 10 computation computation NOUN iajs-1811 29 11 of of ADP iajs-1811 29 12 maximum maximum ADJ iajs-1811 29 13 - - PUNCT iajs-1811 29 14 likelihood likelihood NOUN iajs-1811 29 15 estimates estimate NOUN iajs-1811 29 16 when when SCONJ iajs-1811 29 17 the the DET iajs-1811 29 18 observations observation NOUN iajs-1811 29 19 can can AUX iajs-1811 29 20 be be AUX iajs-1811 29 21 viewed view VERB iajs-1811 29 22 as as ADP iajs-1811 29 23 incomplete incomplete ADJ iajs-1811 29 24 data datum NOUN iajs-1811 29 25 . . PUNCT iajs-1811 30 1 now now ADV iajs-1811 30 2 , , PUNCT iajs-1811 30 3 since since SCONJ iajs-1811 30 4 the the DET iajs-1811 30 5 observed observe VERB iajs-1811 30 6 fuzzy fuzzy ADJ iajs-1811 30 7 data datum NOUN iajs-1811 30 8 𝑥 𝑥 NOUN iajs-1811 30 9 can can AUX iajs-1811 30 10 be be AUX iajs-1811 30 11 seen see VERB iajs-1811 30 12 as as ADP iajs-1811 30 13 an an DET iajs-1811 30 14 incomplete incomplete ADJ iajs-1811 30 15 specification specification NOUN iajs-1811 30 16 of of ADP iajs-1811 30 17 a a DET iajs-1811 30 18 complete complete ADJ iajs-1811 30 19 data data NOUN iajs-1811 30 20 vector vector NOUN iajs-1811 30 21 x x NOUN iajs-1811 30 22 , , PUNCT iajs-1811 30 23 the the DET iajs-1811 30 24 em em PROPN iajs-1811 30 25 algorithm algorithm NOUN iajs-1811 30 26 is be AUX iajs-1811 30 27 appropriate appropriate ADJ iajs-1811 30 28 to to PART iajs-1811 30 29 find find VERB iajs-1811 30 30 the the DET iajs-1811 30 31 mles mle NOUN iajs-1811 30 32 of of ADP iajs-1811 30 33 the the DET iajs-1811 30 34 unknown unknown ADJ iajs-1811 30 35 parameters parameter NOUN iajs-1811 30 36 [ [ X iajs-1811 30 37 3][5 3][5 NUM iajs-1811 30 38 ] ] PUNCT iajs-1811 30 39 . . PUNCT iajs-1811 31 1 form form NOUN iajs-1811 31 2 equation equation NOUN iajs-1811 31 3 ( ( PUNCT iajs-1811 31 4 6 6 NUM iajs-1811 31 5 ) ) PUNCT iajs-1811 31 6 , , PUNCT iajs-1811 31 7 the the DET iajs-1811 31 8 natural natural ADJ iajs-1811 31 9 log log NOUN iajs-1811 31 10 - - PUNCT iajs-1811 31 11 likelihood likelihood NOUN iajs-1811 31 12 function function NOUN iajs-1811 31 13 for for ADP iajs-1811 31 14 x x SYM iajs-1811 31 15 becomes become NOUN iajs-1811 31 16 : : PUNCT iajs-1811 31 17 ℓ ℓ PROPN iajs-1811 31 18 𝛽 𝛽 PROPN iajs-1811 31 19 , , PUNCT iajs-1811 31 20 𝜆 𝜆 NOUN iajs-1811 31 21 ; ; PUNCT iajs-1811 31 22 𝑥 𝑥 DET iajs-1811 31 23 𝑙𝑛 𝑙𝑛 X iajs-1811 31 24 𝐿 𝐿 PROPN iajs-1811 31 25 𝛽 𝛽 PROPN iajs-1811 31 26 , , PUNCT iajs-1811 31 27 𝜆 𝜆 NOUN iajs-1811 31 28 ; ; PUNCT iajs-1811 31 29 𝑥 𝑥 PRON iajs-1811 31 30 ihsciconf ihsciconf ADJ iajs-1811 31 31 2017 2017 NUM iajs-1811 31 32 special special ADJ iajs-1811 31 33 issue issue NOUN iajs-1811 31 34 ibn ibn PROPN iajs-1811 31 35 al al PROPN iajs-1811 31 36 - - PUNCT iajs-1811 31 37 haitham haitham PROPN iajs-1811 31 38 journal journal PROPN iajs-1811 31 39 for for ADP iajs-1811 31 40 pure pure ADJ iajs-1811 31 41 and and CCONJ iajs-1811 31 42 applied apply VERB iajs-1811 31 43 science science NOUN iajs-1811 31 44 https://doi.org/ https://doi.org/ NOUN iajs-1811 31 45 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 31 46 for for ADP iajs-1811 31 47 more more ADJ iajs-1811 31 48 information information NOUN iajs-1811 31 49 about about ADP iajs-1811 31 50 the the DET iajs-1811 31 51 conference conference NOUN iajs-1811 31 52 please please INTJ iajs-1811 31 53 visit visit VERB iajs-1811 31 54 the the DET iajs-1811 31 55 websites website NOUN iajs-1811 31 56 : : PUNCT iajs-1811 31 57 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 31 58         SPACE iajs-1811 31 59 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 31 60       SPACE iajs-1811 31 61 mathematics|381 mathematics|381 PROPN iajs-1811 31 62         SPACE iajs-1811 31 63 ⇒ ⇒ PROPN iajs-1811 31 64 ℓ ℓ PROPN iajs-1811 31 65 𝛽 𝛽 PROPN iajs-1811 31 66 , , PUNCT iajs-1811 31 67 𝜆 𝜆 NOUN iajs-1811 31 68 ; ; PUNCT iajs-1811 32 1 𝑥 𝑥 PART iajs-1811 32 2 𝑛 𝑛 PROPN iajs-1811 32 3 𝑙𝑛 𝑙𝑛 X iajs-1811 32 4 𝛽 𝛽 NOUN iajs-1811 32 5 𝑛 𝑛 ADJ iajs-1811 32 6 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 32 7 𝜆 𝜆 PROPN iajs-1811 32 8 𝛽 𝛽 PROPN iajs-1811 32 9 1 1 NUM iajs-1811 32 10 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 32 11 𝑥 𝑥 X iajs-1811 32 12 𝜆 𝜆 ADP iajs-1811 32 13 𝑥 𝑥 X iajs-1811 32 14 … … PUNCT iajs-1811 32 15 10 10 NUM iajs-1811 32 16 the the DET iajs-1811 32 17 em em PROPN iajs-1811 32 18 algorithm algorithm NOUN iajs-1811 32 19 is be AUX iajs-1811 32 20 given give VERB iajs-1811 32 21 by by ADP iajs-1811 32 22 the the DET iajs-1811 32 23 following follow VERB iajs-1811 32 24 iterative iterative NOUN iajs-1811 32 25 process process NOUN iajs-1811 32 26 : : PUNCT iajs-1811 32 27 1 1 X iajs-1811 32 28 . . X iajs-1811 32 29 set set VERB iajs-1811 32 30 ℎ ℎ PROPN iajs-1811 32 31 0 0 PUNCT iajs-1811 32 32 and and CCONJ iajs-1811 32 33 initial initial ADJ iajs-1811 32 34 values value NOUN iajs-1811 32 35 of of ADP iajs-1811 32 36 𝛽 𝛽 NOUN iajs-1811 32 37 and and CCONJ iajs-1811 32 38 λ λ PROPN iajs-1811 32 39 , , PUNCT iajs-1811 32 40 say say VERB iajs-1811 32 41 𝛽 𝛽 NOUN iajs-1811 32 42 and and CCONJ iajs-1811 32 43 λ λ PROPN iajs-1811 32 44 . . PUNCT iajs-1811 33 1 2 2 X iajs-1811 33 2 . . X iajs-1811 33 3 at at ADP iajs-1811 33 4 iteration iteration NOUN iajs-1811 33 5 h h NOUN iajs-1811 33 6 1 1 NUM iajs-1811 33 7 , , PUNCT iajs-1811 33 8 compute compute VERB iajs-1811 33 9 the the DET iajs-1811 33 10 e e NOUN iajs-1811 33 11 and and CCONJ iajs-1811 33 12 m m NOUN iajs-1811 33 13 steps step NOUN iajs-1811 33 14 . . PUNCT iajs-1811 34 1 3 3 X iajs-1811 34 2 . . X iajs-1811 34 3 repeat repeat NOUN iajs-1811 34 4 step step NOUN iajs-1811 34 5 ( ( PUNCT iajs-1811 34 6 2 2 NUM iajs-1811 34 7 ) ) PUNCT iajs-1811 34 8 until until SCONJ iajs-1811 34 9 the the DET iajs-1811 34 10 convergence convergence NOUN iajs-1811 34 11 occurs occur VERB iajs-1811 34 12 , , PUNCT iajs-1811 34 13 i.e. i.e. X iajs-1811 34 14 the the DET iajs-1811 34 15 absolute absolute ADJ iajs-1811 34 16 difference difference NOUN iajs-1811 34 17 between between ADP iajs-1811 34 18 two two NUM iajs-1811 34 19 successive successive ADJ iajs-1811 34 20 iterations iteration NOUN iajs-1811 34 21 is be AUX iajs-1811 34 22 less less ADJ iajs-1811 34 23 than than ADP iajs-1811 34 24 ε ε PROPN iajs-1811 34 25 for for ADP iajs-1811 34 26 some some DET iajs-1811 34 27 pre pre ADJ iajs-1811 34 28 - - ADJ iajs-1811 34 29 fixed fixed ADJ iajs-1811 34 30 ε ε PROPN iajs-1811 34 31 0 0 NUM iajs-1811 34 32 . . PUNCT iajs-1811 35 1 when when SCONJ iajs-1811 35 2 the the DET iajs-1811 35 3 convergence convergence NOUN iajs-1811 35 4 occurs occur VERB iajs-1811 35 5 then then ADV iajs-1811 35 6 the the DET iajs-1811 35 7 present present ADJ iajs-1811 35 8 β β X iajs-1811 35 9 and and CCONJ iajs-1811 35 10 λ λ PROPN iajs-1811 35 11 be be VERB iajs-1811 35 12 the the DET iajs-1811 35 13 mles mle NOUN iajs-1811 35 14 of of ADP iajs-1811 35 15 𝛽 𝛽 NOUN iajs-1811 35 16 and and CCONJ iajs-1811 35 17 𝜆 𝜆 NOUN iajs-1811 35 18 via via ADP iajs-1811 35 19 em em PRON iajs-1811 35 20 algorithm algorithm NOUN iajs-1811 35 21 which which PRON iajs-1811 35 22 we we PRON iajs-1811 35 23 referred refer VERB iajs-1811 35 24 to to ADP iajs-1811 35 25 as as ADP iajs-1811 35 26 β β X iajs-1811 35 27 , , PUNCT iajs-1811 35 28 λ λ X iajs-1811 35 29 . . PUNCT iajs-1811 36 1 e e X iajs-1811 36 2 - - NOUN iajs-1811 36 3 step step NOUN iajs-1811 36 4 : : PUNCT iajs-1811 36 5 the the DET iajs-1811 36 6 e e NOUN iajs-1811 36 7 - - NOUN iajs-1811 36 8 step step NOUN iajs-1811 36 9 of of ADP iajs-1811 36 10 the the DET iajs-1811 36 11 em em PROPN iajs-1811 36 12 algorithm algorithm NOUN iajs-1811 36 13 at at ADP iajs-1811 36 14 iteration iteration NOUN iajs-1811 36 15 h h NOUN iajs-1811 36 16 1 1 NUM iajs-1811 36 17 requires require VERB iajs-1811 36 18 to to PART iajs-1811 36 19 compute compute VERB iajs-1811 36 20 the the DET iajs-1811 36 21 following follow VERB iajs-1811 36 22 conditional conditional ADJ iajs-1811 36 23 expectations expectation NOUN iajs-1811 36 24 using use VERB iajs-1811 36 25 the the DET iajs-1811 36 26 expression expression NOUN iajs-1811 36 27 ( ( PUNCT iajs-1811 36 28 5 5 NUM iajs-1811 36 29 ) ) PUNCT iajs-1811 36 30 , , PUNCT iajs-1811 36 31 𝐸 𝐸 PROPN iajs-1811 36 32 , , PUNCT iajs-1811 36 33 ℓ ℓ PROPN iajs-1811 36 34 𝛽 𝛽 PROPN iajs-1811 36 35 , , PUNCT iajs-1811 36 36 𝜆 𝜆 NOUN iajs-1811 36 37 ; ; PUNCT iajs-1811 36 38 𝑥|𝑥 𝑥|𝑥 X iajs-1811 36 39 𝑛 𝑛 DET iajs-1811 36 40 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 36 41 𝛽 𝛽 PROPN iajs-1811 36 42 𝑛 𝑛 ADV iajs-1811 36 43 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 36 44 𝜆 𝜆 ADP iajs-1811 36 45 𝛽 𝛽 PROPN iajs-1811 36 46 1 1 NUM iajs-1811 36 47 𝐸 𝐸 PROPN iajs-1811 36 48 , , PUNCT iajs-1811 36 49 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 36 50 𝑥 𝑥 PROPN iajs-1811 36 51 |𝑥 |𝑥 PROPN iajs-1811 37 1 𝜆 𝜆 PROPN iajs-1811 37 2 𝐸 𝐸 PROPN iajs-1811 37 3 , , PUNCT iajs-1811 37 4 𝑥 𝑥 PROPN iajs-1811 37 5 |𝑥 |𝑥 NOUN iajs-1811 37 6 … … PUNCT iajs-1811 37 7 11 11 NUM iajs-1811 37 8 where where SCONJ iajs-1811 37 9 the the DET iajs-1811 37 10 conditional conditional ADJ iajs-1811 37 11 expectations expectation NOUN iajs-1811 37 12 of of ADP iajs-1811 37 13 x x PUNCT iajs-1811 37 14 given give VERB iajs-1811 37 15 x x PROPN iajs-1811 37 16 is be AUX iajs-1811 37 17 computed compute VERB iajs-1811 37 18 as as ADP iajs-1811 37 19 : : PUNCT iajs-1811 37 20 𝐸 𝐸 PROPN iajs-1811 37 21 , , PUNCT iajs-1811 37 22 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 37 23 𝑋 𝑋 PROPN iajs-1811 37 24 |𝑥 |𝑥 PROPN iajs-1811 37 25 𝑥 𝑥 PROPN iajs-1811 37 26 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 37 27 𝑥 𝑥 X iajs-1811 37 28 𝑒 𝑒 NOUN iajs-1811 37 29 𝜇 𝜇 ADP iajs-1811 37 30 𝑥 𝑥 NOUN iajs-1811 37 31 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 37 32 𝑥 𝑥 NOUN iajs-1811 37 33 𝑒 𝑒 NOUN iajs-1811 37 34 𝜇 𝜇 ADP iajs-1811 37 35 𝑥 𝑥 PRON iajs-1811 37 36 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 37 37 … … PUNCT iajs-1811 37 38 12 12 NUM iajs-1811 37 39 𝐸 𝐸 PROPN iajs-1811 37 40 , , PUNCT iajs-1811 37 41 𝑋 𝑋 NOUN iajs-1811 37 42 |𝑥 |𝑥 NOUN iajs-1811 37 43 𝑥 𝑥 X iajs-1811 37 44 𝑒 𝑒 VERB iajs-1811 37 45 𝜇 𝜇 SCONJ iajs-1811 37 46 𝑥 𝑥 NOUN iajs-1811 37 47 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 37 48 𝑥 𝑥 NOUN iajs-1811 37 49 𝑒 𝑒 NOUN iajs-1811 37 50 𝜇 𝜇 ADP iajs-1811 37 51 𝑥 𝑥 PRON iajs-1811 37 52 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 37 53 … … PUNCT iajs-1811 37 54 13 13 NUM iajs-1811 37 55 m m NOUN iajs-1811 37 56 - - PUNCT iajs-1811 37 57 step step NOUN iajs-1811 37 58 : : PUNCT iajs-1811 37 59 the the DET iajs-1811 37 60 m m NOUN iajs-1811 37 61 - - NOUN iajs-1811 37 62 step step NOUN iajs-1811 37 63 of of ADP iajs-1811 37 64 em em PRON iajs-1811 37 65 algorithm algorithm NOUN iajs-1811 37 66 involves involve VERB iajs-1811 37 67 maximizing maximize VERB iajs-1811 37 68 equation equation NOUN iajs-1811 37 69 ( ( PUNCT iajs-1811 37 70 11 11 NUM iajs-1811 37 71 ) ) PUNCT iajs-1811 37 72 with with ADP iajs-1811 37 73 respect respect NOUN iajs-1811 37 74 to to ADP iajs-1811 37 75 β β PROPN iajs-1811 37 76 and and CCONJ iajs-1811 37 77 λ λ PROPN iajs-1811 37 78 . . PUNCT iajs-1811 38 1 this this PRON iajs-1811 38 2 is be AUX iajs-1811 38 3 easily easily ADV iajs-1811 38 4 achieved achieve VERB iajs-1811 38 5 by by ADP iajs-1811 38 6 differentiating differentiate VERB iajs-1811 38 7 equation equation NOUN iajs-1811 38 8 ( ( PUNCT iajs-1811 38 9 11 11 NUM iajs-1811 38 10 ) ) PUNCT iajs-1811 38 11 partially partially ADV iajs-1811 38 12 with with ADP iajs-1811 38 13 respect respect NOUN iajs-1811 38 14 to to ADP iajs-1811 38 15 β β PROPN iajs-1811 38 16 and and CCONJ iajs-1811 38 17 λ λ PROPN iajs-1811 38 18 and and CCONJ iajs-1811 38 19 then then ADV iajs-1811 38 20 equating equate VERB iajs-1811 38 21 to to ADP iajs-1811 38 22 zero zero NUM iajs-1811 38 23 which which PRON iajs-1811 38 24 implies imply VERB iajs-1811 38 25 that that SCONJ iajs-1811 38 26 : : PUNCT iajs-1811 38 27 𝛽 𝛽 X iajs-1811 38 28 𝑛 𝑛 PRON iajs-1811 38 29 ∑ ∑ PUNCT iajs-1811 38 30 𝐸 𝐸 PROPN iajs-1811 38 31 , , PUNCT iajs-1811 38 32 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 38 33 𝑋 𝑋 PROPN iajs-1811 38 34 |𝑥 |𝑥 PROPN iajs-1811 38 35 𝜆 𝜆 ADP iajs-1811 38 36 ∑ ∑ PUNCT iajs-1811 38 37 𝐸 𝐸 PROPN iajs-1811 38 38 , , PUNCT iajs-1811 38 39 𝑋 𝑋 NOUN iajs-1811 38 40 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 38 41 𝑋 𝑋 PROPN iajs-1811 38 42 |𝑥 |𝑥 PROPN iajs-1811 38 43 … … PUNCT iajs-1811 38 44 14 14 NUM iajs-1811 38 45 𝜆 𝜆 SYM iajs-1811 38 46 𝑛 𝑛 PRON iajs-1811 38 47 ∑ ∑ PROPN iajs-1811 38 48 𝐸 𝐸 PROPN iajs-1811 38 49 , , PUNCT iajs-1811 38 50 𝑋 𝑋 PROPN iajs-1811 38 51 |𝑥 |𝑥 PROPN iajs-1811 38 52 … … PUNCT iajs-1811 38 53 15 15 NUM iajs-1811 38 54 where where SCONJ iajs-1811 38 55 𝐸 𝐸 PROPN iajs-1811 38 56 , , PUNCT iajs-1811 38 57 𝑋 𝑋 PROPN iajs-1811 38 58 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 38 59 𝑋 𝑋 PROPN iajs-1811 38 60 |𝑥 |𝑥 PROPN iajs-1811 38 61 computed compute VERB iajs-1811 38 62 as as ADP iajs-1811 38 63 : : PUNCT iajs-1811 38 64 𝐸 𝐸 PROPN iajs-1811 38 65 , , PUNCT iajs-1811 38 66 𝑋 𝑋 PROPN iajs-1811 38 67 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 38 68 𝑋 𝑋 PROPN iajs-1811 39 1 |𝑥 |𝑥 PROPN iajs-1811 39 2 𝑥 𝑥 PROPN iajs-1811 39 3 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 40 1 𝑥 𝑥 X iajs-1811 40 2 𝑒 𝑒 NOUN iajs-1811 40 3 𝜇 𝜇 ADP iajs-1811 40 4 𝑥 𝑥 NOUN iajs-1811 40 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 40 6 𝑥 𝑥 NOUN iajs-1811 40 7 𝑒 𝑒 NOUN iajs-1811 40 8 𝜇 𝜇 ADP iajs-1811 40 9 𝑥 𝑥 NOUN iajs-1811 40 10 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 40 11 … … PUNCT iajs-1811 40 12 16 16 NUM iajs-1811 40 13 ihsciconf ihsciconf NOUN iajs-1811 40 14 2017 2017 NUM iajs-1811 40 15 special special ADJ iajs-1811 40 16 issue issue NOUN iajs-1811 40 17 ibn ibn PROPN iajs-1811 40 18 al al PROPN iajs-1811 40 19 - - PUNCT iajs-1811 40 20 haitham haitham PROPN iajs-1811 40 21 journal journal PROPN iajs-1811 40 22 for for ADP iajs-1811 40 23 pure pure ADJ iajs-1811 40 24 and and CCONJ iajs-1811 40 25 applied apply VERB iajs-1811 40 26 science science NOUN iajs-1811 40 27 https://doi.org/ https://doi.org/ NOUN iajs-1811 40 28 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 40 29 for for ADP iajs-1811 40 30 more more ADJ iajs-1811 40 31 information information NOUN iajs-1811 40 32 about about ADP iajs-1811 40 33 the the DET iajs-1811 40 34 conference conference NOUN iajs-1811 40 35 please please INTJ iajs-1811 40 36 visit visit VERB iajs-1811 40 37 the the DET iajs-1811 40 38 websites website NOUN iajs-1811 40 39 : : PUNCT iajs-1811 40 40 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 40 41         SPACE iajs-1811 40 42 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 40 43       SPACE iajs-1811 40 44 mathematics|382 mathematics|382 PROPN iajs-1811 40 45         SPACE iajs-1811 40 46 𝐸 𝐸 PROPN iajs-1811 40 47 , , PUNCT iajs-1811 40 48 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 40 49 𝑋 𝑋 PROPN iajs-1811 40 50 |𝑥 |𝑥 PROPN iajs-1811 40 51 and and CCONJ iajs-1811 40 52 𝐸 𝐸 PROPN iajs-1811 40 53 , , PUNCT iajs-1811 40 54 𝑋 𝑋 PROPN iajs-1811 40 55 |𝑥 |𝑥 PROPN iajs-1811 40 56 as as ADP iajs-1811 40 57 in in ADP iajs-1811 40 58 ( ( PUNCT iajs-1811 40 59 12 12 NUM iajs-1811 40 60 ) ) PUNCT iajs-1811 40 61 and and CCONJ iajs-1811 40 62 ( ( PUNCT iajs-1811 40 63 13 13 NUM iajs-1811 40 64 ) ) PUNCT iajs-1811 40 65 . . PUNCT iajs-1811 41 1 we we PRON iajs-1811 41 2 can can AUX iajs-1811 41 3 rewrite rewrite VERB iajs-1811 41 4 𝛽 𝛽 NOUN iajs-1811 41 5 and and CCONJ iajs-1811 41 6 𝜆 𝜆 X iajs-1811 41 7 in in ADP iajs-1811 41 8 ( ( PUNCT iajs-1811 41 9 14 14 NUM iajs-1811 41 10 ) ) PUNCT iajs-1811 41 11 and and CCONJ iajs-1811 41 12 ( ( PUNCT iajs-1811 41 13 15 15 NUM iajs-1811 41 14 ) ) PUNCT iajs-1811 41 15 as as ADP iajs-1811 41 16 : : PUNCT iajs-1811 41 17 𝛽 𝛽 PROPN iajs-1811 41 18 1 1 NUM iajs-1811 41 19 𝑛 𝑛 PRON iajs-1811 41 20 𝐸 𝐸 PROPN iajs-1811 41 21 𝜆 𝜆 PROPN iajs-1811 41 22 𝐸 𝐸 PROPN iajs-1811 41 23 … … PUNCT iajs-1811 41 24 17 17 NUM iajs-1811 41 25 𝜆 𝜆 SYM iajs-1811 41 26 𝑛 𝑛 PRON iajs-1811 41 27 ∑ ∑ PROPN iajs-1811 41 28 𝐸 𝐸 PROPN iajs-1811 41 29 … … PUNCT iajs-1811 41 30 18 18 NUM iajs-1811 41 31 where where SCONJ iajs-1811 41 32 : : PUNCT iajs-1811 41 33 𝐸 𝐸 PROPN iajs-1811 41 34 𝐸 𝐸 PROPN iajs-1811 41 35 , , PUNCT iajs-1811 41 36 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 41 37 𝑋 𝑋 PROPN iajs-1811 41 38 |𝑥 |𝑥 PROPN iajs-1811 41 39 , , PUNCT iajs-1811 41 40 𝐸 𝐸 PROPN iajs-1811 41 41 𝐸 𝐸 PROPN iajs-1811 41 42 , , PUNCT iajs-1811 41 43 𝑋 𝑋 PROPN iajs-1811 41 44 |𝑥 |𝑥 PROPN iajs-1811 41 45 and and CCONJ iajs-1811 41 46 𝐸 𝐸 PROPN iajs-1811 41 47 𝐸 𝐸 PROPN iajs-1811 41 48 , , PUNCT iajs-1811 41 49 𝑋 𝑋 PROPN iajs-1811 41 50 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 41 51 𝑋 𝑋 PROPN iajs-1811 41 52 |𝑥 |𝑥 PROPN iajs-1811 41 53 newton newton PROPN iajs-1811 41 54 - - PUNCT iajs-1811 41 55 raphson raphson PROPN iajs-1811 41 56 algorithm algorithm NOUN iajs-1811 41 57 the the DET iajs-1811 41 58 steps step NOUN iajs-1811 41 59 of of ADP iajs-1811 41 60 the the DET iajs-1811 41 61 nr nr PROPN iajs-1811 41 62 algorithm algorithm NOUN iajs-1811 41 63 are be AUX iajs-1811 41 64 [ [ X iajs-1811 41 65 5][7 5][7 NOUN iajs-1811 41 66 ] ] X iajs-1811 41 67 : : PUNCT iajs-1811 41 68 1 1 X iajs-1811 41 69 . . X iajs-1811 41 70 set set VERB iajs-1811 41 71 ℎ ℎ PROPN iajs-1811 41 72 0 0 PUNCT iajs-1811 41 73 and and CCONJ iajs-1811 41 74 initial initial ADJ iajs-1811 41 75 values value NOUN iajs-1811 41 76 of of ADP iajs-1811 41 77 𝛽 𝛽 NOUN iajs-1811 41 78 and and CCONJ iajs-1811 41 79 λ λ PROPN iajs-1811 41 80 , , PUNCT iajs-1811 41 81 say say VERB iajs-1811 41 82 𝛽 𝛽 NOUN iajs-1811 41 83 and and CCONJ iajs-1811 41 84 λ λ PROPN iajs-1811 41 85 . . PUNCT iajs-1811 42 1 2 2 X iajs-1811 42 2 . . X iajs-1811 42 3 at at ADP iajs-1811 42 4 iteration iteration NOUN iajs-1811 42 5 ℎ ℎ PROPN iajs-1811 42 6 1 1 NUM iajs-1811 42 7 , , PUNCT iajs-1811 42 8 estimate estimate VERB iajs-1811 42 9 the the DET iajs-1811 42 10 new new ADJ iajs-1811 42 11 value value NOUN iajs-1811 42 12 of of ADP iajs-1811 42 13 β β PROPN iajs-1811 42 14 and and CCONJ iajs-1811 42 15 λ λ PROPN iajs-1811 42 16 , , PUNCT iajs-1811 42 17 as as ADP iajs-1811 42 18 : : PUNCT iajs-1811 42 19 𝛽 𝛽 NOUN iajs-1811 42 20 𝜆 𝜆 PRON iajs-1811 42 21 𝛽 𝛽 PROPN iajs-1811 42 22 𝜆 𝜆 PROPN iajs-1811 42 23 ⎣ ⎣ PROPN iajs-1811 42 24 ⎢ ⎢ NOUN iajs-1811 42 25 ⎢ ⎢ NOUN iajs-1811 42 26 ⎢ ⎢ NOUN iajs-1811 42 27 ⎡𝜕 ⎡𝜕 PROPN iajs-1811 42 28 ℓ ℓ PROPN iajs-1811 42 29 𝛽 𝛽 PROPN iajs-1811 42 30 , , PUNCT iajs-1811 42 31 𝜆 𝜆 NOUN iajs-1811 42 32 ; ; PUNCT iajs-1811 42 33 𝑥 𝑥 PROPN iajs-1811 42 34 𝜕𝛽 𝜕𝛽 PROPN iajs-1811 42 35 𝜕 𝜕 PROPN iajs-1811 42 36 ℓ ℓ PROPN iajs-1811 42 37 𝛽 𝛽 PROPN iajs-1811 42 38 , , PUNCT iajs-1811 42 39 𝜆 𝜆 NOUN iajs-1811 42 40 ; ; PUNCT iajs-1811 42 41 𝑥 𝑥 PRON iajs-1811 42 42 𝜕𝛽𝜕𝜆 𝜕𝛽𝜕𝜆 PROPN iajs-1811 42 43 𝜕 𝜕 PROPN iajs-1811 42 44 ℓ ℓ PROPN iajs-1811 42 45 𝛽 𝛽 PROPN iajs-1811 42 46 , , PUNCT iajs-1811 42 47 𝜆 𝜆 NOUN iajs-1811 42 48 ; ; PUNCT iajs-1811 42 49 𝑥 𝑥 PRON iajs-1811 42 50 𝜕𝛽𝜕𝜆 𝜕𝛽𝜕𝜆 PROPN iajs-1811 42 51 𝜕 𝜕 PROPN iajs-1811 42 52 ℓ ℓ PROPN iajs-1811 42 53 𝛽 𝛽 PROPN iajs-1811 42 54 , , PUNCT iajs-1811 42 55 𝜆 𝜆 NOUN iajs-1811 42 56 ; ; PUNCT iajs-1811 42 57 𝑥 𝑥 DET iajs-1811 42 58 𝜕𝜆 𝜕𝜆 NOUN iajs-1811 42 59 ⎦ ⎦ NOUN iajs-1811 42 60 ⎥ ⎥ PROPN iajs-1811 42 61 ⎥ ⎥ PROPN iajs-1811 42 62 ⎥ ⎥ PROPN iajs-1811 42 63 ⎤ ⎤ VERB iajs-1811 42 64 ⎣ ⎣ ADV iajs-1811 42 65 ⎢ ⎢ NOUN iajs-1811 42 66 ⎢ ⎢ NOUN iajs-1811 42 67 ⎢ ⎢ NOUN iajs-1811 42 68 ⎡𝜕ℓ ⎡𝜕ℓ PRON iajs-1811 42 69 𝛽 𝛽 NOUN iajs-1811 42 70 , , PUNCT iajs-1811 42 71 𝜆 𝜆 NOUN iajs-1811 42 72 ; ; PUNCT iajs-1811 42 73 𝑥 𝑥 DET iajs-1811 42 74 𝜕𝛽 𝜕𝛽 ADJ iajs-1811 42 75 𝜕ℓ 𝜕ℓ PROPN iajs-1811 42 76 𝛽 𝛽 NOUN iajs-1811 42 77 , , PUNCT iajs-1811 42 78 𝜆 𝜆 NOUN iajs-1811 42 79 ; ; PUNCT iajs-1811 42 80 𝑥 𝑥 DET iajs-1811 42 81 𝜕𝜆 𝜕𝜆 NOUN iajs-1811 42 82 ⎦ ⎦ NOUN iajs-1811 42 83 ⎥ ⎥ PROPN iajs-1811 42 84 ⎥ ⎥ PROPN iajs-1811 42 85 ⎥ ⎥ PROPN iajs-1811 42 86 ⎤ ⎤ PROPN iajs-1811 42 87 … … PUNCT iajs-1811 42 88 19 19 NUM iajs-1811 42 89 where where SCONJ iajs-1811 42 90 the the DET iajs-1811 42 91 first first ADJ iajs-1811 42 92 – – PUNCT iajs-1811 42 93 order order NOUN iajs-1811 42 94 derivatives derivative NOUN iajs-1811 42 95 of of ADP iajs-1811 42 96 the the DET iajs-1811 42 97 natural natural ADJ iajs-1811 42 98 log log NOUN iajs-1811 42 99 - - PUNCT iajs-1811 42 100 likelihood likelihood NOUN iajs-1811 42 101 with with ADP iajs-1811 42 102 respect respect NOUN iajs-1811 42 103 to to ADP iajs-1811 42 104 β β PROPN iajs-1811 42 105 and and CCONJ iajs-1811 42 106 λ λ PROPN iajs-1811 42 107 , , PUNCT iajs-1811 42 108 required require VERB iajs-1811 42 109 for for ADP iajs-1811 42 110 proceeding proceed VERB iajs-1811 42 111 with with ADP iajs-1811 42 112 the the DET iajs-1811 42 113 nr nr PROPN iajs-1811 42 114 algorithm algorithm NOUN iajs-1811 42 115 , , PUNCT iajs-1811 42 116 are be AUX iajs-1811 42 117 obtained obtain VERB iajs-1811 42 118 as as ADP iajs-1811 42 119 in in ADP iajs-1811 42 120 ( ( PUNCT iajs-1811 42 121 8) 8) NUM iajs-1811 42 122 and and CCONJ iajs-1811 42 123 ( ( PUNCT iajs-1811 42 124 9 9 NUM iajs-1811 42 125 ) ) PUNCT iajs-1811 42 126 and and CCONJ iajs-1811 42 127 the the DET iajs-1811 42 128 second second ADJ iajs-1811 42 129 – – PUNCT iajs-1811 42 130 order order NOUN iajs-1811 42 131 derivatives derivative NOUN iajs-1811 42 132 are be AUX iajs-1811 42 133 obtained obtain VERB iajs-1811 42 134 as as ADP iajs-1811 42 135 follows follow VERB iajs-1811 42 136 . . PUNCT iajs-1811 43 1 𝜕 𝜕 NOUN iajs-1811 43 2 ℓ ℓ PROPN iajs-1811 43 3 𝛽 𝛽 PROPN iajs-1811 43 4 , , PUNCT iajs-1811 43 5 𝜆 𝜆 NOUN iajs-1811 43 6 ; ; PUNCT iajs-1811 43 7 𝑥 𝑥 PRON iajs-1811 43 8 𝜕𝛽 𝜕𝛽 VERB iajs-1811 43 9 𝑛 𝑛 PRON iajs-1811 43 10 𝛽 𝛽 NOUN iajs-1811 43 11 𝜆 𝜆 ADP iajs-1811 43 12 𝑥 𝑥 X iajs-1811 43 13 𝜆 𝜆 NOUN iajs-1811 43 14 𝑥 𝑥 X iajs-1811 43 15 𝑒 𝑒 NOUN iajs-1811 43 16 𝑙𝑛 𝑙𝑛 X iajs-1811 43 17 𝑥 𝑥 NOUN iajs-1811 43 18 𝜇 𝜇 ADP iajs-1811 43 19 𝑥 𝑥 NOUN iajs-1811 43 20 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 43 21 1 1 NUM iajs-1811 43 22 𝑥 𝑥 NOUN iajs-1811 43 23 𝑒 𝑒 NOUN iajs-1811 43 24 𝜇 𝜇 ADP iajs-1811 43 25 𝑥 𝑥 NOUN iajs-1811 43 26 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 43 27 1 1 NUM iajs-1811 43 28 𝑥 𝑥 PRON iajs-1811 43 29 2𝜆 2𝜆 NUM iajs-1811 43 30 𝑥 𝑥 INTJ iajs-1811 43 31 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 44 1 𝑥 𝑥 X iajs-1811 44 2 𝑒 𝑒 NOUN iajs-1811 44 3 𝜇 𝜇 ADP iajs-1811 44 4 𝑥 𝑥 NOUN iajs-1811 44 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 44 6 1 1 NUM iajs-1811 44 7 𝑥 𝑥 NOUN iajs-1811 44 8 𝑒 𝑒 NOUN iajs-1811 44 9 𝜇 𝜇 ADP iajs-1811 44 10 𝑥 𝑥 NOUN iajs-1811 44 11 𝑑𝑥 𝑑𝑥 VERB iajs-1811 44 12 𝜆 𝜆 ADP iajs-1811 44 13 𝑥 𝑥 ADP iajs-1811 44 14 1 1 NUM iajs-1811 44 15 𝑥 𝑥 NOUN iajs-1811 44 16 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 45 1 𝑥 𝑥 X iajs-1811 45 2 𝑒 𝑒 NOUN iajs-1811 45 3 𝜇 𝜇 ADP iajs-1811 45 4 𝑥 𝑥 NOUN iajs-1811 45 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 6 1 1 NUM iajs-1811 45 7 𝑥 𝑥 NOUN iajs-1811 45 8 𝑒 𝑒 NOUN iajs-1811 45 9 𝜇 𝜇 ADP iajs-1811 45 10 𝑥 𝑥 PRON iajs-1811 45 11 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 12 … … PUNCT iajs-1811 45 13 20 20 NUM iajs-1811 45 14 𝜕 𝜕 PROPN iajs-1811 45 15 ℓ ℓ PROPN iajs-1811 45 16 𝛽 𝛽 PROPN iajs-1811 45 17 , , PUNCT iajs-1811 45 18 𝜆 𝜆 NOUN iajs-1811 45 19 ; ; PUNCT iajs-1811 45 20 𝑥 𝑥 DET iajs-1811 45 21 𝜕𝜆 𝜕𝜆 NOUN iajs-1811 45 22 𝑛 𝑛 PRON iajs-1811 45 23 𝜆 𝜆 ADP iajs-1811 45 24 1 1 NUM iajs-1811 45 25 𝑥 𝑥 NOUN iajs-1811 45 26 𝑒 𝑒 ADV iajs-1811 45 27 𝜇 𝜇 ADP iajs-1811 45 28 𝑥 𝑥 NOUN iajs-1811 45 29 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 30 1 1 NUM iajs-1811 45 31 𝑥 𝑥 NOUN iajs-1811 45 32 𝑒 𝑒 NOUN iajs-1811 45 33 𝜇 𝜇 ADP iajs-1811 45 34 𝑥 𝑥 NOUN iajs-1811 45 35 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 36 1 1 NUM iajs-1811 45 37 𝑥 𝑥 NOUN iajs-1811 45 38 𝑒 𝑒 NOUN iajs-1811 45 39 𝜇 𝜇 ADP iajs-1811 45 40 𝑥 𝑥 NOUN iajs-1811 45 41 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 42 1 1 NUM iajs-1811 45 43 𝑥 𝑥 NOUN iajs-1811 45 44 𝑒 𝑒 NOUN iajs-1811 45 45 𝜇 𝜇 ADP iajs-1811 45 46 𝑥 𝑥 PRON iajs-1811 45 47 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 45 48 … … PUNCT iajs-1811 45 49 21 21 NUM iajs-1811 45 50 ihsciconf ihsciconf NOUN iajs-1811 45 51 2017 2017 NUM iajs-1811 45 52 special special ADJ iajs-1811 45 53 issue issue NOUN iajs-1811 45 54 ibn ibn PROPN iajs-1811 45 55 al al PROPN iajs-1811 45 56 - - PUNCT iajs-1811 45 57 haitham haitham PROPN iajs-1811 45 58 journal journal PROPN iajs-1811 45 59 for for ADP iajs-1811 45 60 pure pure ADJ iajs-1811 45 61 and and CCONJ iajs-1811 45 62 applied apply VERB iajs-1811 45 63 science science NOUN iajs-1811 45 64 https://doi.org/ https://doi.org/ NOUN iajs-1811 45 65 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 45 66 for for ADP iajs-1811 45 67 more more ADJ iajs-1811 45 68 information information NOUN iajs-1811 45 69 about about ADP iajs-1811 45 70 the the DET iajs-1811 45 71 conference conference NOUN iajs-1811 45 72 please please INTJ iajs-1811 45 73 visit visit VERB iajs-1811 45 74 the the DET iajs-1811 45 75 websites website NOUN iajs-1811 45 76 : : PUNCT iajs-1811 45 77 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 45 78         SPACE iajs-1811 45 79 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 45 80       SPACE iajs-1811 45 81 mathematics|383 mathematics|383 PROPN iajs-1811 45 82         SPACE iajs-1811 45 83 𝜕 𝜕 PROPN iajs-1811 45 84 ℓ ℓ PROPN iajs-1811 45 85 𝛽 𝛽 PROPN iajs-1811 45 86 , , PUNCT iajs-1811 45 87 𝜆 𝜆 NOUN iajs-1811 45 88 ; ; PUNCT iajs-1811 45 89 𝑥 𝑥 PRON iajs-1811 45 90 𝜕𝛽𝜕𝜆 𝜕𝛽𝜕𝜆 VERB iajs-1811 45 91 𝜆 𝜆 DET iajs-1811 45 92 𝑥 𝑥 SYM iajs-1811 45 93 2 2 NUM iajs-1811 45 94 𝑥 𝑥 NOUN iajs-1811 45 95 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 46 1 𝑥 𝑥 X iajs-1811 46 2 𝑒 𝑒 NOUN iajs-1811 46 3 𝜇 𝜇 ADP iajs-1811 46 4 𝑥 𝑥 NOUN iajs-1811 46 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 46 6 1 1 NUM iajs-1811 46 7 𝑥 𝑥 NOUN iajs-1811 46 8 𝑒 𝑒 NOUN iajs-1811 46 9 𝜇 𝜇 ADP iajs-1811 46 10 𝑥 𝑥 NOUN iajs-1811 46 11 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 46 12 1 1 NUM iajs-1811 46 13 𝜆 𝜆 PRON iajs-1811 46 14 𝑥 𝑥 PRON iajs-1811 46 15 1 1 NUM iajs-1811 46 16 𝑥 𝑥 NOUN iajs-1811 46 17 𝑙𝑛 𝑙𝑛 NOUN iajs-1811 47 1 𝑥 𝑥 X iajs-1811 47 2 𝑒 𝑒 NOUN iajs-1811 47 3 𝜇 𝜇 ADP iajs-1811 47 4 𝑥 𝑥 NOUN iajs-1811 47 5 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 47 6 1 1 NUM iajs-1811 47 7 𝑥 𝑥 NOUN iajs-1811 47 8 𝑒 𝑒 NOUN iajs-1811 47 9 𝜇 𝜇 ADP iajs-1811 47 10 𝑥 𝑥 NOUN iajs-1811 47 11 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 47 12 1 1 NUM iajs-1811 47 13 𝑥 𝑥 NOUN iajs-1811 47 14 𝑒 𝑒 NOUN iajs-1811 47 15 𝜇 𝜇 ADP iajs-1811 47 16 𝑥 𝑥 NOUN iajs-1811 47 17 𝑑𝑥 𝑑𝑥 NOUN iajs-1811 47 18 … … PUNCT iajs-1811 47 19 22 22 NUM iajs-1811 47 20 3 3 NUM iajs-1811 47 21 . . PUNCT iajs-1811 47 22 repeat repeat NOUN iajs-1811 47 23 step step NOUN iajs-1811 47 24 ( ( PUNCT iajs-1811 47 25 2 2 NUM iajs-1811 47 26 ) ) PUNCT iajs-1811 47 27 until until SCONJ iajs-1811 47 28 the the DET iajs-1811 47 29 convergence convergence NOUN iajs-1811 47 30 occurs occur VERB iajs-1811 47 31 . . PUNCT iajs-1811 48 1 when when SCONJ iajs-1811 48 2 the the DET iajs-1811 48 3 convergence convergence NOUN iajs-1811 48 4 occurs occur VERB iajs-1811 48 5 then then ADV iajs-1811 48 6 the the DET iajs-1811 48 7 present present ADJ iajs-1811 48 8 β β X iajs-1811 48 9 and and CCONJ iajs-1811 48 10 λ λ PROPN iajs-1811 48 11 be be VERB iajs-1811 48 12 the the DET iajs-1811 48 13 mles mle NOUN iajs-1811 48 14 of of ADP iajs-1811 48 15 β β X iajs-1811 48 16 and and CCONJ iajs-1811 48 17 λ λ PROPN iajs-1811 48 18 via via ADP iajs-1811 48 19 nr nr PROPN iajs-1811 48 20 algorithm algorithm NOUN iajs-1811 48 21 which which PRON iajs-1811 48 22 we we PRON iajs-1811 48 23 referred refer VERB iajs-1811 48 24 to to ADP iajs-1811 48 25 as as ADP iajs-1811 48 26 β β X iajs-1811 48 27 , , PUNCT iajs-1811 48 28 λ λ INTJ iajs-1811 48 29 . . PUNCT iajs-1811 49 1 now now ADV iajs-1811 49 2 , , PUNCT iajs-1811 49 3 depending depend VERB iajs-1811 49 4 on on ADP iajs-1811 49 5 the the DET iajs-1811 49 6 invariant invariant ADJ iajs-1811 49 7 property property NOUN iajs-1811 49 8 of of ADP iajs-1811 49 9 mle mle PROPN iajs-1811 49 10 , , PUNCT iajs-1811 49 11 the the DET iajs-1811 49 12 mle mle NOUN iajs-1811 49 13 of of ADP iajs-1811 49 14 the the DET iajs-1811 49 15 reliability reliability NOUN iajs-1811 49 16 function function NOUN iajs-1811 49 17 of of ADP iajs-1811 49 18 inverse inverse ADJ iajs-1811 49 19 weibull weibull NOUN iajs-1811 49 20 distribution distribution NOUN iajs-1811 49 21 via via ADP iajs-1811 49 22 em em PRON iajs-1811 49 23 and and CCONJ iajs-1811 49 24 nr nr PROPN iajs-1811 49 25 algorithms algorithm NOUN iajs-1811 49 26 , , PUNCT iajs-1811 49 27 denoted denote VERB iajs-1811 49 28 by by ADP iajs-1811 49 29 r r PROPN iajs-1811 49 30 t t NOUN iajs-1811 49 31 and and CCONJ iajs-1811 49 32 r r NOUN iajs-1811 49 33 t t NOUN iajs-1811 49 34 respectively respectively ADV iajs-1811 49 35 , , PUNCT iajs-1811 49 36 can can AUX iajs-1811 49 37 be be AUX iajs-1811 49 38 obtained obtain VERB iajs-1811 49 39 by by ADP iajs-1811 49 40 replacing replace VERB iajs-1811 49 41 β β PRON iajs-1811 49 42 and and CCONJ iajs-1811 49 43 λ λ X iajs-1811 49 44 in in ADP iajs-1811 49 45 ( ( PUNCT iajs-1811 49 46 3 3 NUM iajs-1811 49 47 ) ) PUNCT iajs-1811 49 48 by by ADP iajs-1811 49 49 their their PRON iajs-1811 49 50 mle mle PROPN iajs-1811 49 51 estimates estimate NOUN iajs-1811 49 52 as as ADP iajs-1811 49 53 : : PUNCT iajs-1811 49 54 𝑅 𝑅 PROPN iajs-1811 49 55 𝑡 𝑡 NOUN iajs-1811 49 56 1 1 NUM iajs-1811 49 57 𝑒 𝑒 ADV iajs-1811 49 58 ; ; PUNCT iajs-1811 49 59 𝑡 𝑡 PROPN iajs-1811 49 60 0 0 NUM iajs-1811 49 61 … … SYM iajs-1811 49 62 23 23 NUM iajs-1811 49 63 𝑅 𝑅 PROPN iajs-1811 49 64 𝑡 𝑡 PROPN iajs-1811 49 65 1 1 NUM iajs-1811 49 66 𝑒 𝑒 NOUN iajs-1811 49 67 ; ; PUNCT iajs-1811 49 68 𝑡 𝑡 PROPN iajs-1811 49 69 0 0 NUM iajs-1811 49 70 … … SYM iajs-1811 49 71 24 24 NUM iajs-1811 49 72 moment moment NOUN iajs-1811 49 73 estimations estimation VERB iajs-1811 49 74 the the DET iajs-1811 49 75 method method NOUN iajs-1811 49 76 of of ADP iajs-1811 49 77 moments moment NOUN iajs-1811 49 78 is be AUX iajs-1811 49 79 one one NUM iajs-1811 49 80 the the DET iajs-1811 49 81 oldest old ADJ iajs-1811 49 82 method method NOUN iajs-1811 49 83 for for ADP iajs-1811 49 84 deriving derive VERB iajs-1811 49 85 point point NOUN iajs-1811 49 86 estimators estimator NOUN iajs-1811 49 87 . . PUNCT iajs-1811 50 1 the the DET iajs-1811 50 2 moment moment NOUN iajs-1811 50 3 estimates estimate VERB iajs-1811 50 4 for for ADP iajs-1811 50 5 β β PROPN iajs-1811 50 6 and and CCONJ iajs-1811 50 7 λ λ PROPN iajs-1811 50 8 of of ADP iajs-1811 50 9 inverse inverse ADJ iajs-1811 50 10 weibull weibull NOUN iajs-1811 50 11 distribution distribution NOUN iajs-1811 50 12 can can AUX iajs-1811 50 13 be be AUX iajs-1811 50 14 found find VERB iajs-1811 50 15 by by ADP iajs-1811 50 16 the the DET iajs-1811 50 17 following follow VERB iajs-1811 50 18 two two NUM iajs-1811 50 19 equations equation NOUN iajs-1811 50 20 which which PRON iajs-1811 50 21 are be AUX iajs-1811 50 22 obtained obtain VERB iajs-1811 50 23 by by ADP iajs-1811 50 24 equating equate VERB iajs-1811 50 25 the the DET iajs-1811 50 26 first first ADJ iajs-1811 50 27 and and CCONJ iajs-1811 50 28 the the DET iajs-1811 50 29 second second ADJ iajs-1811 50 30 population population NOUN iajs-1811 50 31 moments moment NOUN iajs-1811 50 32 to to ADP iajs-1811 50 33 the the DET iajs-1811 50 34 corresponding correspond VERB iajs-1811 50 35 sample sample NOUN iajs-1811 50 36 moments moment NOUN iajs-1811 50 37 , , PUNCT iajs-1811 50 38 that that PRON iajs-1811 50 39 is be AUX iajs-1811 50 40 : : PUNCT iajs-1811 50 41 λ λ X iajs-1811 50 42 г г PROPN iajs-1811 50 43 1 1 NUM iajs-1811 50 44 1 1 NUM iajs-1811 50 45 β β SYM iajs-1811 50 46 1 1 NUM iajs-1811 50 47 n n PROPN iajs-1811 50 48 e e NOUN iajs-1811 50 49 , , PUNCT iajs-1811 50 50 x|x x|x PROPN iajs-1811 50 51 … … PUNCT iajs-1811 50 52 25 25 NUM iajs-1811 50 53 λ λ NOUN iajs-1811 50 54 г г PROPN iajs-1811 50 55 1 1 NUM iajs-1811 50 56 2 2 NUM iajs-1811 50 57 β β SYM iajs-1811 50 58 1 1 NUM iajs-1811 50 59 n n NOUN iajs-1811 50 60 e e NOUN iajs-1811 50 61 , , PUNCT iajs-1811 50 62 x x PRON iajs-1811 50 63 |x |x NOUN iajs-1811 50 64 … … PUNCT iajs-1811 50 65 26 26 NUM iajs-1811 50 66 note note NOUN iajs-1811 50 67 that that SCONJ iajs-1811 50 68 , , PUNCT iajs-1811 50 69 the the DET iajs-1811 50 70 direct direct ADJ iajs-1811 50 71 form form NOUN iajs-1811 50 72 of of ADP iajs-1811 50 73 the the DET iajs-1811 50 74 solutions solution NOUN iajs-1811 50 75 to to ADP iajs-1811 50 76 equations equation NOUN iajs-1811 50 77 ( ( PUNCT iajs-1811 50 78 25 25 NUM iajs-1811 50 79 ) ) PUNCT iajs-1811 50 80 and and CCONJ iajs-1811 50 81 ( ( PUNCT iajs-1811 50 82 26 26 NUM iajs-1811 50 83 ) ) PUNCT iajs-1811 50 84 could could AUX iajs-1811 50 85 not not PART iajs-1811 50 86 be be AUX iajs-1811 50 87 obtained obtain VERB iajs-1811 50 88 . . PUNCT iajs-1811 51 1 however however ADV iajs-1811 51 2 , , PUNCT iajs-1811 51 3 by by ADP iajs-1811 51 4 using use VERB iajs-1811 51 5 an an DET iajs-1811 51 6 iterative iterative ADJ iajs-1811 51 7 numerical numerical ADJ iajs-1811 51 8 process process NOUN iajs-1811 51 9 , , PUNCT iajs-1811 51 10 we we PRON iajs-1811 51 11 can can AUX iajs-1811 51 12 obtain obtain VERB iajs-1811 51 13 the the DET iajs-1811 51 14 parameter parameter NOUN iajs-1811 51 15 estimates estimate NOUN iajs-1811 51 16 as as SCONJ iajs-1811 51 17 described describe VERB iajs-1811 51 18 below below ADV iajs-1811 51 19 : : PUNCT iajs-1811 51 20 step step NOUN iajs-1811 51 21 ( ( PUNCT iajs-1811 51 22 1 1 X iajs-1811 51 23 ) ) PUNCT iajs-1811 51 24 set set VERB iajs-1811 51 25 ℎ ℎ PROPN iajs-1811 51 26 0 0 PUNCT iajs-1811 52 1 and and CCONJ iajs-1811 52 2 initial initial ADJ iajs-1811 52 3 values value NOUN iajs-1811 52 4 of of ADP iajs-1811 52 5 𝛽 𝛽 NOUN iajs-1811 52 6 and and CCONJ iajs-1811 52 7 λ λ PROPN iajs-1811 52 8 , , PUNCT iajs-1811 52 9 say say VERB iajs-1811 52 10 𝛽 𝛽 NOUN iajs-1811 52 11 and and CCONJ iajs-1811 52 12 λ λ PROPN iajs-1811 52 13 . . PUNCT iajs-1811 53 1 step step NOUN iajs-1811 53 2 ( ( PUNCT iajs-1811 53 3 2 2 NUM iajs-1811 53 4 ) ) PUNCT iajs-1811 53 5 at at ADP iajs-1811 53 6 h h NOUN iajs-1811 53 7 1 1 NUM iajs-1811 53 8 iteration iteration NOUN iajs-1811 53 9 , , PUNCT iajs-1811 53 10 using use VERB iajs-1811 53 11 the the DET iajs-1811 53 12 expression expression NOUN iajs-1811 53 13 ( ( PUNCT iajs-1811 53 14 5 5 NUM iajs-1811 53 15 ) ) PUNCT iajs-1811 53 16 to to PART iajs-1811 53 17 compute compute VERB iajs-1811 53 18 the the DET iajs-1811 53 19 following follow VERB iajs-1811 53 20 conditional conditional ADJ iajs-1811 53 21 expectation expectation NOUN iajs-1811 53 22 , , PUNCT iajs-1811 53 23 ihsciconf ihsciconf NOUN iajs-1811 53 24 2017 2017 NUM iajs-1811 53 25 special special ADJ iajs-1811 53 26 issue issue NOUN iajs-1811 53 27 ibn ibn PROPN iajs-1811 53 28 al al PROPN iajs-1811 53 29 - - PUNCT iajs-1811 53 30 haitham haitham PROPN iajs-1811 53 31 journal journal PROPN iajs-1811 53 32 for for ADP iajs-1811 53 33 pure pure ADJ iajs-1811 53 34 and and CCONJ iajs-1811 53 35 applied apply VERB iajs-1811 53 36 science science NOUN iajs-1811 53 37 https://doi.org/ https://doi.org/ NOUN iajs-1811 53 38 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 53 39 for for ADP iajs-1811 53 40 more more ADJ iajs-1811 53 41 information information NOUN iajs-1811 53 42 about about ADP iajs-1811 53 43 the the DET iajs-1811 53 44 conference conference NOUN iajs-1811 53 45 please please INTJ iajs-1811 53 46 visit visit VERB iajs-1811 53 47 the the DET iajs-1811 53 48 websites website NOUN iajs-1811 53 49 : : PUNCT iajs-1811 53 50 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 53 51         SPACE iajs-1811 53 52 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 53 53       SPACE iajs-1811 53 54 mathematics|384 mathematics|384 NOUN iajs-1811 53 55         SPACE iajs-1811 53 56 e e PROPN iajs-1811 53 57 , , PUNCT iajs-1811 53 58 x x X iajs-1811 53 59 |x |x NOUN iajs-1811 53 60 x x X iajs-1811 53 61 e e NOUN iajs-1811 53 62 μ μ PROPN iajs-1811 53 63 x x X iajs-1811 53 64 dx dx PROPN iajs-1811 53 65 x x X iajs-1811 53 66 e e PROPN iajs-1811 53 67 μ μ PROPN iajs-1811 53 68 x x X iajs-1811 53 69 dx dx PROPN iajs-1811 53 70 ; ; PUNCT iajs-1811 53 71 r r NOUN iajs-1811 53 72 1,2 1,2 NUM iajs-1811 53 73 step step NOUN iajs-1811 53 74 ( ( PUNCT iajs-1811 53 75 3 3 X iajs-1811 53 76 ) ) PUNCT iajs-1811 53 77 solve solve VERB iajs-1811 53 78 the the DET iajs-1811 53 79 following follow VERB iajs-1811 53 80 equation equation NOUN iajs-1811 53 81 for for ADP iajs-1811 53 82 β β X iajs-1811 53 83 , , PUNCT iajs-1811 53 84 based base VERB iajs-1811 53 85 on on ADP iajs-1811 53 86 equations equation NOUN iajs-1811 53 87 ( ( PUNCT iajs-1811 53 88 25 25 NUM iajs-1811 53 89 ) ) PUNCT iajs-1811 53 90 and and CCONJ iajs-1811 53 91 ( ( PUNCT iajs-1811 53 92 26 26 NUM iajs-1811 53 93 ) ) PUNCT iajs-1811 53 94 , , PUNCT iajs-1811 53 95 to to PART iajs-1811 53 96 obtain obtain VERB iajs-1811 53 97 the the DET iajs-1811 53 98 solution solution NOUN iajs-1811 53 99 as as ADP iajs-1811 53 100 β β PROPN iajs-1811 53 101 , , PUNCT iajs-1811 53 102 г г PROPN iajs-1811 53 103 1 1 NUM iajs-1811 53 104 1 1 NUM iajs-1811 53 105 β β X iajs-1811 53 106 г г PROPN iajs-1811 53 107 1 1 NUM iajs-1811 53 108 2 2 NUM iajs-1811 53 109 β β X iajs-1811 53 110 ∑ ∑ PART iajs-1811 53 111 e e PROPN iajs-1811 53 112 , , PUNCT iajs-1811 53 113 x|x x|x PUNCT iajs-1811 54 1 n n CCONJ iajs-1811 54 2 ∑ ∑ PUNCT iajs-1811 54 3 e e X iajs-1811 54 4 , , PUNCT iajs-1811 54 5 x x SYM iajs-1811 54 6 |x |x NOUN iajs-1811 54 7 step step NOUN iajs-1811 54 8 ( ( PUNCT iajs-1811 54 9 4 4 X iajs-1811 54 10 ) ) PUNCT iajs-1811 54 11 obtain obtain VERB iajs-1811 54 12 the the DET iajs-1811 54 13 solution solution NOUN iajs-1811 54 14 for for ADP iajs-1811 54 15 λ λ NOUN iajs-1811 54 16 , , PUNCT iajs-1811 54 17 say say VERB iajs-1811 54 18 λ λ INTJ iajs-1811 54 19 , , PUNCT iajs-1811 54 20 through through ADP iajs-1811 54 21 the the DET iajs-1811 54 22 following follow VERB iajs-1811 54 23 equation equation NOUN iajs-1811 54 24 , , PUNCT iajs-1811 54 25 λ λ X iajs-1811 54 26 ∑ ∑ PROPN iajs-1811 54 27 e e PROPN iajs-1811 54 28 , , PUNCT iajs-1811 54 29 x|x x|x PUNCT iajs-1811 55 1 n n PROPN iajs-1811 55 2 г г PROPN iajs-1811 55 3 1 1 NUM iajs-1811 55 4 1 1 NUM iajs-1811 55 5 β β NOUN iajs-1811 55 6 step step NOUN iajs-1811 55 7 ( ( PUNCT iajs-1811 55 8 5 5 X iajs-1811 55 9 ) ) PUNCT iajs-1811 55 10 setting set VERB iajs-1811 55 11 h h NOUN iajs-1811 55 12 h h NOUN iajs-1811 55 13 1 1 NUM iajs-1811 55 14 , , PUNCT iajs-1811 55 15 repeat repeat NOUN iajs-1811 55 16 step step NOUN iajs-1811 55 17 ( ( PUNCT iajs-1811 55 18 2 2 NUM iajs-1811 55 19 ) ) PUNCT iajs-1811 55 20 to to PART iajs-1811 55 21 step step VERB iajs-1811 55 22 ( ( PUNCT iajs-1811 55 23 4 4 NUM iajs-1811 55 24 ) ) PUNCT iajs-1811 55 25 until until SCONJ iajs-1811 55 26 convergence convergence NOUN iajs-1811 55 27 occurs occur VERB iajs-1811 55 28 . . PUNCT iajs-1811 56 1 when when SCONJ iajs-1811 56 2 the the DET iajs-1811 56 3 convergence convergence NOUN iajs-1811 56 4 occurs occur VERB iajs-1811 56 5 then then ADV iajs-1811 56 6 the the DET iajs-1811 56 7 present present ADJ iajs-1811 56 8 β β X iajs-1811 56 9 and and CCONJ iajs-1811 56 10 λ λ PROPN iajs-1811 56 11 be be VERB iajs-1811 56 12 the the DET iajs-1811 56 13 moment moment NOUN iajs-1811 56 14 estimates estimate NOUN iajs-1811 56 15 of of ADP iajs-1811 56 16 β β PROPN iajs-1811 56 17 and and CCONJ iajs-1811 56 18 λ λ PROPN iajs-1811 56 19 which which PRON iajs-1811 56 20 we we PRON iajs-1811 56 21 referred refer VERB iajs-1811 56 22 to to ADP iajs-1811 56 23 as as ADP iajs-1811 56 24 β β X iajs-1811 56 25 , , PUNCT iajs-1811 56 26 λ λ INTJ iajs-1811 56 27 . . PUNCT iajs-1811 57 1 now now ADV iajs-1811 57 2 , , PUNCT iajs-1811 57 3 depending depend VERB iajs-1811 57 4 on on ADP iajs-1811 57 5 the the DET iajs-1811 57 6 moment moment NOUN iajs-1811 57 7 estimates estimate NOUN iajs-1811 57 8 of of ADP iajs-1811 57 9 the the DET iajs-1811 57 10 shape shape NOUN iajs-1811 57 11 and and CCONJ iajs-1811 57 12 scale scale NOUN iajs-1811 57 13 parameters parameter NOUN iajs-1811 57 14 , , PUNCT iajs-1811 57 15 the the DET iajs-1811 57 16 approximated approximate VERB iajs-1811 57 17 moment moment NOUN iajs-1811 57 18 estimate estimate NOUN iajs-1811 57 19 of of ADP iajs-1811 57 20 the the DET iajs-1811 57 21 reliability reliability NOUN iajs-1811 57 22 function function NOUN iajs-1811 57 23 of of ADP iajs-1811 57 24 inverse inverse ADJ iajs-1811 57 25 weibull weibull NOUN iajs-1811 57 26 distribution distribution NOUN iajs-1811 57 27 at at ADP iajs-1811 57 28 mission mission NOUN iajs-1811 57 29 time time PROPN iajs-1811 57 30 t t PROPN iajs-1811 57 31 , , PUNCT iajs-1811 57 32 denoted denote VERB iajs-1811 57 33 by by ADP iajs-1811 57 34 r r PROPN iajs-1811 57 35 t t PROPN iajs-1811 57 36 , , PUNCT iajs-1811 57 37 can can AUX iajs-1811 57 38 be be AUX iajs-1811 57 39 obtained obtain VERB iajs-1811 57 40 by by ADP iajs-1811 57 41 replacing replace VERB iajs-1811 57 42 β β PRON iajs-1811 57 43 and and CCONJ iajs-1811 57 44 λ λ PROPN iajs-1811 57 45 in in ADP iajs-1811 57 46 equation equation NOUN iajs-1811 57 47 ( ( PUNCT iajs-1811 57 48 3 3 NUM iajs-1811 57 49 ) ) PUNCT iajs-1811 57 50 by by ADP iajs-1811 57 51 their their PRON iajs-1811 57 52 moment moment NOUN iajs-1811 57 53 estimates estimate NOUN iajs-1811 57 54 as as ADP iajs-1811 57 55 : : PUNCT iajs-1811 57 56 r r NOUN iajs-1811 57 57 t t PROPN iajs-1811 57 58 1 1 NUM iajs-1811 57 59 e e NOUN iajs-1811 57 60 ; ; PUNCT iajs-1811 57 61 t t PROPN iajs-1811 57 62 0 0 NUM iajs-1811 57 63 … … SYM iajs-1811 57 64 27 27 NUM iajs-1811 57 65 simulation simulation NOUN iajs-1811 57 66 study study NOUN iajs-1811 57 67 in in ADP iajs-1811 57 68 trying try VERB iajs-1811 57 69 to to PART iajs-1811 57 70 illustrate illustrate VERB iajs-1811 57 71 and and CCONJ iajs-1811 57 72 compare compare VERB iajs-1811 57 73 the the DET iajs-1811 57 74 algorithms algorithm NOUN iajs-1811 57 75 as as SCONJ iajs-1811 57 76 described describe VERB iajs-1811 57 77 above above ADV iajs-1811 57 78 , , PUNCT iajs-1811 57 79 a a DET iajs-1811 57 80 monte monte PROPN iajs-1811 57 81 - - PUNCT iajs-1811 57 82 carlo carlo PROPN iajs-1811 57 83 simulation simulation NOUN iajs-1811 57 84 study study NOUN iajs-1811 57 85 was be AUX iajs-1811 57 86 perform perform VERB iajs-1811 57 87 to to PART iajs-1811 57 88 generate generate VERB iajs-1811 57 89 an an DET iajs-1811 57 90 independent independent ADJ iajs-1811 57 91 identical identical ADJ iajs-1811 57 92 distributed distribute VERB iajs-1811 57 93 random random ADJ iajs-1811 57 94 samples sample NOUN iajs-1811 57 95 , , PUNCT iajs-1811 57 96 say say VERB iajs-1811 57 97 x x X iajs-1811 57 98 , , PUNCT iajs-1811 57 99 according accord VERB iajs-1811 57 100 to to ADP iajs-1811 57 101 inverse inverse ADJ iajs-1811 57 102 weibull weibull NOUN iajs-1811 57 103 distribution distribution NOUN iajs-1811 57 104 through through ADP iajs-1811 57 105 the the DET iajs-1811 57 106 adoption adoption NOUN iajs-1811 57 107 of of ADP iajs-1811 57 108 inverse inverse NOUN iajs-1811 57 109 transformation transformation NOUN iajs-1811 57 110 method method NOUN iajs-1811 57 111 with with ADP iajs-1811 57 112 size size NOUN iajs-1811 57 113 n n NOUN iajs-1811 57 114 = = SYM iajs-1811 57 115 20 20 NUM iajs-1811 57 116 , , PUNCT iajs-1811 57 117 30 30 NUM iajs-1811 57 118 and and CCONJ iajs-1811 57 119 90 90 NUM iajs-1811 57 120 to to PART iajs-1811 57 121 take take VERB iajs-1811 57 122 care care NOUN iajs-1811 57 123 of of ADP iajs-1811 57 124 small small ADJ iajs-1811 57 125 , , PUNCT iajs-1811 57 126 medium medium ADJ iajs-1811 57 127 and and CCONJ iajs-1811 57 128 large large ADJ iajs-1811 57 129 data datum NOUN iajs-1811 57 130 sets set NOUN iajs-1811 57 131 . . PUNCT iajs-1811 58 1 the the DET iajs-1811 58 2 number number NOUN iajs-1811 58 3 of of ADP iajs-1811 58 4 sample sample NOUN iajs-1811 58 5 replicated replicate VERB iajs-1811 58 6 chosen choose VERB iajs-1811 58 7 to to PART iajs-1811 58 8 be be AUX iajs-1811 58 9 ( ( PUNCT iajs-1811 58 10 100 100 NUM iajs-1811 58 11 ) ) PUNCT iajs-1811 58 12 . . PUNCT iajs-1811 59 1 the the DET iajs-1811 59 2 shape shape NOUN iajs-1811 59 3 parameter parameter NOUN iajs-1811 59 4 was be AUX iajs-1811 59 5 chosen choose VERB iajs-1811 59 6 to to PART iajs-1811 59 7 be be AUX iajs-1811 59 8 3 3 NUM iajs-1811 59 9 , , PUNCT iajs-1811 59 10 2.1 2.1 NUM iajs-1811 59 11 , , PUNCT iajs-1811 59 12 1 1 NUM iajs-1811 59 13 and and CCONJ iajs-1811 59 14 0.5 0.5 NUM iajs-1811 59 15 and and CCONJ iajs-1811 59 16 the the DET iajs-1811 59 17 scale scale NOUN iajs-1811 59 18 parameter parameter NOUN iajs-1811 59 19 0.5 0.5 NUM iajs-1811 59 20 , , PUNCT iajs-1811 59 21 1 1 NUM iajs-1811 59 22 , , PUNCT iajs-1811 59 23 3 3 NUM iajs-1811 59 24 . . PUNCT iajs-1811 60 1 then then ADV iajs-1811 60 2 , , PUNCT iajs-1811 60 3 each each DET iajs-1811 60 4 observation observation NOUN iajs-1811 60 5 of of ADP iajs-1811 60 6 x x PRON iajs-1811 60 7 was be AUX iajs-1811 60 8 made make VERB iajs-1811 60 9 fuzzy fuzzy ADJ iajs-1811 60 10 based base VERB iajs-1811 60 11 on on ADP iajs-1811 60 12 an an DET iajs-1811 60 13 appropriate appropriate ADJ iajs-1811 60 14 selected select VERB iajs-1811 60 15 membership membership NOUN iajs-1811 60 16 function function NOUN iajs-1811 60 17 among among ADP iajs-1811 60 18 the the DET iajs-1811 60 19 following follow VERB iajs-1811 60 20 eight eight NUM iajs-1811 60 21 membership membership NOUN iajs-1811 60 22 functions function NOUN iajs-1811 60 23 in in ADP iajs-1811 60 24 the the DET iajs-1811 60 25 fis fis PROPN iajs-1811 60 26 shown show VERB iajs-1811 60 27 in in ADP iajs-1811 60 28 figure figure NOUN iajs-1811 60 29 ( ( PUNCT iajs-1811 60 30 1 1 NUM iajs-1811 60 31 ) ) PUNCT iajs-1811 60 32 . . PUNCT iajs-1811 61 1 the the DET iajs-1811 61 2 simulation simulation NOUN iajs-1811 61 3 program program NOUN iajs-1811 61 4 has have AUX iajs-1811 61 5 been be AUX iajs-1811 61 6 written write VERB iajs-1811 61 7 by by ADP iajs-1811 61 8 using use VERB iajs-1811 61 9 matlab matlab PROPN iajs-1811 61 10 ( ( PUNCT iajs-1811 61 11 r2010b r2010b NOUN iajs-1811 61 12 ) ) PUNCT iajs-1811 61 13 program program NOUN iajs-1811 61 14 . . PUNCT iajs-1811 62 1 the the DET iajs-1811 62 2 results result NOUN iajs-1811 62 3 of of ADP iajs-1811 62 4 montecarlo montecarlo PROPN iajs-1811 62 5 simulation simulation NOUN iajs-1811 62 6 have have AUX iajs-1811 62 7 been be AUX iajs-1811 62 8 summarized summarize VERB iajs-1811 62 9 in in ADP iajs-1811 62 10 the the DET iajs-1811 62 11 tables table NOUN iajs-1811 62 12 ( ( PUNCT iajs-1811 62 13 1) 1) NUM iajs-1811 62 14 … … SYM iajs-1811 62 15 (3 (3 X iajs-1811 62 16 ) ) PUNCT iajs-1811 62 17 . . PUNCT iajs-1811 63 1 ihsciconf ihsciconf PROPN iajs-1811 63 2 2017 2017 NUM iajs-1811 63 3 special special ADJ iajs-1811 63 4 issue issue NOUN iajs-1811 63 5 ibn ibn PROPN iajs-1811 63 6 al al PROPN iajs-1811 63 7 - - PUNCT iajs-1811 63 8 haitham haitham PROPN iajs-1811 63 9 journal journal PROPN iajs-1811 63 10 for for ADP iajs-1811 63 11 pure pure ADJ iajs-1811 63 12 and and CCONJ iajs-1811 63 13 applied apply VERB iajs-1811 63 14 science science NOUN iajs-1811 63 15 https://doi.org/ https://doi.org/ NOUN iajs-1811 63 16 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 63 17 for for ADP iajs-1811 63 18 more more ADJ iajs-1811 63 19 information information NOUN iajs-1811 63 20 about about ADP iajs-1811 63 21 the the DET iajs-1811 63 22 conference conference NOUN iajs-1811 63 23 please please INTJ iajs-1811 63 24 visit visit VERB iajs-1811 63 25 the the DET iajs-1811 63 26 websites website NOUN iajs-1811 63 27 : : PUNCT iajs-1811 63 28 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 63 29         SPACE iajs-1811 63 30 www.ihsciconf.org www.ihsciconf.org ADJ iajs-1811 63 31       SPACE iajs-1811 63 32 mathematics|385 mathematics|385 NOUN iajs-1811 63 33         SPACE iajs-1811 63 34 figure figure NOUN iajs-1811 63 35 ( ( PUNCT iajs-1811 63 36 1 1 NUM iajs-1811 63 37 ): ): PUNCT iajs-1811 63 38 fis fis PROPN iajs-1811 63 39 used use VERB iajs-1811 63 40 to to PART iajs-1811 63 41 encode encode VERB iajs-1811 63 42 the the DET iajs-1811 63 43 simulated simulate VERB iajs-1811 63 44 data datum NOUN iajs-1811 64 1 [ [ X iajs-1811 64 2 5 5 NUM iajs-1811 64 3 & & CCONJ iajs-1811 64 4 6 6 NUM iajs-1811 64 5 ] ] SYM iajs-1811 64 6 μ μ NOUN iajs-1811 64 7 x x SYM iajs-1811 64 8 1 1 NUM iajs-1811 64 9 ; ; PUNCT iajs-1811 64 10 x x SYM iajs-1811 64 11 0.05 0.05 NUM iajs-1811 64 12 0.25 0.25 NUM iajs-1811 64 13 x x SYM iajs-1811 64 14 0.2 0.2 NUM iajs-1811 64 15 ; ; PUNCT iajs-1811 64 16 0.05 0.05 NUM iajs-1811 64 17 x x SYM iajs-1811 64 18 0.25 0.25 NUM iajs-1811 64 19 0 0 NUM iajs-1811 64 20 ; ; PUNCT iajs-1811 64 21 otherwise otherwise ADV iajs-1811 64 22 μ μ PROPN iajs-1811 64 23 x x PROPN iajs-1811 64 24 ⎩ ⎩ NUM iajs-1811 64 25 ⎪ ⎪ NOUN iajs-1811 64 26 ⎨ ⎨ ADJ iajs-1811 64 27 ⎪ ⎪ NOUN iajs-1811 64 28 ⎧ ⎧ PROPN iajs-1811 64 29 x x PUNCT iajs-1811 64 30 0.75 0.75 NUM iajs-1811 64 31 0.25 0.25 NUM iajs-1811 64 32 ; ; PUNCT iajs-1811 64 33 0.75 0.75 NUM iajs-1811 64 34 x x SYM iajs-1811 64 35 1 1 NUM iajs-1811 64 36 1.5 1.5 NUM iajs-1811 64 37 x x SYM iajs-1811 64 38 0.5 0.5 NUM iajs-1811 64 39 ; ; PUNCT iajs-1811 64 40 1 1 NUM iajs-1811 64 41 x x SYM iajs-1811 64 42 1.5 1.5 NUM iajs-1811 64 43 0 0 NUM iajs-1811 64 44 ; ; PUNCT iajs-1811 64 45 otherwise otherwise ADV iajs-1811 64 46 μ μ PROPN iajs-1811 64 47 x x PROPN iajs-1811 64 48 ⎩ ⎩ NUM iajs-1811 64 49 ⎪ ⎪ NOUN iajs-1811 64 50 ⎨ ⎨ ADJ iajs-1811 64 51 ⎪ ⎪ NOUN iajs-1811 64 52 ⎧ ⎧ PROPN iajs-1811 64 53 x x PUNCT iajs-1811 64 54 0.05 0.05 NUM iajs-1811 64 55 0.2 0.2 NUM iajs-1811 64 56 ; ; PUNCT iajs-1811 64 57 0.05 0.05 NUM iajs-1811 64 58 x x SYM iajs-1811 64 59 0.25 0.25 NUM iajs-1811 64 60 0.5 0.5 NUM iajs-1811 64 61 x x SYM iajs-1811 64 62 0.25 0.25 NUM iajs-1811 64 63 ; ; PUNCT iajs-1811 64 64 0.25 0.25 NUM iajs-1811 64 65 x x SYM iajs-1811 64 66 0.5 0.5 NUM iajs-1811 64 67 0 0 NUM iajs-1811 64 68 ; ; PUNCT iajs-1811 64 69 otherwise otherwise ADV iajs-1811 64 70 μ μ PROPN iajs-1811 64 71 x x PROPN iajs-1811 64 72 ⎩ ⎩ NUM iajs-1811 64 73 ⎪ ⎪ NOUN iajs-1811 64 74 ⎨ ⎨ ADJ iajs-1811 64 75 ⎪ ⎪ NOUN iajs-1811 64 76 ⎧ ⎧ NOUN iajs-1811 64 77 x x SYM iajs-1811 64 78 1 1 NUM iajs-1811 64 79 0.5 0.5 NUM iajs-1811 64 80 ; ; PUNCT iajs-1811 64 81 1 1 NUM iajs-1811 64 82 x x SYM iajs-1811 64 83 1.5 1.5 NUM iajs-1811 64 84 2 2 NUM iajs-1811 64 85 x x SYM iajs-1811 64 86 0.5 0.5 NUM iajs-1811 64 87 ; ; PUNCT iajs-1811 64 88 1.5 1.5 NUM iajs-1811 64 89 x x SYM iajs-1811 64 90 2 2 NUM iajs-1811 64 91 0 0 NUM iajs-1811 64 92 ; ; PUNCT iajs-1811 64 93 otherwise otherwise ADV iajs-1811 64 94 μ μ PROPN iajs-1811 64 95 x x PROPN iajs-1811 64 96 ⎩ ⎩ NUM iajs-1811 64 97 ⎪ ⎪ NOUN iajs-1811 64 98 ⎨ ⎨ ADJ iajs-1811 64 99 ⎪ ⎪ NOUN iajs-1811 64 100 ⎧ ⎧ NOUN iajs-1811 64 101 x x PUNCT iajs-1811 64 102 0.25 0.25 NUM iajs-1811 64 103 0.25 0.25 NUM iajs-1811 64 104 ; ; PUNCT iajs-1811 64 105 0.25 0.25 NUM iajs-1811 64 106 x x SYM iajs-1811 64 107 0.5 0.5 NUM iajs-1811 64 108 0.75 0.75 NUM iajs-1811 64 109 x x SYM iajs-1811 64 110 0.25 0.25 NUM iajs-1811 64 111 ; ; PUNCT iajs-1811 64 112 0.5 0.5 NUM iajs-1811 64 113 x x SYM iajs-1811 64 114 0.75 0.75 NUM iajs-1811 64 115 0 0 NUM iajs-1811 64 116 ; ; PUNCT iajs-1811 64 117 otherwise otherwise ADV iajs-1811 64 118 μ μ NOUN iajs-1811 64 119 x x SYM iajs-1811 64 120 x x PROPN iajs-1811 64 121 1.5 1.5 NUM iajs-1811 64 122 0.5 0.5 NUM iajs-1811 64 123 ; ; PUNCT iajs-1811 64 124 1.5 1.5 NUM iajs-1811 64 125 x x SYM iajs-1811 64 126 2 2 NUM iajs-1811 64 127 3 3 NUM iajs-1811 64 128 x x SYM iajs-1811 64 129 ; ; PUNCT iajs-1811 64 130 2 2 NUM iajs-1811 64 131 x x SYM iajs-1811 64 132 3 3 NUM iajs-1811 64 133 0 0 NUM iajs-1811 64 134 ; ; PUNCT iajs-1811 64 135 otherwise otherwise ADV iajs-1811 64 136 μ μ PROPN iajs-1811 64 137 x x PROPN iajs-1811 64 138 ⎩ ⎩ NUM iajs-1811 64 139 ⎪ ⎪ NOUN iajs-1811 64 140 ⎨ ⎨ ADJ iajs-1811 64 141 ⎪ ⎪ NOUN iajs-1811 64 142 ⎧ ⎧ PROPN iajs-1811 64 143 x x PUNCT iajs-1811 64 144 0.5 0.5 NUM iajs-1811 64 145 0.25 0.25 NUM iajs-1811 64 146 ; ; PUNCT iajs-1811 64 147 0.5 0.5 NUM iajs-1811 64 148 x x SYM iajs-1811 64 149 0.75 0.75 NUM iajs-1811 64 150 1 1 NUM iajs-1811 64 151 x x SYM iajs-1811 64 152 0.25 0.25 NUM iajs-1811 64 153 ; ; PUNCT iajs-1811 64 154 0.75 0.75 NUM iajs-1811 64 155 x x SYM iajs-1811 64 156 1 1 NUM iajs-1811 64 157 0 0 NUM iajs-1811 64 158 ; ; PUNCT iajs-1811 64 159 otherwise otherwise ADV iajs-1811 64 160 μ μ NOUN iajs-1811 64 161 x x SYM iajs-1811 64 162 x x SYM iajs-1811 64 163 2 2 NUM iajs-1811 64 164 ; ; PUNCT iajs-1811 64 165 2 2 NUM iajs-1811 64 166 x x SYM iajs-1811 64 167 3 3 NUM iajs-1811 64 168 1 1 NUM iajs-1811 64 169 ; ; PUNCT iajs-1811 64 170 x x SYM iajs-1811 64 171 3 3 NUM iajs-1811 64 172 0 0 NUM iajs-1811 64 173 ; ; PUNCT iajs-1811 64 174 otherwise otherwise ADV iajs-1811 64 175 the the DET iajs-1811 64 176 initial initial ADJ iajs-1811 64 177 values value NOUN iajs-1811 64 178 required require VERB iajs-1811 64 179 for for ADP iajs-1811 64 180 proceeding proceed VERB iajs-1811 64 181 with with ADP iajs-1811 64 182 the the DET iajs-1811 64 183 expectation expectation NOUN iajs-1811 64 184 - - PUNCT iajs-1811 64 185 maximization maximization NOUN iajs-1811 64 186 , , PUNCT iajs-1811 64 187 newtonraphson newtonraphson ADJ iajs-1811 64 188 algorithms algorithm NOUN iajs-1811 64 189 and and CCONJ iajs-1811 64 190 moment moment NOUN iajs-1811 64 191 method method NOUN iajs-1811 64 192 chosen choose VERB iajs-1811 64 193 to to PART iajs-1811 64 194 be be AUX iajs-1811 64 195 the the DET iajs-1811 64 196 symmetrical symmetrical ADJ iajs-1811 64 197 rank rank NOUN iajs-1811 64 198 regression regression NOUN iajs-1811 64 199 estimators estimator NOUN iajs-1811 64 200 and and CCONJ iajs-1811 64 201 the the DET iajs-1811 64 202 iterative iterative NOUN iajs-1811 64 203 process process NOUN iajs-1811 64 204 stops stop VERB iajs-1811 64 205 when when SCONJ iajs-1811 64 206 the the DET iajs-1811 64 207 absolute absolute ADJ iajs-1811 64 208 difference difference NOUN iajs-1811 64 209 between between ADP iajs-1811 64 210 two two NUM iajs-1811 64 211 successive successive ADJ iajs-1811 64 212 iterations iteration NOUN iajs-1811 64 213 becomes become VERB iajs-1811 64 214 less less ADJ iajs-1811 64 215 than than ADP iajs-1811 64 216 ε ε PROPN iajs-1811 64 217 0.0001 0.0001 NUM iajs-1811 64 218 . . PUNCT iajs-1811 65 1 the the DET iajs-1811 65 2 comparisons comparison NOUN iajs-1811 65 3 between between ADP iajs-1811 65 4 parameter parameter NOUN iajs-1811 65 5 estimates estimate NOUN iajs-1811 65 6 were be AUX iajs-1811 65 7 based base VERB iajs-1811 65 8 on on ADP iajs-1811 65 9 values value NOUN iajs-1811 65 10 from from ADP iajs-1811 65 11 mean mean ADJ iajs-1811 65 12 square square ADJ iajs-1811 65 13 error error NOUN iajs-1811 65 14 ( ( PUNCT iajs-1811 65 15 mse mse NOUN iajs-1811 65 16 ) ) PUNCT iajs-1811 65 17 while while SCONJ iajs-1811 65 18 it it PRON iajs-1811 65 19 were be AUX iajs-1811 65 20 based base VERB iajs-1811 65 21 on on ADP iajs-1811 65 22 values value NOUN iajs-1811 65 23 from from ADP iajs-1811 65 24 integrated integrate VERB iajs-1811 65 25 mean mean ADJ iajs-1811 65 26 square square NOUN iajs-1811 65 27 error error NOUN iajs-1811 65 28 ( ( PUNCT iajs-1811 65 29 imse imse NOUN iajs-1811 65 30 ) ) PUNCT iajs-1811 65 31 for for ADP iajs-1811 65 32 the the DET iajs-1811 65 33 estimates estimate NOUN iajs-1811 65 34 of of ADP iajs-1811 65 35 the the DET iajs-1811 65 36 reliability reliability NOUN iajs-1811 65 37 function function NOUN iajs-1811 66 1 [ [ X iajs-1811 66 2 1 1 NUM iajs-1811 66 3 ] ] PUNCT iajs-1811 66 4 , , PUNCT iajs-1811 66 5 where where SCONJ iajs-1811 66 6 : : PUNCT iajs-1811 66 7 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-1811 66 8 𝛽 𝛽 PROPN iajs-1811 66 9 ∑ ∑ ADP iajs-1811 66 10 𝛽 𝛽 PROPN iajs-1811 66 11 𝛽𝐿 𝛽𝐿 PROPN iajs-1811 66 12 𝐿 𝐿 PROPN iajs-1811 66 13 … … SYM iajs-1811 66 14 28 28 NUM iajs-1811 66 15 ihsciconf ihsciconf NOUN iajs-1811 66 16 2017 2017 NUM iajs-1811 66 17 special special ADJ iajs-1811 66 18 issue issue NOUN iajs-1811 66 19 ibn ibn PROPN iajs-1811 66 20 al al PROPN iajs-1811 66 21 - - PUNCT iajs-1811 66 22 haitham haitham PROPN iajs-1811 66 23 journal journal PROPN iajs-1811 66 24 for for ADP iajs-1811 66 25 pure pure ADJ iajs-1811 66 26 and and CCONJ iajs-1811 66 27 applied apply VERB iajs-1811 66 28 science science NOUN iajs-1811 66 29 https://doi.org/ https://doi.org/ NOUN iajs-1811 66 30 10.30526/2017.ihsciconf.1811 10.30526/2017.ihsciconf.1811 NUM iajs-1811 66 31 for for ADP iajs-1811 66 32 more more ADJ iajs-1811 66 33 information information NOUN iajs-1811 66 34 about about ADP iajs-1811 66 35 the the DET iajs-1811 66 36 conference conference NOUN iajs-1811 66 37 please please INTJ iajs-1811 66 38 visit visit VERB iajs-1811 66 39 the the DET iajs-1811 66 40 websites website NOUN iajs-1811 66 41 : : PUNCT iajs-1811 66 42 http://www.ihsciconf.org/conf/ http://www.ihsciconf.org/conf/ VERB iajs-1811 66 43         SPACE iajs-1811 66 44 www.ihsciconf.org www.ihsciconf.org X iajs-1811 66 45       SPACE iajs-1811 66 46 mathematics|386 mathematics|386 ADJ iajs-1811 66 47         SPACE iajs-1811 66 48 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-1811 66 49 𝜆 𝜆 ADP iajs-1811 66 50 ∑ ∑ PROPN iajs-1811 66 51 𝜆 𝜆 DET iajs-1811 66 52 𝜆𝐿 𝜆𝐿 PROPN iajs-1811 66 53 𝐿 𝐿 PROPN iajs-1811 66 54 … … PUNCT iajs-1811 66 55 29 29 NUM iajs-1811 66 56 𝐼𝑀𝑆𝐸 𝐼𝑀𝑆𝐸 PROPN iajs-1811 66 57 𝑅 𝑅 PROPN iajs-1811 66 58 𝑡 𝑡 PROPN iajs-1811 66 59 1 1 NUM iajs-1811 66 60 𝐿 𝐿 PROPN iajs-1811 66 61 1 1 NUM iajs-1811 66 62 𝑛 𝑛 PRON iajs-1811 66 63 𝑅 𝑅 PROPN iajs-1811 66 64 𝑡 𝑡 PROPN iajs-1811 66 65 𝑅 𝑅 PROPN iajs-1811 66 66 𝑡 𝑡 PROPN iajs-1811 66 67 … … PUNCT iajs-1811 66 68 30 30 NUM iajs-1811 66 69 𝛽 𝛽 NOUN iajs-1811 66 70 , , PUNCT iajs-1811 66 71 𝜆 𝜆 X iajs-1811 66 72 : : PUNCT iajs-1811 66 73 is be AUX iajs-1811 66 74 the the DET iajs-1811 66 75 estimate estimate NOUN iajs-1811 66 76 of of ADP iajs-1811 66 77 𝛽 𝛽 NOUN iajs-1811 66 78 and and CCONJ iajs-1811 66 79 𝜆 𝜆 ADV iajs-1811 66 80 respectively respectively ADV iajs-1811 66 81 at at ADP iajs-1811 66 82 the the DET iajs-1811 66 83 j j PROPN iajs-1811 66 84 th th X iajs-1811 66 85 replicate replicate NOUN iajs-1811 66 86 ( ( PUNCT iajs-1811 66 87 run run NOUN iajs-1811 66 88 ) ) PUNCT iajs-1811 66 89 . . PUNCT iajs-1811 67 1 𝐿 𝐿 NOUN iajs-1811 67 2 : : PUNCT iajs-1811 67 3 is be AUX iajs-1811 67 4 the the DET iajs-1811 67 5 number number NOUN iajs-1811 67 6 of of ADP iajs-1811 67 7 sample sample NOUN iajs-1811 67 8 replicated replicate VERB iajs-1811 67 9 . . PUNCT iajs-1811 68 1 𝑛 𝑛 PROPN iajs-1811 68 2 : : PUNCT iajs-1811 68 3 is be AUX iajs-1811 68 4 the the DET iajs-1811 68 5 number number NOUN iajs-1811 68 6 of of ADP iajs-1811 68 7 times time NOUN iajs-1811 68 8 chosen choose VERB iajs-1811 68 9 to to PART iajs-1811 68 10 be be AUX iajs-1811 68 11 ( ( PUNCT iajs-1811 68 12 4 4 NUM iajs-1811 68 13 ) ) PUNCT iajs-1811 68 14 where where SCONJ iajs-1811 68 15 𝑡 𝑡 PROPN iajs-1811 68 16 1,2,3,4 1,2,3,4 NUM iajs-1811 68 17 . . PUNCT iajs-1811 69 1 𝑅 𝑅 NOUN iajs-1811 69 2 𝑡 𝑡 PROPN iajs-1811 69 3 : : PUNCT iajs-1811 69 4 is be AUX iajs-1811 69 5 the the DET iajs-1811 69 6 estimates estimate NOUN iajs-1811 69 7 of of ADP iajs-1811 69 8 𝑅 𝑅 PROPN iajs-1811 69 9 𝑡 𝑡 PROPN iajs-1811 69 10 at at ADP iajs-1811 69 11 the the DET iajs-1811 69 12 𝑗 𝑗 PROPN iajs-1811 69 13 replicate replicate NOUN iajs-1811 69 14 ( ( PUNCT iajs-1811 69 15 run run NOUN iajs-1811 69 16 ) ) PUNCT iajs-1811 69 17 and and CCONJ iajs-1811 69 18 𝑖 𝑖 DET iajs-1811 69 19 time time NOUN iajs-1811 69 20 . . PUNCT iajs-1811 70 1 2 2 X iajs-1811 70 2 . . X iajs-1811 70 3 conclusions conclusion NOUN iajs-1811 70 4 and and CCONJ iajs-1811 70 5 recommendations recommendation NOUN iajs-1811 70 6 approximate approximate VERB iajs-1811 70 7 maximum maximum ADJ iajs-1811 70 8 likelihood likelihood NOUN iajs-1811 70 9 and and CCONJ iajs-1811 70 10 moment moment NOUN iajs-1811 70 11 estimations estimation NOUN iajs-1811 70 12 as as SCONJ iajs-1811 70 13 non non ADJ iajs-1811 70 14 - - ADJ iajs-1811 70 15 bayesian bayesian ADJ iajs-1811 70 16 estimations estimation NOUN iajs-1811 70 17 have have AUX iajs-1811 70 18 been be AUX iajs-1811 70 19 used use VERB iajs-1811 70 20 to to PART iajs-1811 70 21 estimate estimate VERB iajs-1811 70 22 the the DET iajs-1811 70 23 parameters parameter NOUN iajs-1811 70 24 and and CCONJ iajs-1811 70 25 reliability reliability NOUN iajs-1811 70 26 function function NOUN iajs-1811 70 27 of of ADP iajs-1811 70 28 inverse inverse ADJ iajs-1811 70 29 weibull weibull NOUN iajs-1811 70 30 distribution distribution NOUN iajs-1811 70 31 according accord VERB iajs-1811 70 32 to to ADP iajs-1811 70 33 fuzzy fuzzy ADJ iajs-1811 70 34 data datum NOUN iajs-1811 70 35 . . PUNCT iajs-1811 71 1 the the DET iajs-1811 71 2 maximum maximum ADJ iajs-1811 71 3 likelihood likelihood NOUN iajs-1811 71 4 estimators estimator NOUN iajs-1811 71 5 have have AUX iajs-1811 71 6 been be AUX iajs-1811 71 7 derived derive VERB iajs-1811 71 8 numerically numerically ADV iajs-1811 71 9 based base VERB iajs-1811 71 10 on on ADP iajs-1811 71 11 two two NUM iajs-1811 71 12 iterative iterative NOUN iajs-1811 71 13 techniques technique NOUN iajs-1811 71 14 namely namely ADV iajs-1811 71 15 “ " PUNCT iajs-1811 71 16 newton newton PROPN iajs-1811 71 17 - - PUNCT iajs-1811 71 18 raphson raphson NOUN iajs-1811 71 19 ” " PUNCT iajs-1811 71 20 and and CCONJ iajs-1811 71 21 the the DET iajs-1811 71 22 “ " PUNCT iajs-1811 71 23 expectation expectation NOUN iajs-1811 71 24 - - PUNCT iajs-1811 71 25 maximization maximization NOUN iajs-1811 71 26 ” " PUNCT iajs-1811 71 27 techniques technique NOUN iajs-1811 71 28 . . 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- PUNCT iajs-1811 79 115 nr nr NOUN iajs-1811 79 116 β β NOUN iajs-1811 79 117 2.1 2.1 NUM iajs-1811 79 118 , , PUNCT iajs-1811 79 119 λ λ PROPN iajs-1811 79 120 1 1 NUM iajs-1811 79 121 20 20 NUM iajs-1811 79 122 1.0234089 1.0234089 NUM iajs-1811 79 123 0.4793374 0.4793374 NUM iajs-1811 79 124 0.4697234 0.4697234 NUM iajs-1811 79 125 ml ml NOUN iajs-1811 79 126 - - PUNCT iajs-1811 79 127 nr nr NOUN iajs-1811 79 128 30 30 NUM iajs-1811 79 129 0.8987515 0.8987515 NUM iajs-1811 79 130 0.3765942 0.3765942 NUM iajs-1811 79 131 0.3700855 0.3700855 NUM iajs-1811 79 132 ml ml NOUN iajs-1811 79 133 - - PUNCT iajs-1811 79 134 nr nr PRON iajs-1811 79 135 90 90 NUM iajs-1811 79 136 0.8584988 0.8584988 NUM iajs-1811 79 137 0.1780456 0.1780456 NUM iajs-1811 79 138 0.1764240 0.1764240 NUM iajs-1811 79 139 ml ml NOUN iajs-1811 79 140 - - PUNCT iajs-1811 79 141 nr nr NOUN iajs-1811 79 142 β β NOUN iajs-1811 79 143 3 3 NUM iajs-1811 79 144 , , PUNCT iajs-1811 79 145 λ λ PROPN iajs-1811 79 146 1 1 NUM iajs-1811 79 147 20 20 NUM iajs-1811 79 148 0.8207644 0.8207644 NUM iajs-1811 79 149 0.7696865 0.7696865 NUM iajs-1811 79 150 0.7355563 0.7355563 NUM iajs-1811 79 151 ml ml NOUN iajs-1811 79 152 - - PUNCT iajs-1811 79 153 nr nr PRON iajs-1811 79 154 30 30 NUM iajs-1811 79 155 0.6615921 0.6615921 NUM iajs-1811 79 156 0.3721112 0.3721112 NUM iajs-1811 79 157 0.3652719 0.3652719 NUM iajs-1811 79 158 ml ml NOUN iajs-1811 79 159 - - PUNCT iajs-1811 79 160 nr nr PRON iajs-1811 79 161 90 90 NUM iajs-1811 79 162 0.5914806 0.5914806 NUM iajs-1811 79 163 0.1426038 0.1426038 NUM iajs-1811 79 164 0.1412609 0.1412609 NUM iajs-1811 79 165 ml ml NOUN iajs-1811 79 166 - - PUNCT iajs-1811 79 167 nr nr NOUN iajs-1811 79 168 β β NOUN iajs-1811 79 169 2.1 2.1 NUM iajs-1811 79 170 , , PUNCT iajs-1811 79 171 λ λ PROPN iajs-1811 79 172 3 3 NUM iajs-1811 79 173 20 20 NUM iajs-1811 79 174 2.4264343 2.4264343 NUM iajs-1811 79 175 1.4173415 1.4173415 NUM iajs-1811 79 176 1.3050008 1.3050008 NUM iajs-1811 79 177 ml ml NOUN iajs-1811 79 178 - - PUNCT iajs-1811 79 179 nr nr NOUN iajs-1811 79 180 30 30 NUM iajs-1811 79 181 2.1658246 2.1658246 NUM iajs-1811 79 182 0.9206690 0.9206690 NUM iajs-1811 79 183 0.8674874 0.8674874 NUM iajs-1811 79 184 ml ml NOUN iajs-1811 79 185 - - PUNCT iajs-1811 79 186 nr nr PRON iajs-1811 79 187 90 90 NUM iajs-1811 79 188 2.1064719 2.1064719 NUM iajs-1811 79 189 0.5787366 0.5787366 NUM iajs-1811 79 190 0.5542025 0.5542025 NUM iajs-1811 79 191 ml ml NOUN iajs-1811 79 192 - - PUNCT iajs-1811 79 193 nr nr NOUN iajs-1811 79 194 β β NOUN iajs-1811 79 195 3 3 NUM iajs-1811 79 196 , , PUNCT iajs-1811 79 197 λ λ PROPN iajs-1811 79 198 3 3 NUM iajs-1811 79 199 20 20 NUM iajs-1811 79 200 1.2356461 1.2356461 NUM iajs-1811 79 201 0.8079456 0.8079456 NUM iajs-1811 79 202 0.8175703 0.8175703 NUM iajs-1811 79 203 ml ml NOUN iajs-1811 79 204 - - PUNCT iajs-1811 79 205 em em PRON iajs-1811 79 206 30 30 NUM iajs-1811 79 207 1.2346853 1.2346853 NUM iajs-1811 79 208 0.7552212 0.7552212 NUM iajs-1811 79 209 0.7170664 0.7170664 NUM iajs-1811 79 210 ml ml VERB iajs-1811 79 211 - - PUNCT iajs-1811 79 212 nr nr NOUN iajs-1811 79 213 90 90 NUM iajs-1811 79 214 1.1146329 1.1146329 NUM iajs-1811 79 215 0.2692730 0.2692730 NUM iajs-1811 79 216 0.2583540 0.2583540 NUM iajs-1811 79 217 ml ml NOUN iajs-1811 79 218 - 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