id sid tid token lemma pos iajs-2006 1 1 microsoft microsoft PROPN iajs-2006 1 2 word word NOUN iajs-2006 1 3 135 135 NUM iajs-2006 1 4 - - SYM iajs-2006 1 5 142 142 NUM iajs-2006 1 6 mathematics mathematic NOUN iajs-2006 1 7 | | ADV iajs-2006 1 8 135 135 NUM iajs-2006 1 9 ibn ibn PROPN iajs-2006 1 10 al al PROPN iajs-2006 1 11 - - PUNCT iajs-2006 1 12 haitham haitham PROPN iajs-2006 1 13 jour jour X iajs-2006 1 14 . . PROPN iajs-2006 2 1 for for ADP iajs-2006 2 2 pure pure ADJ iajs-2006 2 3 & & CCONJ iajs-2006 2 4 appl appl PROPN iajs-2006 2 5 . . PUNCT iajs-2006 3 1 sci sci PROPN iajs-2006 3 2 . . PROPN iajs-2006 3 3 ihjpas ihjpa VERB iajs-2006 3 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 3 5 vol vol NOUN iajs-2006 3 6 . . PROPN iajs-2006 3 7 31 31 NUM iajs-2006 3 8 ( ( PUNCT iajs-2006 3 9 3 3 NUM iajs-2006 3 10 ) ) PUNCT iajs-2006 3 11 2018 2018 NUM iajs-2006 3 12 the the DET iajs-2006 3 13 comparison comparison NOUN iajs-2006 3 14 between between ADP iajs-2006 3 15 standard standard ADJ iajs-2006 3 16 bayes bayes NOUN iajs-2006 3 17 estimators estimator NOUN iajs-2006 3 18 of of ADP iajs-2006 3 19 the the DET iajs-2006 3 20 reliability reliability NOUN iajs-2006 3 21 function function NOUN iajs-2006 3 22 of of ADP iajs-2006 3 23 exponential exponential ADJ iajs-2006 3 24 distribution distribution NOUN iajs-2006 3 25 mohammed mohammed PROPN iajs-2006 3 26 jamel jamel PROPN iajs-2006 3 27 ali ali PROPN iajs-2006 3 28 moham198999@gmail.com moham198999@gmail.com PROPN iajs-2006 3 29 hazim hazim PROPN iajs-2006 3 30 mansoor mansoor PROPN iajs-2006 3 31 gorgees gorgees PROPN iajs-2006 3 32 hazim5656@yahoo.com hazim5656@yahoo.com PUNCT iajs-2006 4 1 adel adel PROPN iajs-2006 4 2 abdul abdul PROPN iajs-2006 4 3 kadhim kadhim PROPN iajs-2006 4 4 hussein hussein PROPN iajs-2006 4 5 adilabed57@yahoo.com adilabed57@yahoo.com PROPN iajs-2006 4 6 department department PROPN iajs-2006 4 7 , , PUNCT iajs-2006 4 8 of of ADP iajs-2006 4 9 mathematics mathematic NOUN iajs-2006 4 10 , , PUNCT iajs-2006 4 11 college college NOUN iajs-2006 4 12 of of ADP iajs-2006 4 13 education education NOUN iajs-2006 4 14 for for ADP iajs-2006 4 15 pure pure ADJ iajs-2006 4 16 science science NOUN iajs-2006 4 17 ibn ibn PROPN iajs-2006 4 18 al al PROPN iajs-2006 4 19 - - PUNCT iajs-2006 4 20 haitham haitham PROPN iajs-2006 4 21 , , PUNCT iajs-2006 4 22 university university PROPN iajs-2006 4 23 of of ADP iajs-2006 4 24 baghdad baghdad PROPN iajs-2006 4 25 , , PUNCT iajs-2006 4 26 iraq iraq PROPN iajs-2006 4 27 , , PUNCT iajs-2006 4 28 baghdad baghdad PROPN iajs-2006 4 29 article article NOUN iajs-2006 4 30 history history NOUN iajs-2006 4 31 : : PUNCT iajs-2006 4 32 received receive VERB iajs-2006 4 33 10 10 NUM iajs-2006 4 34 june june PROPN iajs-2006 4 35 2018 2018 NUM iajs-2006 4 36 , , PUNCT iajs-2006 4 37 accepted accept VERB iajs-2006 4 38 15 15 NUM iajs-2006 4 39 august august PROPN iajs-2006 4 40 2018 2018 NUM iajs-2006 4 41 , , PUNCT iajs-2006 4 42 published publish VERB iajs-2006 4 43 december december PROPN iajs-2006 4 44 2018 2018 NUM iajs-2006 4 45 " " PUNCT iajs-2006 4 46 " " PUNCT iajs-2006 4 47 abstract abstract ADV iajs-2006 4 48 in in ADP iajs-2006 4 49 this this DET iajs-2006 4 50 paper paper NOUN iajs-2006 4 51 , , PUNCT iajs-2006 4 52 a a DET iajs-2006 4 53 monte monte PROPN iajs-2006 4 54 carlo carlo PROPN iajs-2006 4 55 simulation simulation NOUN iajs-2006 4 56 technique technique NOUN iajs-2006 4 57 is be AUX iajs-2006 4 58 used use VERB iajs-2006 4 59 to to PART iajs-2006 4 60 compare compare VERB iajs-2006 4 61 the the DET iajs-2006 4 62 performance performance NOUN iajs-2006 4 63 of of ADP iajs-2006 4 64 the the DET iajs-2006 4 65 standard standard ADJ iajs-2006 4 66 bayes bayes NOUN iajs-2006 4 67 estimators estimator NOUN iajs-2006 4 68 of of ADP iajs-2006 4 69 the the DET iajs-2006 4 70 reliability reliability NOUN iajs-2006 4 71 function function NOUN iajs-2006 4 72 of of ADP iajs-2006 4 73 the the DET iajs-2006 4 74 one one NUM iajs-2006 4 75 parameter parameter NOUN iajs-2006 4 76 exponential exponential ADJ iajs-2006 4 77 distribution distribution NOUN iajs-2006 5 1 .three .three NUM iajs-2006 5 2 types type NOUN iajs-2006 5 3 of of ADP iajs-2006 5 4 loss loss NOUN iajs-2006 5 5 functions function NOUN iajs-2006 5 6 are be AUX iajs-2006 5 7 adopted adopt VERB iajs-2006 5 8 , , PUNCT iajs-2006 5 9 namely namely ADV iajs-2006 5 10 , , PUNCT iajs-2006 5 11 squared square VERB iajs-2006 5 12 error error NOUN iajs-2006 5 13 loss loss NOUN iajs-2006 5 14 function function NOUN iajs-2006 5 15 ( ( PUNCT iajs-2006 5 16 self self NOUN iajs-2006 5 17 ) ) PUNCT iajs-2006 5 18 , , PUNCT iajs-2006 5 19 precautionary precautionary ADJ iajs-2006 5 20 error error NOUN iajs-2006 5 21 loss loss NOUN iajs-2006 5 22 function function NOUN iajs-2006 5 23 ( ( PUNCT iajs-2006 5 24 pelf pelf PRON iajs-2006 5 25 ) ) PUNCT iajs-2006 5 26 and and CCONJ iajs-2006 5 27 linear linear ADJ iajs-2006 5 28 exponential exponential ADJ iajs-2006 5 29 error error NOUN iajs-2006 5 30 loss loss NOUN iajs-2006 5 31 function function NOUN iajs-2006 5 32 ( ( PUNCT iajs-2006 5 33 linex linex ADV iajs-2006 5 34 ) ) PUNCT iajs-2006 5 35 with with ADP iajs-2006 5 36 informative informative ADJ iajs-2006 5 37 and and CCONJ iajs-2006 5 38 noninformative noninformative ADJ iajs-2006 5 39 prior prior ADV iajs-2006 5 40 .the .the PRON iajs-2006 5 41 criterion criterion NOUN iajs-2006 5 42 integrated integrate VERB iajs-2006 5 43 mean mean ADJ iajs-2006 5 44 square square NOUN iajs-2006 5 45 error error NOUN iajs-2006 5 46 ( ( PUNCT iajs-2006 5 47 imse imse NOUN iajs-2006 5 48 ) ) PUNCT iajs-2006 5 49 is be AUX iajs-2006 5 50 employed employ VERB iajs-2006 5 51 to to PART iajs-2006 5 52 assess assess VERB iajs-2006 5 53 the the DET iajs-2006 5 54 performance performance NOUN iajs-2006 5 55 of of ADP iajs-2006 5 56 such such ADJ iajs-2006 5 57 estimators estimator NOUN iajs-2006 5 58 . . PUNCT iajs-2006 6 1 key key ADJ iajs-2006 6 2 words word NOUN iajs-2006 6 3 : : PUNCT iajs-2006 6 4 standard standard ADJ iajs-2006 6 5 bayes bayes PROPN iajs-2006 6 6 estimator estimator NOUN iajs-2006 6 7 , , PUNCT iajs-2006 6 8 loss loss NOUN iajs-2006 6 9 function function NOUN iajs-2006 6 10 , , PUNCT iajs-2006 6 11 imse imse NOUN iajs-2006 6 12 1 1 NUM iajs-2006 6 13 . . PUNCT iajs-2006 6 14 introduction introduction NOUN iajs-2006 6 15 the the DET iajs-2006 6 16 reliability reliability NOUN iajs-2006 6 17 theory theory NOUN iajs-2006 6 18 is be AUX iajs-2006 6 19 associated associate VERB iajs-2006 6 20 with with ADP iajs-2006 6 21 random random ADJ iajs-2006 6 22 occurrence occurrence NOUN iajs-2006 6 23 of of ADP iajs-2006 6 24 undesirable undesirable ADJ iajs-2006 6 25 events event NOUN iajs-2006 6 26 or or CCONJ iajs-2006 6 27 failure failure NOUN iajs-2006 6 28 during during ADP iajs-2006 6 29 the the DET iajs-2006 6 30 life life NOUN iajs-2006 6 31 of of ADP iajs-2006 6 32 a a DET iajs-2006 6 33 physical physical ADJ iajs-2006 6 34 or or CCONJ iajs-2006 6 35 biological biological ADJ iajs-2006 6 36 system system NOUN iajs-2006 7 1 [ [ X iajs-2006 7 2 1 1 NUM iajs-2006 7 3 ] ] PUNCT iajs-2006 7 4 . . PUNCT iajs-2006 8 1 reliability reliability NOUN iajs-2006 8 2 is be AUX iajs-2006 8 3 a a DET iajs-2006 8 4 substantial substantial ADJ iajs-2006 8 5 feature feature NOUN iajs-2006 8 6 of of ADP iajs-2006 8 7 a a DET iajs-2006 8 8 system system NOUN iajs-2006 8 9 . . PUNCT iajs-2006 9 1 basic basic ADJ iajs-2006 9 2 concepts concept NOUN iajs-2006 9 3 related relate VERB iajs-2006 9 4 with with ADP iajs-2006 9 5 reliability reliability NOUN iajs-2006 9 6 has have AUX iajs-2006 9 7 been be AUX iajs-2006 9 8 recognized recognize VERB iajs-2006 9 9 for for ADP iajs-2006 9 10 a a DET iajs-2006 9 11 number number NOUN iajs-2006 9 12 of of ADP iajs-2006 9 13 years year NOUN iajs-2006 9 14 , , PUNCT iajs-2006 9 15 however however ADV iajs-2006 9 16 , , PUNCT iajs-2006 9 17 it it PRON iajs-2006 9 18 has have AUX iajs-2006 9 19 got get VERB iajs-2006 9 20 greatest great ADJ iajs-2006 9 21 importance importance NOUN iajs-2006 9 22 during during ADP iajs-2006 9 23 the the DET iajs-2006 9 24 past past ADJ iajs-2006 9 25 decennium decennium NOUN iajs-2006 9 26 as as ADP iajs-2006 9 27 a a DET iajs-2006 9 28 consequence consequence NOUN iajs-2006 9 29 of of ADP iajs-2006 9 30 the the DET iajs-2006 9 31 use use NOUN iajs-2006 9 32 of of ADP iajs-2006 9 33 highly highly ADV iajs-2006 9 34 complex complex ADJ iajs-2006 9 35 systems system NOUN iajs-2006 9 36 . . PUNCT iajs-2006 10 1 in in ADP iajs-2006 10 2 reliability reliability NOUN iajs-2006 10 3 theory theory NOUN iajs-2006 10 4 , , PUNCT iajs-2006 10 5 the the DET iajs-2006 10 6 exponential exponential ADJ iajs-2006 10 7 distribution distribution NOUN iajs-2006 10 8 has have VERB iajs-2006 10 9 a a DET iajs-2006 10 10 distinctive distinctive ADJ iajs-2006 10 11 role role NOUN iajs-2006 10 12 in in ADP iajs-2006 10 13 life life NOUN iajs-2006 10 14 testing testing NOUN iajs-2006 10 15 experiments experiment NOUN iajs-2006 10 16 . . PUNCT iajs-2006 11 1 historically historically ADV iajs-2006 11 2 , , PUNCT iajs-2006 11 3 it it PRON iajs-2006 11 4 was be AUX iajs-2006 11 5 the the DET iajs-2006 11 6 first first ADJ iajs-2006 11 7 life life NOUN iajs-2006 11 8 time time NOUN iajs-2006 11 9 model model NOUN iajs-2006 11 10 for for ADP iajs-2006 11 11 which which PRON iajs-2006 11 12 statistical statistical ADJ iajs-2006 11 13 procedures procedure NOUN iajs-2006 11 14 were be AUX iajs-2006 11 15 widely widely ADV iajs-2006 11 16 developed develop VERB iajs-2006 11 17 . . PUNCT iajs-2006 12 1 many many ADJ iajs-2006 12 2 researchers researcher NOUN iajs-2006 12 3 gave give VERB iajs-2006 12 4 numerous numerous ADJ iajs-2006 12 5 results result NOUN iajs-2006 12 6 and and CCONJ iajs-2006 12 7 generalized generalize VERB iajs-2006 12 8 the the DET iajs-2006 12 9 exponential exponential ADJ iajs-2006 12 10 distribution distribution NOUN iajs-2006 12 11 as as ADP iajs-2006 12 12 a a DET iajs-2006 12 13 life life NOUN iajs-2006 12 14 time time NOUN iajs-2006 12 15 distribution distribution NOUN iajs-2006 12 16 , , PUNCT iajs-2006 12 17 particularly particularly ADV iajs-2006 12 18 , , PUNCT iajs-2006 12 19 in in ADP iajs-2006 12 20 the the DET iajs-2006 12 21 field field NOUN iajs-2006 12 22 of of ADP iajs-2006 12 23 industrial industrial ADJ iajs-2006 12 24 life life NOUN iajs-2006 12 25 testing testing NOUN iajs-2006 12 26 . . PUNCT iajs-2006 13 1 the the DET iajs-2006 13 2 exponential exponential ADJ iajs-2006 13 3 distribution distribution NOUN iajs-2006 13 4 is be AUX iajs-2006 13 5 desirable desirable ADJ iajs-2006 13 6 because because SCONJ iajs-2006 13 7 of of ADP iajs-2006 13 8 its its PRON iajs-2006 13 9 simplicity simplicity NOUN iajs-2006 13 10 and and CCONJ iajs-2006 13 11 its its PRON iajs-2006 13 12 own own ADJ iajs-2006 13 13 features feature NOUN iajs-2006 13 14 such such ADJ iajs-2006 13 15 as as ADP iajs-2006 13 16 lacks lack NOUN iajs-2006 13 17 memory memory NOUN iajs-2006 13 18 and and CCONJ iajs-2006 13 19 self self NOUN iajs-2006 13 20 - - PUNCT iajs-2006 13 21 producing produce VERB iajs-2006 13 22 property property NOUN iajs-2006 13 23 . . PUNCT iajs-2006 14 1 the the DET iajs-2006 14 2 probability probability NOUN iajs-2006 14 3 density density NOUN iajs-2006 14 4 , , PUNCT iajs-2006 14 5 cumulative cumulative ADJ iajs-2006 14 6 distribution distribution NOUN iajs-2006 14 7 and and CCONJ iajs-2006 14 8 reliability reliability NOUN iajs-2006 14 9 functions function NOUN iajs-2006 14 10 of of ADP iajs-2006 14 11 one one NUM iajs-2006 14 12 parameter parameter NOUN iajs-2006 14 13 exponential exponential ADJ iajs-2006 14 14 distribution distribution NOUN iajs-2006 14 15 are be AUX iajs-2006 14 16 respectively respectively ADV iajs-2006 14 17 defined define VERB iajs-2006 14 18 as as ADP iajs-2006 14 19 [ [ X iajs-2006 14 20 2 2 NUM iajs-2006 14 21 ] ] PUNCT iajs-2006 14 22 : : PUNCT iajs-2006 14 23 𝑓 𝑓 DET iajs-2006 14 24 𝑑 𝑑 NOUN iajs-2006 14 25 , , PUNCT iajs-2006 14 26 Ι΅ Ι΅ NOUN iajs-2006 14 27 ɡ𝑒 ɡ𝑒 PROPN iajs-2006 14 28 Ι΅ Ι΅ SYM iajs-2006 14 29 , , PUNCT iajs-2006 14 30 𝑑 𝑑 PROPN iajs-2006 14 31 , , PUNCT iajs-2006 14 32 Ι΅ Ι΅ NOUN iajs-2006 14 33 0 0 NUM iajs-2006 14 34 1 1 NUM iajs-2006 14 35 the the DET iajs-2006 14 36 cumulative cumulative ADJ iajs-2006 14 37 distribution distribution NOUN iajs-2006 14 38 function function NOUN iajs-2006 14 39 is be AUX iajs-2006 14 40 given give VERB iajs-2006 14 41 by by ADP iajs-2006 14 42 f f PROPN iajs-2006 14 43 t t PROPN iajs-2006 14 44 pr pr NOUN iajs-2006 14 45 t t PROPN iajs-2006 14 46 t t PROPN iajs-2006 14 47 1 1 NUM iajs-2006 14 48 e e NOUN iajs-2006 14 49 Ι΅ Ι΅ SYM iajs-2006 14 50 2 2 NUM iajs-2006 14 51 r r NOUN iajs-2006 14 52 t t NOUN iajs-2006 14 53 1 1 NUM iajs-2006 14 54 f f NOUN iajs-2006 14 55 t t X iajs-2006 14 56 e e X iajs-2006 14 57 Ι΅ Ι΅ SYM iajs-2006 14 58 3 3 NUM iajs-2006 14 59 the the DET iajs-2006 14 60 one one NUM iajs-2006 14 61 parameter parameter NOUN iajs-2006 14 62 exponential exponential ADJ iajs-2006 14 63 distribution distribution NOUN iajs-2006 14 64 is be AUX iajs-2006 14 65 a a DET iajs-2006 14 66 member member NOUN iajs-2006 14 67 of of ADP iajs-2006 14 68 exponential exponential ADJ iajs-2006 14 69 class class NOUN iajs-2006 14 70 of of ADP iajs-2006 14 71 probability probability NOUN iajs-2006 14 72 density density NOUN iajs-2006 14 73 functions function NOUN iajs-2006 14 74 which which PRON iajs-2006 14 75 has have VERB iajs-2006 14 76 the the DET iajs-2006 14 77 general general ADJ iajs-2006 14 78 form form NOUN iajs-2006 15 1 [ [ X iajs-2006 15 2 3 3 X iajs-2006 15 3 ] ] X iajs-2006 15 4 f f PROPN iajs-2006 15 5 t t PROPN iajs-2006 15 6 , , PUNCT iajs-2006 15 7 Ι΅ Ι΅ NUM iajs-2006 15 8 exp exp NOUN iajs-2006 15 9 p p NOUN iajs-2006 15 10 Ι΅ Ι΅ PROPN iajs-2006 15 11 k k PROPN iajs-2006 15 12 t t PROPN iajs-2006 15 13 s s PROPN iajs-2006 15 14 t t PROPN iajs-2006 15 15 q q PROPN iajs-2006 15 16 Ι΅ Ι΅ SYM iajs-2006 15 17 4 4 NUM iajs-2006 15 18 then then ADV iajs-2006 15 19 the the DET iajs-2006 15 20 exponential exponential ADJ iajs-2006 15 21 distribution distribution NOUN iajs-2006 15 22 the the DET iajs-2006 15 23 p.d.f p.d.f NOUN iajs-2006 15 24 . . PUNCT iajs-2006 16 1 can can AUX iajs-2006 16 2 be be AUX iajs-2006 16 3 written write VERB iajs-2006 16 4 as as ADP iajs-2006 16 5 mathematics mathematic NOUN iajs-2006 16 6 | | ADV iajs-2006 16 7 136 136 NUM iajs-2006 16 8 ibn ibn PROPN iajs-2006 16 9 al al PROPN iajs-2006 16 10 - - PUNCT iajs-2006 16 11 haitham haitham PROPN iajs-2006 16 12 jour jour X iajs-2006 16 13 . . PROPN iajs-2006 17 1 for for ADP iajs-2006 17 2 pure pure ADJ iajs-2006 17 3 & & CCONJ iajs-2006 17 4 appl appl PROPN iajs-2006 17 5 . . PUNCT iajs-2006 18 1 sci sci PROPN iajs-2006 18 2 . . PROPN iajs-2006 18 3 ihjpas ihjpa VERB iajs-2006 18 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 18 5 vol vol NOUN iajs-2006 18 6 . . PROPN iajs-2006 18 7 31 31 NUM iajs-2006 18 8 ( ( PUNCT iajs-2006 18 9 3 3 NUM iajs-2006 18 10 ) ) PUNCT iajs-2006 18 11 2018 2018 NUM iajs-2006 18 12 f f PROPN iajs-2006 18 13 t t PROPN iajs-2006 18 14 , , PUNCT iajs-2006 18 15 Ι΅ Ι΅ NUM iajs-2006 18 16 exp exp NOUN iajs-2006 18 17 ɡ𝑑 ɡ𝑑 NOUN iajs-2006 18 18 𝑙𝑛ɡ 𝑙𝑛ɡ NOUN iajs-2006 18 19 hence hence ADV iajs-2006 18 20 t t PROPN iajs-2006 18 21 βˆ‘ βˆ‘ PROPN iajs-2006 18 22 π‘˜ π‘˜ ADP iajs-2006 18 23 𝑑 𝑑 PROPN iajs-2006 18 24 βˆ‘ βˆ‘ PROPN iajs-2006 18 25 𝑑 𝑑 PROPN iajs-2006 18 26 is be AUX iajs-2006 18 27 the the DET iajs-2006 18 28 complete complete ADJ iajs-2006 18 29 sufficient sufficient ADJ iajs-2006 18 30 statistic statistic NOUN iajs-2006 18 31 for for ADP iajs-2006 18 32 Ι΅ Ι΅ NOUN iajs-2006 18 33 and and CCONJ iajs-2006 18 34 it it PRON iajs-2006 18 35 can can AUX iajs-2006 18 36 be be AUX iajs-2006 18 37 easily easily ADV iajs-2006 18 38 shown show VERB iajs-2006 18 39 that that SCONJ iajs-2006 18 40 t t PROPN iajs-2006 18 41 follows follow VERB iajs-2006 18 42 gamma gamma NOUN iajs-2006 18 43 distribution distribution NOUN iajs-2006 18 44 with with ADP iajs-2006 18 45 parameters parameter NOUN iajs-2006 18 46 n n CCONJ iajs-2006 18 47 and and CCONJ iajs-2006 18 48 Ι΅ Ι΅ NOUN iajs-2006 18 49 . . PUNCT iajs-2006 19 1 2 2 X iajs-2006 19 2 . . X iajs-2006 19 3 standard standard ADJ iajs-2006 19 4 bayes bayes PROPN iajs-2006 19 5 estimators estimator VERB iajs-2006 19 6 the the DET iajs-2006 19 7 researchers researcher NOUN iajs-2006 19 8 employed employ VERB iajs-2006 19 9 three three NUM iajs-2006 19 10 types type NOUN iajs-2006 19 11 of of ADP iajs-2006 19 12 loss loss NOUN iajs-2006 19 13 functions function NOUN iajs-2006 19 14 , , PUNCT iajs-2006 19 15 namely namely ADV iajs-2006 19 16 , , PUNCT iajs-2006 19 17 the the DET iajs-2006 19 18 squared square VERB iajs-2006 19 19 error error NOUN iajs-2006 19 20 loss loss NOUN iajs-2006 19 21 function function NOUN iajs-2006 19 22 ( ( PUNCT iajs-2006 19 23 self self NOUN iajs-2006 19 24 ) ) PUNCT iajs-2006 19 25 , , PUNCT iajs-2006 19 26 precautionary precautionary ADJ iajs-2006 19 27 error error NOUN iajs-2006 19 28 loss loss NOUN iajs-2006 19 29 function function NOUN iajs-2006 19 30 ( ( PUNCT iajs-2006 19 31 pelf pelf PRON iajs-2006 19 32 ) ) PUNCT iajs-2006 19 33 and and CCONJ iajs-2006 19 34 linear linear ADJ iajs-2006 19 35 exponential exponential ADJ iajs-2006 19 36 error error NOUN iajs-2006 19 37 loss loss NOUN iajs-2006 19 38 function(linex function(linex NOUN iajs-2006 19 39 ) ) PUNCT iajs-2006 19 40 . . PUNCT iajs-2006 20 1 the the DET iajs-2006 20 2 bayes bayes PROPN iajs-2006 20 3 estimator estimator NOUN iajs-2006 20 4 of of ADP iajs-2006 20 5 the the DET iajs-2006 20 6 parameter parameter NOUN iajs-2006 20 7 Ι΅ Ι΅ NOUN iajs-2006 20 8 is be AUX iajs-2006 20 9 the the DET iajs-2006 20 10 value value NOUN iajs-2006 20 11 of of ADP iajs-2006 20 12 Ι΅ Ι΅ PRON iajs-2006 20 13 that that PRON iajs-2006 20 14 minimize minimize VERB iajs-2006 20 15 the the DET iajs-2006 20 16 risk risk NOUN iajs-2006 20 17 function function NOUN iajs-2006 20 18 r(Ι΅ r(Ι΅ NOUN iajs-2006 20 19 , , PUNCT iajs-2006 20 20 Ι΅ Ι΅ NUM iajs-2006 20 21 where where SCONJ iajs-2006 20 22 [ [ X iajs-2006 20 23 4 4 NUM iajs-2006 20 24 ] ] X iajs-2006 20 25 𝑅 𝑅 PROPN iajs-2006 20 26 Ι΅ Ι΅ NOUN iajs-2006 20 27 , , PUNCT iajs-2006 20 28 Ι΅ Ι΅ NOUN iajs-2006 20 29 𝐸 𝐸 PROPN iajs-2006 20 30 𝐿 𝐿 PROPN iajs-2006 20 31 Ι΅ Ι΅ NOUN iajs-2006 20 32 , , PUNCT iajs-2006 20 33 Ι΅ Ι΅ PROPN iajs-2006 20 34 𝐿 𝐿 PROPN iajs-2006 20 35 Ι΅ Ι΅ NOUN iajs-2006 20 36 , , PUNCT iajs-2006 20 37 Ι΅ Ι΅ ADJ iajs-2006 20 38 β„Ž β„Ž PROPN iajs-2006 20 39 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 20 40 π‘‘πœƒ π‘‘πœƒ PROPN iajs-2006 20 41 Ι΅ Ι΅ SYM iajs-2006 20 42 5 5 NUM iajs-2006 20 43 in in ADP iajs-2006 20 44 the the DET iajs-2006 20 45 case case NOUN iajs-2006 20 46 of of ADP iajs-2006 20 47 squared square VERB iajs-2006 20 48 error error NOUN iajs-2006 20 49 loss loss NOUN iajs-2006 20 50 function function NOUN iajs-2006 20 51 we we PRON iajs-2006 20 52 have have VERB iajs-2006 20 53 𝐿 𝐿 PROPN iajs-2006 20 54 πœƒ πœƒ PROPN iajs-2006 20 55 , , PUNCT iajs-2006 20 56 πœƒ πœƒ X iajs-2006 20 57 πœƒ πœƒ NOUN iajs-2006 20 58 πœƒ πœƒ NOUN iajs-2006 20 59 6 6 NUM iajs-2006 20 60 then then ADV iajs-2006 20 61 , , PUNCT iajs-2006 20 62 the the DET iajs-2006 20 63 risk risk NOUN iajs-2006 20 64 function function NOUN iajs-2006 20 65 will will AUX iajs-2006 20 66 be be AUX iajs-2006 20 67 r r NOUN iajs-2006 20 68 Ι΅ Ι΅ NUM iajs-2006 20 69 , , PUNCT iajs-2006 20 70 Ι΅ Ι΅ PRON iajs-2006 20 71 Ι΅ Ι΅ ADP iajs-2006 20 72 Ι΅ Ι΅ ADP iajs-2006 20 73 Ι΅ Ι΅ ADP iajs-2006 20 74 h h NOUN iajs-2006 20 75 Ι΅Χ€t Ι΅Χ€t INTJ iajs-2006 20 76 dΙ΅ dΙ΅ VERB iajs-2006 20 77 = = NOUN iajs-2006 20 78 Ι΅ Ι΅ SYM iajs-2006 20 79 β„Ž β„Ž X iajs-2006 20 80 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 20 81 𝑑ɡ 𝑑ɡ NOUN iajs-2006 20 82 2Ι΅ 2Ι΅ NUM iajs-2006 20 83 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 20 84 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 20 85 𝑑ɡɡɡ 𝑑ɡɡɡ PROPN iajs-2006 20 86 Ι΅ Ι΅ SYM iajs-2006 20 87 β„Ž β„Ž PROPN iajs-2006 20 88 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 20 89 𝑑ɡɡ 𝑑ɡɡ NOUN iajs-2006 20 90 𝑅 𝑅 PROPN iajs-2006 20 91 Ι΅ Ι΅ NOUN iajs-2006 20 92 , , PUNCT iajs-2006 20 93 Ι΅ Ι΅ PRON iajs-2006 20 94 Ι΅ Ι΅ SYM iajs-2006 20 95 2ɡ𝐸 2ɡ𝐸 NUM iajs-2006 20 96 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 20 97 𝐸 𝐸 PROPN iajs-2006 20 98 Ι΅ Ι΅ ADP iajs-2006 20 99 𝑑׀ 𝑑׀ NOUN iajs-2006 20 100 differentiating𝑅 differentiating𝑅 NOUN iajs-2006 20 101 Ι΅ Ι΅ NOUN iajs-2006 20 102 , , PUNCT iajs-2006 20 103 Ι΅ Ι΅ ADJ iajs-2006 20 104 with with ADP iajs-2006 20 105 respect respect NOUN iajs-2006 20 106 to to ADP iajs-2006 20 107 Ι΅ Ι΅ NOUN iajs-2006 20 108 and and CCONJ iajs-2006 20 109 setting set VERB iajs-2006 20 110 the the DET iajs-2006 20 111 resultant resultant NOUN iajs-2006 20 112 derivative derivative NOUN iajs-2006 20 113 equal equal ADJ iajs-2006 20 114 to to ADP iajs-2006 20 115 zero zero NUM iajs-2006 20 116 , , PUNCT iajs-2006 20 117 we we PRON iajs-2006 20 118 get get VERB iajs-2006 20 119 : : PUNCT iajs-2006 20 120 2Ι΅ 2Ι΅ NUM iajs-2006 20 121 2e 2e PROPN iajs-2006 20 122 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 20 123 0 0 NUM iajs-2006 20 124 solving solve VERB iajs-2006 20 125 for for ADP iajs-2006 20 126 Ι΅ Ι΅ PRON iajs-2006 20 127 implies imply VERB iajs-2006 20 128 that that SCONJ iajs-2006 20 129 Ι΅ Ι΅ NUM iajs-2006 20 130 e e X iajs-2006 20 131 Ι΅Χ€t Ι΅Χ€t NUM iajs-2006 20 132 7 7 NUM iajs-2006 20 133 theprecautionary theprecautionary ADJ iajs-2006 20 134 error error NOUN iajs-2006 20 135 loss loss NOUN iajs-2006 20 136 function function NOUN iajs-2006 20 137 is be AUX iajs-2006 20 138 defined define VERB iajs-2006 20 139 as as ADP iajs-2006 20 140 [ [ X iajs-2006 20 141 5 5 NUM iajs-2006 20 142 ] ] PUNCT iajs-2006 20 143 : : PUNCT iajs-2006 20 144 l l NOUN iajs-2006 20 145 Ι΅ Ι΅ X iajs-2006 20 146 , , PUNCT iajs-2006 20 147 Ι΅ Ι΅ DET iajs-2006 20 148 Ι΅ Ι΅ SYM iajs-2006 20 149 Ι΅ Ι΅ ADP iajs-2006 20 150 Ι΅ Ι΅ NUM iajs-2006 20 151 8 8 NUM iajs-2006 20 152 if if SCONJ iajs-2006 20 153 ( ( PUNCT iajs-2006 20 154 pelf)is pelf)is ADJ iajs-2006 20 155 adopted adopt VERB iajs-2006 20 156 , , PUNCT iajs-2006 20 157 it it PRON iajs-2006 20 158 can can AUX iajs-2006 20 159 be be AUX iajs-2006 20 160 in in ADP iajs-2006 20 161 the the DET iajs-2006 20 162 same same ADJ iajs-2006 20 163 manner manner NOUN iajs-2006 20 164 show show VERB iajs-2006 20 165 that that SCONJ iajs-2006 20 166 the the DET iajs-2006 20 167 bayes bayes PROPN iajs-2006 20 168 estimator estimator NOUN iajs-2006 20 169 of of ADP iajs-2006 20 170 Ι΅ Ι΅ NOUN iajs-2006 20 171 is be AUX iajs-2006 20 172 Ι΅ Ι΅ ADP iajs-2006 20 173 𝐸 𝐸 PROPN iajs-2006 20 174 Ι΅ Ι΅ ADP iajs-2006 20 175 𝑑׀ 𝑑׀ ADP iajs-2006 20 176 9 9 NUM iajs-2006 20 177 varian varian NOUN iajs-2006 20 178 ( ( PUNCT iajs-2006 20 179 1975 1975 NUM iajs-2006 20 180 ) ) PUNCT iajs-2006 20 181 developed develop VERB iajs-2006 20 182 the the DET iajs-2006 20 183 following follow VERB iajs-2006 20 184 a a DET iajs-2006 20 185 symmetric symmetric ADJ iajs-2006 20 186 linear linear ADJ iajs-2006 20 187 exponential exponential NOUN iajs-2006 20 188 ( ( PUNCT iajs-2006 20 189 linex linex ADJ iajs-2006 20 190 ) ) PUNCT iajs-2006 20 191 loss loss NOUN iajs-2006 20 192 function function NOUN iajs-2006 20 193 𝐿 𝐿 PROPN iajs-2006 20 194 βˆ† βˆ† PROPN iajs-2006 20 195 π‘’βˆ† π‘’βˆ† NOUN iajs-2006 20 196 βˆ† βˆ† PROPN iajs-2006 20 197 1 1 NUM iajs-2006 20 198 10 10 NUM iajs-2006 20 199 where where SCONJ iajs-2006 20 200 βˆ† βˆ† PROPN iajs-2006 20 201 Ι΅ Ι΅ SYM iajs-2006 20 202 Ι΅ Ι΅ NOUN iajs-2006 20 203 and and CCONJ iajs-2006 20 204 when when SCONJ iajs-2006 20 205 the the PRON iajs-2006 20 206 ( ( PUNCT iajs-2006 20 207 ( ( PUNCT iajs-2006 20 208 linex linex ADV iajs-2006 20 209 ) ) PUNCT iajs-2006 20 210 is be AUX iajs-2006 20 211 adopted adopt VERB iajs-2006 20 212 , , PUNCT iajs-2006 20 213 similarity similarity NOUN iajs-2006 20 214 the the DET iajs-2006 20 215 bayes bayes PROPN iajs-2006 20 216 estimator estimator NOUN iajs-2006 20 217 of of ADP iajs-2006 20 218 Ι΅ Ι΅ NOUN iajs-2006 20 219 is be AUX iajs-2006 20 220 Ι΅ Ι΅ ADP iajs-2006 20 221 𝑙𝑛 𝑙𝑛 X iajs-2006 20 222 𝑒 𝑒 PROPN iajs-2006 20 223 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 20 224 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 20 225 π‘‘πœƒ π‘‘πœƒ ADP iajs-2006 20 226 11 11 NUM iajs-2006 20 227 Ι΅ Ι΅ SYM iajs-2006 20 228 4 4 NUM iajs-2006 20 229 . . PUNCT iajs-2006 20 230 posterior posterior ADJ iajs-2006 20 231 density density NOUN iajs-2006 20 232 based base VERB iajs-2006 20 233 on on ADP iajs-2006 20 234 jeffrey jeffrey PROPN iajs-2006 20 235 's 's PART iajs-2006 20 236 prior prior ADJ iajs-2006 20 237 information information NOUN iajs-2006 20 238 let let VERB iajs-2006 20 239 us we PRON iajs-2006 20 240 assume assume VERB iajs-2006 20 241 that that SCONJ iajs-2006 20 242 Ι΅ Ι΅ PRON iajs-2006 20 243 has have VERB iajs-2006 20 244 non non ADJ iajs-2006 20 245 informative informative ADJ iajs-2006 20 246 prior prior ADJ iajs-2006 20 247 density density NOUN iajs-2006 20 248 . . PUNCT iajs-2006 21 1 jeffrey jeffrey PROPN iajs-2006 21 2 's 's PART iajs-2006 21 3 ( ( PUNCT iajs-2006 21 4 1961 1961 NUM iajs-2006 21 5 ) ) PUNCT iajs-2006 21 6 developed develop VERB iajs-2006 21 7 a a DET iajs-2006 21 8 general general ADJ iajs-2006 21 9 rule rule NOUN iajs-2006 21 10 for for ADP iajs-2006 21 11 obtaining obtain VERB iajs-2006 21 12 the the DET iajs-2006 21 13 prior prior ADJ iajs-2006 21 14 distribution distribution NOUN iajs-2006 21 15 of of ADP iajs-2006 21 16 Ι΅ Ι΅ PRON iajs-2006 21 17 [ [ X iajs-2006 21 18 6 6 NUM iajs-2006 21 19 ] ] PUNCT iajs-2006 21 20 . . PUNCT iajs-2006 22 1 he he PRON iajs-2006 22 2 established establish VERB iajs-2006 22 3 that that SCONJ iajs-2006 22 4 the the DET iajs-2006 22 5 single single ADJ iajs-2006 22 6 unknown unknown ADJ iajs-2006 22 7 parameter parameter NOUN iajs-2006 22 8 Ι΅ Ι΅ ADP iajs-2006 22 9 which which PRON iajs-2006 22 10 is be AUX iajs-2006 22 11 regarded regard VERB iajs-2006 22 12 as as ADP iajs-2006 22 13 a a DET iajs-2006 22 14 random random ADJ iajs-2006 22 15 variable variable NOUN iajs-2006 22 16 follows follow VERB iajs-2006 22 17 such such DET iajs-2006 22 18 a a DET iajs-2006 22 19 distribution distribution NOUN iajs-2006 22 20 that that PRON iajs-2006 22 21 is be AUX iajs-2006 22 22 proportional proportional ADJ iajs-2006 22 23 to to ADP iajs-2006 22 24 the the DET iajs-2006 22 25 square square ADJ iajs-2006 22 26 root root NOUN iajs-2006 22 27 of of ADP iajs-2006 22 28 the the DET iajs-2006 22 29 fisher fisher PROPN iajs-2006 22 30 information information NOUN iajs-2006 22 31 on on ADP iajs-2006 22 32 Ι΅ Ι΅ SYM iajs-2006 22 33 , , PUNCT iajs-2006 22 34 that that PRON iajs-2006 22 35 is be AUX iajs-2006 22 36 [ [ X iajs-2006 22 37 5 5 NUM iajs-2006 22 38 ] ] X iajs-2006 22 39 𝑔 𝑔 PROPN iajs-2006 22 40 Ι΅ Ι΅ SYM iajs-2006 22 41 𝛼 𝛼 VERB iajs-2006 22 42 𝐼 𝐼 ADP iajs-2006 22 43 Ι΅ Ι΅ SYM iajs-2006 22 44 12 12 NUM iajs-2006 22 45 that that PRON iajs-2006 22 46 is be AUX iajs-2006 22 47 mathematics mathematic NOUN iajs-2006 22 48 | | ADV iajs-2006 22 49 137 137 NUM iajs-2006 22 50 ibn ibn PROPN iajs-2006 22 51 al al PROPN iajs-2006 22 52 - - PUNCT iajs-2006 22 53 haitham haitham PROPN iajs-2006 22 54 jour jour X iajs-2006 22 55 . . PROPN iajs-2006 23 1 for for ADP iajs-2006 23 2 pure pure ADJ iajs-2006 23 3 & & CCONJ iajs-2006 23 4 appl appl PROPN iajs-2006 23 5 . . PUNCT iajs-2006 24 1 sci sci PROPN iajs-2006 24 2 . . PROPN iajs-2006 24 3 ihjpas ihjpa VERB iajs-2006 24 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 24 5 vol vol NOUN iajs-2006 24 6 . . PROPN iajs-2006 24 7 31 31 NUM iajs-2006 25 1 ( ( PUNCT iajs-2006 25 2 3 3 NUM iajs-2006 25 3 ) ) SYM iajs-2006 25 4 2018 2018 NUM iajs-2006 25 5 𝑔 𝑔 PROPN iajs-2006 25 6 Ι΅ Ι΅ SYM iajs-2006 25 7 𝑐 𝑐 NOUN iajs-2006 25 8 𝐼 𝐼 NOUN iajs-2006 25 9 Ι΅ Ι΅ ADP iajs-2006 25 10 where where SCONJ iajs-2006 25 11 c c NOUN iajs-2006 25 12 is be AUX iajs-2006 25 13 a a DET iajs-2006 25 14 constant constant ADJ iajs-2006 25 15 of of ADP iajs-2006 25 16 proportionality proportionality NOUN iajs-2006 25 17 and and CCONJ iajs-2006 25 18 i(Ι΅ i(Ι΅ PROPN iajs-2006 25 19 ) ) PUNCT iajs-2006 25 20 represent represent VERB iajs-2006 25 21 fisher fisher PROPN iajs-2006 25 22 information information NOUN iajs-2006 25 23 defined define VERB iajs-2006 25 24 as as SCONJ iajs-2006 25 25 follows follow VERB iajs-2006 25 26 : : PUNCT iajs-2006 25 27 𝐼 𝐼 PROPN iajs-2006 25 28 Ι΅ Ι΅ PROPN iajs-2006 25 29 𝑛𝐸 𝑛𝐸 PROPN iajs-2006 25 30 πœ• πœ• PROPN iajs-2006 25 31 𝑙𝑛𝑓 𝑙𝑛𝑓 PROPN iajs-2006 25 32 𝑑 𝑑 PROPN iajs-2006 25 33 , , PUNCT iajs-2006 25 34 Ι΅ Ι΅ X iajs-2006 25 35 πœ•Ι΅ πœ•Ι΅ NOUN iajs-2006 25 36 if if SCONJ iajs-2006 25 37 g g PROPN iajs-2006 25 38 Ι΅ Ι΅ SYM iajs-2006 25 39 denote denote VERB iajs-2006 25 40 jeffrey jeffrey PROPN iajs-2006 25 41 's 's PART iajs-2006 25 42 prior prior ADJ iajs-2006 25 43 information information NOUN iajs-2006 25 44 then then ADV iajs-2006 25 45 𝑔 𝑔 PROPN iajs-2006 25 46 Ι΅ Ι΅ PROPN iajs-2006 25 47 𝑐 𝑐 PROPN iajs-2006 25 48 𝑛𝐸 𝑛𝐸 PROPN iajs-2006 25 49 πœ• πœ• PROPN iajs-2006 25 50 𝑙𝑛𝑓 𝑙𝑛𝑓 PROPN iajs-2006 25 51 𝑑 𝑑 PROPN iajs-2006 25 52 ; ; PUNCT iajs-2006 25 53 Ι΅ Ι΅ X iajs-2006 25 54 πœ•Ι΅ πœ•Ι΅ NOUN iajs-2006 25 55 13 13 NUM iajs-2006 25 56 for for ADP iajs-2006 25 57 the the DET iajs-2006 25 58 exponential exponential ADJ iajs-2006 25 59 distribution distribution NOUN iajs-2006 25 60 we we PRON iajs-2006 25 61 have have VERB iajs-2006 25 62 𝑙𝑛𝑓 𝑙𝑛𝑓 NOUN iajs-2006 25 63 𝑑 𝑑 PROPN iajs-2006 25 64 , , PUNCT iajs-2006 25 65 Ι΅ Ι΅ PRON iajs-2006 25 66 𝑙𝑛ɡ 𝑙𝑛ɡ NOUN iajs-2006 25 67 ɡ𝑑 ɡ𝑑 X iajs-2006 25 68 ; ; PUNCT iajs-2006 25 69 Ι΅ Ι΅ CCONJ iajs-2006 25 70 Ι΅ Ι΅ ADP iajs-2006 25 71 Ι΅ Ι΅ ADP iajs-2006 25 72 t t NOUN iajs-2006 25 73 hence hence ADV iajs-2006 25 74 , , PUNCT iajs-2006 25 75 βˆ‚ βˆ‚ NUM iajs-2006 25 76 lnf lnf PROPN iajs-2006 25 77 t t PROPN iajs-2006 25 78 ; ; PUNCT iajs-2006 25 79 Ι΅ Ι΅ NUM iajs-2006 25 80 βˆ‚Ι΅ βˆ‚Ι΅ PROPN iajs-2006 25 81 1 1 NUM iajs-2006 25 82 Ι΅ Ι΅ NOUN iajs-2006 25 83 substituting substitute VERB iajs-2006 25 84 in in ADP iajs-2006 25 85 equation equation NOUN iajs-2006 25 86 ( ( PUNCT iajs-2006 25 87 13 13 NUM iajs-2006 25 88 ) ) PUNCT iajs-2006 25 89 it it PRON iajs-2006 25 90 follows follow VERB iajs-2006 25 91 that that SCONJ iajs-2006 25 92 𝑔 𝑔 PROPN iajs-2006 25 93 Ι΅ Ι΅ SYM iajs-2006 25 94 𝑐 𝑐 PROPN iajs-2006 25 95 Ι΅ Ι΅ NUM iajs-2006 25 96 βˆšπ‘› βˆšπ‘› ADP iajs-2006 25 97 from from ADP iajs-2006 25 98 bayes bayes PROPN iajs-2006 25 99 theorem theorem VERB iajs-2006 25 100 the the DET iajs-2006 25 101 posterior posterior ADJ iajs-2006 25 102 density density NOUN iajs-2006 25 103 function function NOUN iajs-2006 25 104 of of ADP iajs-2006 25 105 Ι΅ Ι΅ PRON iajs-2006 25 106 denoted denote VERB iajs-2006 25 107 by by ADP iajs-2006 25 108 β„Ž β„Ž PROPN iajs-2006 25 109 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 25 110 can can AUX iajs-2006 25 111 be be AUX iajs-2006 25 112 derived derive VERB iajs-2006 25 113 as as ADP iajs-2006 25 114 [ [ X iajs-2006 25 115 4 4 NUM iajs-2006 25 116 ] ] PUNCT iajs-2006 25 117 β„Ž β„Ž PROPN iajs-2006 25 118 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 25 119 , , PUNCT iajs-2006 25 120 … … PUNCT iajs-2006 25 121 , , PUNCT iajs-2006 26 1 𝑑 𝑑 PROPN iajs-2006 26 2 𝑔 𝑔 PROPN iajs-2006 26 3 Ι΅ Ι΅ SYM iajs-2006 26 4 𝐿 𝐿 PROPN iajs-2006 26 5 Ι΅ Ι΅ NUM iajs-2006 26 6 ; ; PUNCT iajs-2006 26 7 𝑑 𝑑 X iajs-2006 26 8 , , PUNCT iajs-2006 26 9 … … PUNCT iajs-2006 26 10 , , PUNCT iajs-2006 26 11 𝑑 𝑑 PROPN iajs-2006 26 12 𝑔 𝑔 PROPN iajs-2006 26 13 Ι΅ Ι΅ SYM iajs-2006 26 14 𝐿 𝐿 PROPN iajs-2006 26 15 Ι΅ Ι΅ NUM iajs-2006 26 16 ; ; PUNCT iajs-2006 26 17 𝑑 𝑑 X iajs-2006 26 18 , , PUNCT iajs-2006 26 19 … … PUNCT iajs-2006 26 20 , , PUNCT iajs-2006 26 21 𝑑 𝑑 X iajs-2006 26 22 𝑑ɡ 𝑑ɡ NOUN iajs-2006 26 23 β„Ž β„Ž PRON iajs-2006 26 24 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 26 25 , , PUNCT iajs-2006 26 26 … … PUNCT iajs-2006 26 27 , , PUNCT iajs-2006 26 28 𝑑 𝑑 PROPN iajs-2006 26 29 Ι΅ Ι΅ VERB iajs-2006 26 30 𝑒 𝑒 X iajs-2006 26 31 Ι΅ Ι΅ X iajs-2006 26 32 Ι΅ Ι΅ X iajs-2006 26 33 𝑒 𝑒 X iajs-2006 26 34 Ι΅ Ι΅ NUM iajs-2006 26 35 𝑑ɡ 𝑑ɡ NOUN iajs-2006 26 36 , , PUNCT iajs-2006 26 37 t t PROPN iajs-2006 26 38 𝑑 𝑑 PROPN iajs-2006 26 39 hence hence ADV iajs-2006 26 40 , , PUNCT iajs-2006 26 41 the the DET iajs-2006 26 42 posterior posterior ADJ iajs-2006 26 43 density density NOUN iajs-2006 26 44 function function NOUN iajs-2006 26 45 for for ADP iajs-2006 26 46 Ι΅ Ι΅ NUM iajs-2006 26 47 based base VERB iajs-2006 26 48 on on ADP iajs-2006 26 49 jeffery jeffery PROPN iajs-2006 26 50 's 's PART iajs-2006 26 51 prior prior ADJ iajs-2006 26 52 information information NOUN iajs-2006 26 53 will will AUX iajs-2006 26 54 be be AUX iajs-2006 26 55 β„Ž β„Ž PROPN iajs-2006 26 56 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 26 57 , , PUNCT iajs-2006 26 58 … … PUNCT iajs-2006 26 59 , , PUNCT iajs-2006 26 60 𝑑 𝑑 PROPN iajs-2006 26 61 𝑇 𝑇 PROPN iajs-2006 26 62 Ι΅ Ι΅ CCONJ iajs-2006 26 63 𝑒 𝑒 PROPN iajs-2006 26 64 Ι΅ Ι΅ ADJ iajs-2006 26 65 Π³ Π³ PROPN iajs-2006 26 66 𝑛 𝑛 PROPN iajs-2006 26 67 14 14 NUM iajs-2006 26 68 the the DET iajs-2006 26 69 posterior posterior ADJ iajs-2006 26 70 density density NOUN iajs-2006 26 71 in in ADP iajs-2006 26 72 equation equation NOUN iajs-2006 26 73 ( ( PUNCT iajs-2006 26 74 14 14 NUM iajs-2006 26 75 ) ) PUNCT iajs-2006 26 76 is be AUX iajs-2006 26 77 defined define VERB iajs-2006 26 78 identified identify VERB iajs-2006 26 79 as as ADP iajs-2006 26 80 a a DET iajs-2006 26 81 density density NOUN iajs-2006 26 82 of of ADP iajs-2006 26 83 the the DET iajs-2006 26 84 gamma gamma NOUN iajs-2006 26 85 distribution distribution NOUN iajs-2006 26 86 , , PUNCT iajs-2006 26 87 that that PRON iajs-2006 26 88 is be AUX iajs-2006 26 89 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 26 90 , , PUNCT iajs-2006 26 91 𝑑 𝑑 PROPN iajs-2006 26 92 , , PUNCT iajs-2006 26 93 … … PUNCT iajs-2006 26 94 , , PUNCT iajs-2006 26 95 𝑑 𝑑 X iajs-2006 26 96 ~ ~ PUNCT iajs-2006 26 97 gamma gamma NOUN iajs-2006 26 98 ( ( PUNCT iajs-2006 26 99 n n CCONJ iajs-2006 26 100 , , PUNCT iajs-2006 26 101 ) ) PUNCT iajs-2006 26 102 with with ADP iajs-2006 26 103 e(Ι΅ e(Ι΅ PROPN iajs-2006 26 104 ) ) PUNCT iajs-2006 26 105 = = PUNCT iajs-2006 26 106 and and CCONJ iajs-2006 26 107 var(Ι΅ var(Ι΅ NOUN iajs-2006 26 108 ) ) PUNCT iajs-2006 27 1 = = NOUN iajs-2006 27 2 that that PRON iajs-2006 27 3 is be AUX iajs-2006 27 4 Ι΅ Ι΅ ADP iajs-2006 27 5 ~ ~ NOUN iajs-2006 27 6 gamma gamma NOUN iajs-2006 27 7 ( ( PUNCT iajs-2006 27 8 n n NOUN iajs-2006 27 9 , , PUNCT iajs-2006 27 10 ) ) PUNCT iajs-2006 28 1 4 4 X iajs-2006 28 2 . . X iajs-2006 28 3 posterior posterior ADJ iajs-2006 28 4 density density NOUN iajs-2006 28 5 based base VERB iajs-2006 28 6 on on ADP iajs-2006 28 7 gamma gamma NOUN iajs-2006 28 8 prior prior ADJ iajs-2006 28 9 distribution distribution NOUN iajs-2006 28 10 assuming assume VERB iajs-2006 28 11 that that SCONJ iajs-2006 28 12 Ι΅ Ι΅ PRON iajs-2006 28 13 has have VERB iajs-2006 28 14 informative informative ADJ iajs-2006 28 15 prior prior ADV iajs-2006 28 16 as as ADP iajs-2006 28 17 gamma gamma NOUN iajs-2006 28 18 distribution distribution NOUN iajs-2006 28 19 which which PRON iajs-2006 28 20 takes take VERB iajs-2006 28 21 the the DET iajs-2006 28 22 following follow VERB iajs-2006 28 23 form form NOUN iajs-2006 28 24 : : PUNCT iajs-2006 28 25 𝑔 𝑔 PROPN iajs-2006 28 26 Ι΅ Ι΅ SYM iajs-2006 28 27 𝛽 𝛽 PROPN iajs-2006 28 28 Ι΅ Ι΅ PRON iajs-2006 28 29 𝑒 𝑒 PROPN iajs-2006 28 30 Ι΅ Ι΅ ADJ iajs-2006 28 31 Π³ Π³ PROPN iajs-2006 28 32 𝛼 𝛼 NOUN iajs-2006 28 33 ; ; PUNCT iajs-2006 28 34 Ι΅ Ι΅ X iajs-2006 28 35 0 0 NUM iajs-2006 28 36 , , PUNCT iajs-2006 28 37 𝛽 𝛽 PROPN iajs-2006 28 38 0 0 NUM iajs-2006 28 39 , , PUNCT iajs-2006 28 40 𝛼 𝛼 PROPN iajs-2006 28 41 0 0 NUM iajs-2006 28 42 15 15 NUM iajs-2006 28 43 where where SCONJ iajs-2006 28 44 Ξ± Ξ± X iajs-2006 28 45 , , PUNCT iajs-2006 28 46 Ξ² Ξ² X iajs-2006 28 47 are be AUX iajs-2006 28 48 the the DET iajs-2006 28 49 shape shape NOUN iajs-2006 28 50 parameter parameter NOUN iajs-2006 28 51 and and CCONJ iajs-2006 28 52 scale scale NOUN iajs-2006 28 53 parameter parameter NOUN iajs-2006 28 54 respectively respectively ADV iajs-2006 28 55 the the DET iajs-2006 28 56 posterior posterior ADJ iajs-2006 28 57 density density NOUN iajs-2006 28 58 function function NOUN iajs-2006 28 59 is be AUX iajs-2006 28 60 β„Ž β„Ž PROPN iajs-2006 28 61 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 28 62 𝑔 𝑔 PROPN iajs-2006 28 63 Ι΅ Ι΅ SYM iajs-2006 28 64 𝐿 𝐿 PROPN iajs-2006 28 65 Ι΅ Ι΅ NUM iajs-2006 28 66 ; ; PUNCT iajs-2006 28 67 𝑑 𝑑 X iajs-2006 28 68 , , PUNCT iajs-2006 28 69 … … PUNCT iajs-2006 28 70 , , PUNCT iajs-2006 28 71 𝑑 𝑑 PROPN iajs-2006 28 72 𝑔 𝑔 PROPN iajs-2006 28 73 Ι΅ Ι΅ SYM iajs-2006 28 74 𝐿 𝐿 PROPN iajs-2006 28 75 Ι΅ Ι΅ NUM iajs-2006 28 76 ; ; PUNCT iajs-2006 28 77 𝑑 𝑑 X iajs-2006 28 78 , , PUNCT iajs-2006 28 79 … … PUNCT iajs-2006 28 80 , , PUNCT iajs-2006 28 81 𝑑 𝑑 X iajs-2006 28 82 𝑑ɡ 𝑑ɡ NOUN iajs-2006 28 83 thus thus ADV iajs-2006 28 84 mathematics mathematic NOUN iajs-2006 28 85 | | ADV iajs-2006 28 86 138 138 NUM iajs-2006 28 87 ibn ibn PROPN iajs-2006 28 88 al al PROPN iajs-2006 28 89 - - PUNCT iajs-2006 28 90 haitham haitham PROPN iajs-2006 28 91 jour jour X iajs-2006 28 92 . . PROPN iajs-2006 29 1 for for ADP iajs-2006 29 2 pure pure ADJ iajs-2006 29 3 & & CCONJ iajs-2006 29 4 appl appl PROPN iajs-2006 29 5 . . PUNCT iajs-2006 30 1 sci sci PROPN iajs-2006 30 2 . . PROPN iajs-2006 30 3 ihjpas ihjpa VERB iajs-2006 30 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 30 5 vol vol NOUN iajs-2006 30 6 . . PROPN iajs-2006 30 7 31 31 NUM iajs-2006 30 8 ( ( PUNCT iajs-2006 30 9 3 3 NUM iajs-2006 30 10 ) ) PUNCT iajs-2006 30 11 2018 2018 NUM iajs-2006 30 12 β„Ž β„Ž PROPN iajs-2006 30 13 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 30 14 𝑃 𝑃 PROPN iajs-2006 30 15 Ι΅ Ι΅ NOUN iajs-2006 30 16 𝑒 𝑒 X iajs-2006 30 17 Ι΅ Ι΅ ADJ iajs-2006 30 18 Π³ Π³ PROPN iajs-2006 30 19 𝛼 𝛼 NOUN iajs-2006 30 20 𝑛 𝑛 PROPN iajs-2006 30 21 16 16 NUM iajs-2006 30 22 where where SCONJ iajs-2006 30 23 p p NOUN iajs-2006 30 24 Ξ² Ξ² X iajs-2006 30 25 t t NOUN iajs-2006 30 26 it it PRON iajs-2006 30 27 can can AUX iajs-2006 30 28 easily easily ADV iajs-2006 30 29 be be AUX iajs-2006 30 30 noted note VERB iajs-2006 30 31 that that SCONJ iajs-2006 30 32 ( ( PUNCT iajs-2006 30 33 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 30 34 ~πΊπ‘Žπ‘šπ‘šπ‘Ž ~πΊπ‘Žπ‘šπ‘šπ‘Ž PUNCT iajs-2006 30 35 𝛼 𝛼 PRON iajs-2006 30 36 𝑛 𝑛 NOUN iajs-2006 30 37 , , PUNCT iajs-2006 30 38 with with ADP iajs-2006 30 39 e(Ι΅ e(Ι΅ PROPN iajs-2006 30 40 ) ) PUNCT iajs-2006 30 41 = = PRON iajs-2006 30 42 , , PUNCT iajs-2006 30 43 var(Ι΅ var(Ι΅ NOUN iajs-2006 30 44 ) ) PUNCT iajs-2006 30 45 = = SYM iajs-2006 30 46 ( ( PUNCT iajs-2006 30 47 ) ) PUNCT iajs-2006 30 48 . . PUNCT iajs-2006 31 1 bayes bayes PROPN iajs-2006 31 2 estimator estimator NOUN iajs-2006 31 3 when when SCONJ iajs-2006 31 4 ( ( PUNCT iajs-2006 31 5 self)is self)is INTJ iajs-2006 31 6 adopted adopt VERB iajs-2006 31 7 5 5 NUM iajs-2006 31 8 a a PRON iajs-2006 31 9 : : PUNCT iajs-2006 31 10 the the DET iajs-2006 31 11 case case NOUN iajs-2006 31 12 of of ADP iajs-2006 31 13 jeffrey jeffrey PROPN iajs-2006 31 14 's 's PART iajs-2006 31 15 prior prior ADJ iajs-2006 31 16 information information NOUN iajs-2006 31 17 . . PUNCT iajs-2006 32 1 from from ADP iajs-2006 32 2 equation equation NOUN iajs-2006 32 3 ( ( PUNCT iajs-2006 32 4 7 7 X iajs-2006 32 5 ) ) PUNCT iajs-2006 32 6 we we PRON iajs-2006 32 7 found find VERB iajs-2006 32 8 that that SCONJ iajs-2006 32 9 : : PUNCT iajs-2006 32 10 Ι΅ Ι΅ NUM iajs-2006 32 11 e e X iajs-2006 32 12 Ι΅Χ€t Ι΅Χ€t X iajs-2006 32 13 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 32 14 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 32 15 π‘‘πœƒ π‘‘πœƒ PROPN iajs-2006 32 16 Ι΅ Ι΅ ADP iajs-2006 32 17 n n NOUN iajs-2006 32 18 t t PROPN iajs-2006 32 19 17 17 NUM iajs-2006 32 20 similarly similarly ADV iajs-2006 32 21 , , PUNCT iajs-2006 32 22 the the DET iajs-2006 32 23 bayes bayes PROPN iajs-2006 32 24 estimator estimator NOUN iajs-2006 32 25 of of ADP iajs-2006 32 26 the the DET iajs-2006 32 27 reliability reliability NOUN iajs-2006 32 28 function function NOUN iajs-2006 32 29 can can AUX iajs-2006 32 30 be be AUX iajs-2006 32 31 obtained obtain VERB iajs-2006 32 32 as as SCONJ iajs-2006 32 33 follows follow VERB iajs-2006 32 34 : : PUNCT iajs-2006 33 1 r r NOUN iajs-2006 33 2 t t NOUN iajs-2006 33 3 e e NOUN iajs-2006 33 4 r r NOUN iajs-2006 33 5 t t NOUN iajs-2006 33 6 tΧ€ tΧ€ NOUN iajs-2006 33 7 r r NOUN iajs-2006 33 8 t t NOUN iajs-2006 33 9 h h NOUN iajs-2006 33 10 Ι΅Χ€t Ι΅Χ€t PROPN iajs-2006 33 11 dΞΈ dΞΈ PROPN iajs-2006 33 12 r r NOUN iajs-2006 33 13 t t PROPN iajs-2006 33 14 t t PROPN iajs-2006 33 15 t t PROPN iajs-2006 33 16 t t PROPN iajs-2006 33 17 18 18 NUM iajs-2006 33 18 b b NOUN iajs-2006 33 19 : : PUNCT iajs-2006 33 20 the the DET iajs-2006 33 21 case case NOUN iajs-2006 33 22 of of ADP iajs-2006 33 23 gamma gamma NOUN iajs-2006 33 24 prior prior ADJ iajs-2006 33 25 distribution distribution NOUN iajs-2006 33 26 . . PUNCT iajs-2006 34 1 in in ADP iajs-2006 34 2 this this DET iajs-2006 34 3 case case NOUN iajs-2006 34 4 we we PRON iajs-2006 34 5 have have VERB iajs-2006 34 6 Ι΅ Ι΅ NUM iajs-2006 34 7 e e NOUN iajs-2006 34 8 h h NOUN iajs-2006 35 1 Ι΅Χ€t Ι΅Χ€t PROPN iajs-2006 36 1 Ξ± Ξ± NOUN iajs-2006 37 1 n n NOUN iajs-2006 37 2 p p PROPN iajs-2006 37 3 19 19 NUM iajs-2006 37 4 the the DET iajs-2006 37 5 estimator estimator NOUN iajs-2006 37 6 of of ADP iajs-2006 37 7 the the DET iajs-2006 37 8 reliability reliability NOUN iajs-2006 37 9 function function NOUN iajs-2006 37 10 can can AUX iajs-2006 37 11 be be AUX iajs-2006 37 12 obtained obtain VERB iajs-2006 37 13 as as ADP iajs-2006 37 14 𝑅 𝑅 PROPN iajs-2006 37 15 𝑑 𝑑 PROPN iajs-2006 37 16 e e NOUN iajs-2006 37 17 r r NOUN iajs-2006 37 18 t t NOUN iajs-2006 37 19 tΧ€ tΧ€ NOUN iajs-2006 37 20 𝑅 𝑅 PROPN iajs-2006 37 21 𝑑 𝑑 PROPN iajs-2006 37 22 𝑒 𝑒 VERB iajs-2006 37 23 Ι΅ Ι΅ SYM iajs-2006 37 24 𝑃 𝑃 NOUN iajs-2006 37 25 Ι΅ Ι΅ NOUN iajs-2006 37 26 𝑒 𝑒 X iajs-2006 37 27 Ι΅ Ι΅ ADJ iajs-2006 37 28 Π³ Π³ PROPN iajs-2006 37 29 𝛼 𝛼 NOUN iajs-2006 37 30 𝑛 𝑛 PROPN iajs-2006 37 31 π‘‘πœƒ π‘‘πœƒ ADP iajs-2006 37 32 which which PRON iajs-2006 37 33 , , PUNCT iajs-2006 37 34 implies imply VERB iajs-2006 37 35 that that SCONJ iajs-2006 37 36 𝑅 𝑅 PROPN iajs-2006 37 37 𝑑 𝑑 PROPN iajs-2006 37 38 𝑅 𝑅 PROPN iajs-2006 37 39 𝑑 𝑑 NOUN iajs-2006 37 40 β„Ž β„Ž ADP iajs-2006 37 41 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 37 42 π‘‘πœƒ π‘‘πœƒ ADP iajs-2006 37 43 𝑃 𝑃 NOUN iajs-2006 37 44 𝑃 𝑃 NOUN iajs-2006 37 45 𝑑 𝑑 NOUN iajs-2006 37 46 20 20 NUM iajs-2006 37 47 . . PUNCT iajs-2006 38 1 bayes bayes PROPN iajs-2006 38 2 estimator estimator NOUN iajs-2006 38 3 when when SCONJ iajs-2006 38 4 ( ( PUNCT iajs-2006 38 5 pelf pelf PRON iajs-2006 38 6 ) ) PUNCT iajs-2006 38 7 is be AUX iajs-2006 38 8 adopted adopt VERB iajs-2006 38 9 6 6 NUM iajs-2006 38 10 a a PRON iajs-2006 38 11 : : PUNCT iajs-2006 38 12 the the DET iajs-2006 38 13 case case NOUN iajs-2006 38 14 of of ADP iajs-2006 38 15 jeffrey jeffrey PROPN iajs-2006 38 16 's 's PART iajs-2006 38 17 prior prior ADJ iajs-2006 38 18 information information NOUN iajs-2006 38 19 from from ADP iajs-2006 38 20 equation equation NOUN iajs-2006 38 21 ( ( PUNCT iajs-2006 38 22 9 9 X iajs-2006 38 23 ) ) PUNCT iajs-2006 38 24 we we PRON iajs-2006 38 25 have have VERB iajs-2006 38 26 Ι΅ Ι΅ PART iajs-2006 38 27 𝐸 𝐸 PROPN iajs-2006 38 28 Ι΅ Ι΅ NOUN iajs-2006 38 29 π‘₯Χ€ π‘₯Χ€ VERB iajs-2006 38 30 the the DET iajs-2006 38 31 π‘Ÿ π‘Ÿ NOUN iajs-2006 38 32 moment moment NOUN iajs-2006 38 33 of of ADP iajs-2006 38 34 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 38 35 can can AUX iajs-2006 38 36 be be AUX iajs-2006 38 37 evaluated evaluate VERB iajs-2006 38 38 as as SCONJ iajs-2006 38 39 follows follow VERB iajs-2006 38 40 : : PUNCT iajs-2006 38 41 e(Ι΅ e(Ι΅ PROPN iajs-2006 38 42 𝑑׀ 𝑑׀ NOUN iajs-2006 38 43 Ι΅ Ι΅ SYM iajs-2006 38 44 β„Ž β„Ž PROPN iajs-2006 38 45 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 38 46 𝑑ɡ 𝑑ɡ NOUN iajs-2006 38 47 hence hence ADV iajs-2006 38 48 , , PUNCT iajs-2006 38 49 e e X iajs-2006 38 50 ( ( PUNCT iajs-2006 38 51 Ι΅ Ι΅ ADP iajs-2006 38 52 𝑑׀ 𝑑׀ ADP iajs-2006 38 53 Π³ Π³ PROPN iajs-2006 38 54 Π³ Π³ PROPN iajs-2006 38 55 21 21 NUM iajs-2006 38 56 when when SCONJ iajs-2006 38 57 r=2 r=2 PROPN iajs-2006 38 58 , , PUNCT iajs-2006 38 59 we we PRON iajs-2006 38 60 get get VERB iajs-2006 38 61 𝐸 𝐸 PRON iajs-2006 38 62 Ι΅ Ι΅ SYM iajs-2006 38 63 𝑑׀ 𝑑׀ NOUN iajs-2006 38 64 Π³ Π³ PROPN iajs-2006 38 65 𝑛 𝑛 PROPN iajs-2006 38 66 2 2 NUM iajs-2006 38 67 Π³ Π³ NOUN iajs-2006 38 68 𝑛 𝑛 DET iajs-2006 38 69 𝑇 𝑇 PROPN iajs-2006 38 70 𝑛 𝑛 PRON iajs-2006 38 71 𝑛 𝑛 DET iajs-2006 38 72 1 1 NUM iajs-2006 38 73 𝑇 𝑇 NOUN iajs-2006 38 74 hence hence ADV iajs-2006 38 75 , , PUNCT iajs-2006 38 76 mathematics mathematic NOUN iajs-2006 38 77 | | ADV iajs-2006 38 78 139 139 NUM iajs-2006 38 79 ibn ibn PROPN iajs-2006 38 80 al al PROPN iajs-2006 38 81 - - PUNCT iajs-2006 38 82 haitham haitham PROPN iajs-2006 38 83 jour jour X iajs-2006 38 84 . . PROPN iajs-2006 39 1 for for ADP iajs-2006 39 2 pure pure ADJ iajs-2006 39 3 & & CCONJ iajs-2006 39 4 appl appl PROPN iajs-2006 39 5 . . PUNCT iajs-2006 40 1 sci sci PROPN iajs-2006 40 2 . . PROPN iajs-2006 40 3 ihjpas ihjpa VERB iajs-2006 40 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 40 5 vol vol NOUN iajs-2006 40 6 . . PROPN iajs-2006 40 7 31 31 NUM iajs-2006 40 8 ( ( PUNCT iajs-2006 40 9 3 3 NUM iajs-2006 40 10 ) ) PUNCT iajs-2006 40 11 2018 2018 NUM iajs-2006 41 1 Ι΅ Ι΅ SYM iajs-2006 41 2 𝑛 𝑛 PART iajs-2006 41 3 𝑛 𝑛 PRON iajs-2006 41 4 1 1 NUM iajs-2006 41 5 𝑇 𝑇 PROPN iajs-2006 41 6 22 22 NUM iajs-2006 41 7 similarly similarly ADV iajs-2006 41 8 , , PUNCT iajs-2006 41 9 the the DET iajs-2006 41 10 bayes bayes NOUN iajs-2006 41 11 estimators estimator NOUN iajs-2006 41 12 of of ADP iajs-2006 41 13 the the DET iajs-2006 41 14 reliability reliability NOUN iajs-2006 41 15 function function NOUN iajs-2006 41 16 can can AUX iajs-2006 41 17 be be AUX iajs-2006 41 18 obtained obtain VERB iajs-2006 41 19 as as SCONJ iajs-2006 41 20 follows follow VERB iajs-2006 41 21 𝑅 𝑅 PROPN iajs-2006 41 22 𝑑 𝑑 PROPN iajs-2006 41 23 e e PROPN iajs-2006 41 24 𝑅 𝑅 PROPN iajs-2006 41 25 𝑑 𝑑 PROPN iajs-2006 41 26 𝑑׀ 𝑑׀ ADP iajs-2006 41 27 now now ADV iajs-2006 41 28 , , PUNCT iajs-2006 41 29 we we PRON iajs-2006 41 30 have have VERB iajs-2006 41 31 to to PART iajs-2006 41 32 determine determine VERB iajs-2006 41 33 e e NOUN iajs-2006 41 34 [ [ X iajs-2006 41 35 ( ( PUNCT iajs-2006 41 36 𝑅 𝑅 PROPN iajs-2006 41 37 𝑑 𝑑 PROPN iajs-2006 41 38 𝑑׀ 𝑑׀ ADP iajs-2006 41 39 e e PROPN iajs-2006 41 40 𝑅 𝑅 PROPN iajs-2006 41 41 𝑑 𝑑 PROPN iajs-2006 41 42 𝑑׀ 𝑑׀ ADP iajs-2006 41 43 𝑅 𝑅 PROPN iajs-2006 41 44 𝑑 𝑑 NOUN iajs-2006 41 45 β„Ž β„Ž PROPN iajs-2006 41 46 ɡ׀𝑑 ɡ׀𝑑 NOUN iajs-2006 41 47 𝑑ɡ 𝑑ɡ NOUN iajs-2006 41 48 = = SYM iajs-2006 41 49 hence hence ADV iajs-2006 41 50 , , PUNCT iajs-2006 41 51 𝑅 𝑅 PROPN iajs-2006 41 52 𝑑 𝑑 PROPN iajs-2006 41 53 𝑇 𝑇 PROPN iajs-2006 41 54 𝑇 𝑇 PROPN iajs-2006 41 55 2𝑑 2𝑑 NOUN iajs-2006 41 56 23 23 NUM iajs-2006 41 57 b b NOUN iajs-2006 41 58 : : PUNCT iajs-2006 41 59 the the DET iajs-2006 41 60 case case NOUN iajs-2006 41 61 of of ADP iajs-2006 41 62 gamma gamma NOUN iajs-2006 41 63 prior prior ADJ iajs-2006 41 64 distribution distribution NOUN iajs-2006 41 65 from from ADP iajs-2006 41 66 equation equation NOUN iajs-2006 41 67 ( ( PUNCT iajs-2006 41 68 9 9 X iajs-2006 41 69 ) ) PUNCT iajs-2006 41 70 we we PRON iajs-2006 41 71 have have VERB iajs-2006 41 72 Ι΅ Ι΅ PART iajs-2006 41 73 𝐸 𝐸 PROPN iajs-2006 41 74 Ι΅ Ι΅ NOUN iajs-2006 41 75 π‘₯Χ€ π‘₯Χ€ VERB iajs-2006 41 76 the the DET iajs-2006 41 77 π‘Ÿ π‘Ÿ NOUN iajs-2006 41 78 moment moment NOUN iajs-2006 41 79 of of ADP iajs-2006 41 80 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 41 81 can can AUX iajs-2006 41 82 be be AUX iajs-2006 41 83 evaluated evaluate VERB iajs-2006 41 84 as as SCONJ iajs-2006 41 85 follows follow VERB iajs-2006 41 86 : : PUNCT iajs-2006 41 87 𝐸 𝐸 PROPN iajs-2006 41 88 Ι΅ Ι΅ SYM iajs-2006 41 89 𝑑׀ 𝑑׀ NOUN iajs-2006 41 90 Ι΅ Ι΅ SYM iajs-2006 41 91 β„Ž β„Ž PROPN iajs-2006 41 92 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 41 93 𝑑ɡ 𝑑ɡ NOUN iajs-2006 41 94 𝐸 𝐸 PROPN iajs-2006 41 95 Ι΅ Ι΅ NUM iajs-2006 41 96 𝑑׀ 𝑑׀ ADP iajs-2006 41 97 Π³ Π³ PROPN iajs-2006 41 98 𝛼 𝛼 VERB iajs-2006 41 99 𝑛 𝑛 ADP iajs-2006 41 100 π‘Ÿ π‘Ÿ PRON iajs-2006 41 101 Π³ Π³ X iajs-2006 41 102 𝛼 𝛼 VERB iajs-2006 41 103 𝑛 𝑛 PRON iajs-2006 41 104 𝑃 𝑃 NOUN iajs-2006 41 105 24 24 NUM iajs-2006 41 106 if if SCONJ iajs-2006 41 107 r=2 r=2 PROPN iajs-2006 41 108 then then ADV iajs-2006 41 109 𝐸 𝐸 PROPN iajs-2006 41 110 Ι΅ Ι΅ SYM iajs-2006 41 111 𝑑׀ 𝑑׀ NOUN iajs-2006 41 112 𝛼 𝛼 PART iajs-2006 41 113 𝑛 𝑛 DET iajs-2006 41 114 𝛼 𝛼 NOUN iajs-2006 41 115 𝑛 𝑛 DET iajs-2006 41 116 1 1 NUM iajs-2006 41 117 𝑃 𝑃 NOUN iajs-2006 41 118 hence hence ADV iajs-2006 41 119 , , PUNCT iajs-2006 41 120 Ι΅ Ι΅ NOUN iajs-2006 41 121 𝛼 𝛼 X iajs-2006 41 122 𝑛 𝑛 ADP iajs-2006 41 123 𝛼 𝛼 NOUN iajs-2006 41 124 𝑛 𝑛 PRON iajs-2006 41 125 1 1 NUM iajs-2006 41 126 𝑃 𝑃 NOUN iajs-2006 41 127 25 25 NUM iajs-2006 41 128 similarly similarly ADV iajs-2006 41 129 , , PUNCT iajs-2006 41 130 the the DET iajs-2006 41 131 π‘Ÿ π‘Ÿ NUM iajs-2006 41 132 bayes bayes PROPN iajs-2006 41 133 estimators estimator NOUN iajs-2006 41 134 of of ADP iajs-2006 41 135 the the DET iajs-2006 41 136 reliability reliability NOUN iajs-2006 41 137 function function NOUN iajs-2006 41 138 can can AUX iajs-2006 41 139 be be AUX iajs-2006 41 140 obtained obtain VERB iajs-2006 41 141 as as SCONJ iajs-2006 41 142 follows follow VERB iajs-2006 41 143 𝑅 𝑅 PROPN iajs-2006 41 144 𝑑 𝑑 PROPN iajs-2006 41 145 e e PROPN iajs-2006 41 146 𝑅 𝑅 PROPN iajs-2006 41 147 𝑑 𝑑 PROPN iajs-2006 41 148 𝑑׀ 𝑑׀ ADP iajs-2006 41 149 now now ADV iajs-2006 41 150 , , PUNCT iajs-2006 41 151 we we PRON iajs-2006 41 152 have have VERB iajs-2006 41 153 to to PART iajs-2006 41 154 determine determine VERB iajs-2006 41 155 e e NOUN iajs-2006 41 156 [ [ X iajs-2006 41 157 ( ( PUNCT iajs-2006 41 158 𝑅 𝑅 PROPN iajs-2006 41 159 𝑑 𝑑 PROPN iajs-2006 41 160 𝑑׀ 𝑑׀ ADP iajs-2006 41 161 e e PROPN iajs-2006 41 162 𝑅 𝑅 PROPN iajs-2006 41 163 𝑑 𝑑 PROPN iajs-2006 41 164 𝑑׀ 𝑑׀ ADP iajs-2006 41 165 𝑅 𝑅 PROPN iajs-2006 41 166 𝑑 𝑑 NOUN iajs-2006 41 167 β„Ž β„Ž PROPN iajs-2006 41 168 ɡ׀𝑑 ɡ׀𝑑 ADJ iajs-2006 41 169 𝑑ɡ 𝑑ɡ NOUN iajs-2006 41 170 𝑃 𝑃 NOUN iajs-2006 41 171 𝑃 𝑃 NOUN iajs-2006 41 172 2𝑑 2𝑑 NOUN iajs-2006 41 173 𝑅 𝑅 PROPN iajs-2006 41 174 𝑑 𝑑 NOUN iajs-2006 41 175 𝑃 𝑃 NOUN iajs-2006 41 176 𝑃 𝑃 NOUN iajs-2006 41 177 2𝑑 2𝑑 NOUN iajs-2006 41 178 26 26 NUM iajs-2006 41 179 7 7 NUM iajs-2006 41 180 . . PUNCT iajs-2006 42 1 bayes bayes PROPN iajs-2006 42 2 estimator estimator NOUN iajs-2006 42 3 when when SCONJ iajs-2006 42 4 ( ( PUNCT iajs-2006 42 5 linex linex ADV iajs-2006 42 6 ) ) PUNCT iajs-2006 42 7 is be AUX iajs-2006 42 8 adopted adopt VERB iajs-2006 42 9 a a PRON iajs-2006 42 10 : : PUNCT iajs-2006 42 11 the the DET iajs-2006 42 12 case case NOUN iajs-2006 42 13 of of ADP iajs-2006 42 14 jeffrey jeffrey PROPN iajs-2006 42 15 's 's PART iajs-2006 42 16 prior prior ADJ iajs-2006 42 17 information information NOUN iajs-2006 42 18 from from ADP iajs-2006 42 19 equation equation NOUN iajs-2006 42 20 ( ( PUNCT iajs-2006 42 21 11 11 NUM iajs-2006 42 22 ) ) PUNCT iajs-2006 42 23 we we PRON iajs-2006 42 24 have have VERB iajs-2006 42 25 Ι΅ Ι΅ NUM iajs-2006 42 26 𝑙𝑛 𝑙𝑛 NOUN iajs-2006 42 27 𝑒 𝑒 PROPN iajs-2006 42 28 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 42 29 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 42 30 π‘‘πœƒ π‘‘πœƒ PROPN iajs-2006 42 31 Ι΅ Ι΅ NUM iajs-2006 42 32 mathematics mathematic NOUN iajs-2006 43 1 | | ADV iajs-2006 43 2 140 140 NUM iajs-2006 43 3 ibn ibn PROPN iajs-2006 43 4 al al PROPN iajs-2006 43 5 - - PUNCT iajs-2006 43 6 haitham haitham PROPN iajs-2006 43 7 jour jour X iajs-2006 43 8 . . PROPN iajs-2006 44 1 for for ADP iajs-2006 44 2 pure pure ADJ iajs-2006 44 3 & & CCONJ iajs-2006 44 4 appl appl PROPN iajs-2006 44 5 . . PUNCT iajs-2006 45 1 sci sci PROPN iajs-2006 45 2 . . PROPN iajs-2006 45 3 ihjpas ihjpa VERB iajs-2006 45 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 45 5 vol vol NOUN iajs-2006 45 6 . . PROPN iajs-2006 45 7 31 31 NUM iajs-2006 45 8 ( ( PUNCT iajs-2006 45 9 3 3 NUM iajs-2006 45 10 ) ) PUNCT iajs-2006 45 11 2018 2018 NUM iajs-2006 45 12 hence hence ADV iajs-2006 45 13 , , PUNCT iajs-2006 45 14 Ι΅ Ι΅ ADV iajs-2006 45 15 𝑙𝑛 𝑙𝑛 X iajs-2006 45 16 𝑒 𝑒 PROPN iajs-2006 45 17 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 45 18 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 45 19 𝑑ɡ 𝑑ɡ NOUN iajs-2006 45 20 by by ADP iajs-2006 45 21 evaluating evaluate VERB iajs-2006 45 22 the the DET iajs-2006 45 23 integral integral ADJ iajs-2006 45 24 we we PRON iajs-2006 45 25 get get VERB iajs-2006 45 26 Ι΅ Ι΅ ADP iajs-2006 45 27 𝑙𝑛 𝑙𝑛 NOUN iajs-2006 45 28 𝑇 𝑇 PROPN iajs-2006 45 29 1 1 NUM iajs-2006 45 30 𝑇 𝑇 PROPN iajs-2006 45 31 27 27 NUM iajs-2006 45 32 the the DET iajs-2006 45 33 estimator estimator NOUN iajs-2006 45 34 of of ADP iajs-2006 45 35 the the DET iajs-2006 45 36 reliability reliability NOUN iajs-2006 45 37 function function NOUN iajs-2006 45 38 can can AUX iajs-2006 45 39 be be AUX iajs-2006 45 40 obtained obtain VERB iajs-2006 45 41 as as ADP iajs-2006 45 42 𝑅 𝑅 PROPN iajs-2006 45 43 𝑑 𝑑 PROPN iajs-2006 45 44 𝑒 𝑒 PROPN iajs-2006 45 45 Ι΅ Ι΅ PROPN iajs-2006 45 46 𝑅 𝑅 PROPN iajs-2006 45 47 𝑑 𝑑 PROPN iajs-2006 45 48 𝑇 𝑇 PROPN iajs-2006 45 49 1 1 NUM iajs-2006 45 50 𝑇 𝑇 PROPN iajs-2006 45 51 𝑑 𝑑 ADP iajs-2006 45 52 28 28 NUM iajs-2006 45 53 b b NOUN iajs-2006 45 54 : : PUNCT iajs-2006 45 55 the the DET iajs-2006 45 56 case case NOUN iajs-2006 45 57 of of ADP iajs-2006 45 58 gamma gamma NOUN iajs-2006 45 59 prior prior ADJ iajs-2006 45 60 distribution distribution NOUN iajs-2006 45 61 from from ADP iajs-2006 45 62 equation equation NOUN iajs-2006 45 63 ( ( PUNCT iajs-2006 45 64 11 11 NUM iajs-2006 45 65 ) ) PUNCT iajs-2006 45 66 we we PRON iajs-2006 45 67 have have VERB iajs-2006 45 68 Ι΅ Ι΅ NUM iajs-2006 45 69 𝑙𝑛 𝑙𝑛 NOUN iajs-2006 45 70 𝑒 𝑒 PROPN iajs-2006 45 71 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 45 72 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 45 73 π‘‘πœƒ π‘‘πœƒ PROPN iajs-2006 45 74 Ι΅ Ι΅ SYM iajs-2006 45 75 hence hence ADV iajs-2006 45 76 , , PUNCT iajs-2006 45 77 Ι΅ Ι΅ ADV iajs-2006 45 78 𝑙𝑛 𝑙𝑛 X iajs-2006 45 79 𝑒 𝑒 PROPN iajs-2006 45 80 Ι΅β„Ž Ι΅β„Ž PROPN iajs-2006 45 81 ɡ׀𝑑 ɡ׀𝑑 PROPN iajs-2006 45 82 𝑑ɡ 𝑑ɡ NOUN iajs-2006 45 83 by by ADP iajs-2006 45 84 evaluating evaluate VERB iajs-2006 45 85 the the DET iajs-2006 45 86 integral integral ADJ iajs-2006 45 87 we we PRON iajs-2006 45 88 get get VERB iajs-2006 45 89 Ι΅ Ι΅ ADP iajs-2006 45 90 𝑙𝑛 𝑙𝑛 NOUN iajs-2006 45 91 𝑃 𝑃 ADP iajs-2006 45 92 1 1 NUM iajs-2006 45 93 𝑃 𝑃 NOUN iajs-2006 45 94 29 29 NUM iajs-2006 45 95 the the DET iajs-2006 45 96 estimator estimator NOUN iajs-2006 45 97 of of ADP iajs-2006 45 98 the the DET iajs-2006 45 99 reliability reliability NOUN iajs-2006 45 100 function function NOUN iajs-2006 45 101 can can AUX iajs-2006 45 102 be be AUX iajs-2006 45 103 obtained obtain VERB iajs-2006 45 104 as as ADP iajs-2006 45 105 𝑅 𝑅 PROPN iajs-2006 45 106 𝑑 𝑑 PROPN iajs-2006 45 107 𝑒 𝑒 PROPN iajs-2006 45 108 Ι΅ Ι΅ PROPN iajs-2006 45 109 𝑅 𝑅 PROPN iajs-2006 45 110 𝑑 𝑑 PROPN iajs-2006 45 111 𝑃 𝑃 NOUN iajs-2006 45 112 1 1 NUM iajs-2006 45 113 𝑃 𝑃 NOUN iajs-2006 45 114 𝑑 𝑑 X iajs-2006 45 115 30 30 NUM iajs-2006 45 116 simulation simulation NOUN iajs-2006 45 117 study study NOUN iajs-2006 45 118 8 8 NUM iajs-2006 45 119 . . PUNCT iajs-2006 46 1 the the DET iajs-2006 46 2 simulation simulation NOUN iajs-2006 46 3 study study NOUN iajs-2006 46 4 was be AUX iajs-2006 46 5 conducted conduct VERB iajs-2006 46 6 in in ADP iajs-2006 46 7 order order NOUN iajs-2006 46 8 to to PART iajs-2006 46 9 compare compare VERB iajs-2006 46 10 the the DET iajs-2006 46 11 performance performance NOUN iajs-2006 46 12 of of ADP iajs-2006 46 13 the the DET iajs-2006 46 14 bayesian bayesian NOUN iajs-2006 46 15 estimators estimator NOUN iajs-2006 46 16 of of ADP iajs-2006 46 17 the the DET iajs-2006 46 18 reliability reliability NOUN iajs-2006 46 19 function function NOUN iajs-2006 46 20 r(t)of r(t)of NUM iajs-2006 46 21 one one NUM iajs-2006 46 22 parameter parameter NOUN iajs-2006 46 23 exponential exponential ADJ iajs-2006 46 24 distribution distribution NOUN iajs-2006 46 25 . . PUNCT iajs-2006 47 1 the the DET iajs-2006 47 2 integrated integrate VERB iajs-2006 47 3 mean mean NOUN iajs-2006 47 4 squared square VERB iajs-2006 47 5 error error NOUN iajs-2006 47 6 ( ( PUNCT iajs-2006 47 7 imse imse NOUN iajs-2006 47 8 ) ) PUNCT iajs-2006 47 9 as as ADP iajs-2006 47 10 a a DET iajs-2006 47 11 criterion criterion NOUN iajs-2006 47 12 of of ADP iajs-2006 47 13 comparison comparison NOUN iajs-2006 47 14 where where SCONJ iajs-2006 47 15 𝐼𝑀𝑆𝐸 𝐼𝑀𝑆𝐸 PROPN iajs-2006 47 16 𝑅 𝑅 PROPN iajs-2006 47 17 𝑑𝑖 𝑑𝑖 PUNCT iajs-2006 47 18 βˆ‘ βˆ‘ PUNCT iajs-2006 47 19 βˆ‘ βˆ‘ PROPN iajs-2006 47 20 𝑅 𝑅 PROPN iajs-2006 47 21 𝑑 𝑑 PROPN iajs-2006 47 22 𝑅 𝑅 PROPN iajs-2006 47 23 𝑑 𝑑 PROPN iajs-2006 47 24 1 1 NUM iajs-2006 47 25 𝑛 𝑛 PRON iajs-2006 47 26 𝑀𝑆𝐸 𝑀𝑆𝐸 PROPN iajs-2006 47 27 𝑅 𝑅 PROPN iajs-2006 47 28 𝑑 𝑑 PROPN iajs-2006 47 29 where where SCONJ iajs-2006 47 30 𝑛 𝑛 PROPN iajs-2006 47 31 is be AUX iajs-2006 47 32 the the DET iajs-2006 47 33 random random ADJ iajs-2006 47 34 limitsof limitsof NOUN iajs-2006 47 35 𝑑 𝑑 PROPN iajs-2006 47 36 , , PUNCT iajs-2006 47 37 using use VERB iajs-2006 47 38 t=(0.1,0.2,0.3,0.4 t=(0.1,0.2,0.3,0.4 ADP iajs-2006 47 39 , , PUNCT iajs-2006 47 40 0.5,0.6,0.7,0.8,0.9,1 0.5,0.6,0.7,0.8,0.9,1 NUM iajs-2006 47 41 ) ) PUNCT iajs-2006 47 42 l l NOUN iajs-2006 47 43 is be AUX iajs-2006 47 44 the the DET iajs-2006 47 45 number number NOUN iajs-2006 47 46 of of ADP iajs-2006 47 47 replications replication NOUN iajs-2006 47 48 which which PRON iajs-2006 47 49 we we PRON iajs-2006 47 50 assumed assume VERB iajs-2006 47 51 that that SCONJ iajs-2006 47 52 l=1000 l=1000 PROPN iajs-2006 47 53 in in ADP iajs-2006 47 54 our our PRON iajs-2006 47 55 study study NOUN iajs-2006 47 56 , , PUNCT iajs-2006 47 57 𝑅(𝑑 𝑅(𝑑 X iajs-2006 47 58 ) ) PUNCT iajs-2006 47 59 is be AUX iajs-2006 47 60 the the DET iajs-2006 47 61 estimator estimator NOUN iajs-2006 47 62 of of ADP iajs-2006 47 63 r(t r(t NOUN iajs-2006 47 64 ) ) PUNCT iajs-2006 47 65 at at ADP iajs-2006 47 66 the the DET iajs-2006 47 67 𝐿 𝐿 PROPN iajs-2006 47 68 replication replication NOUN iajs-2006 47 69 . . PUNCT iajs-2006 48 1 the the DET iajs-2006 48 2 bayesian bayesian NOUN iajs-2006 48 3 estimators estimator NOUN iajs-2006 48 4 of of ADP iajs-2006 48 5 r(t r(t NOUN iajs-2006 48 6 ) ) PUNCT iajs-2006 48 7 are be AUX iajs-2006 48 8 derived derive VERB iajs-2006 48 9 with with ADP iajs-2006 48 10 respect respect NOUN iajs-2006 48 11 to to ADP iajs-2006 48 12 three three NUM iajs-2006 48 13 loss loss NOUN iajs-2006 48 14 function function NOUN iajs-2006 48 15 which which PRON iajs-2006 48 16 are be AUX iajs-2006 48 17 the the DET iajs-2006 48 18 square square ADJ iajs-2006 48 19 error error NOUN iajs-2006 48 20 loss loss NOUN iajs-2006 48 21 function function NOUN iajs-2006 48 22 ( ( PUNCT iajs-2006 48 23 self),precautionary self),precautionary ADJ iajs-2006 48 24 error error NOUN iajs-2006 48 25 loss loss NOUN iajs-2006 48 26 function function NOUN iajs-2006 48 27 ( ( PUNCT iajs-2006 48 28 pself pself NOUN iajs-2006 48 29 ) ) PUNCT iajs-2006 48 30 and and CCONJ iajs-2006 48 31 linear linear ADJ iajs-2006 48 32 exponential exponential ADJ iajs-2006 48 33 error error NOUN iajs-2006 48 34 loss loss NOUN iajs-2006 48 35 function(linex function(linex NOUN iajs-2006 48 36 ) ) PUNCT iajs-2006 48 37 , , PUNCT iajs-2006 48 38 moreover moreover ADV iajs-2006 48 39 , , PUNCT iajs-2006 48 40 the the DET iajs-2006 48 41 informative informative ADJ iajs-2006 48 42 and and CCONJ iajs-2006 48 43 non non ADJ iajs-2006 48 44 - - ADJ iajs-2006 48 45 informative informative ADJ iajs-2006 48 46 prior prior ADV iajs-2006 48 47 were be AUX iajs-2006 48 48 postulated postulate VERB iajs-2006 48 49 .the .the PRON iajs-2006 48 50 sample sample NOUN iajs-2006 48 51 sizes size NOUN iajs-2006 48 52 n=10,50 n=10,50 PROPN iajs-2006 48 53 , , PUNCT iajs-2006 48 54 100 100 NUM iajs-2006 48 55 and and CCONJ iajs-2006 48 56 200 200 NUM iajs-2006 48 57 were be AUX iajs-2006 48 58 chosen choose VERB iajs-2006 48 59 to to PART iajs-2006 48 60 represent represent VERB iajs-2006 48 61 small small ADJ iajs-2006 48 62 , , PUNCT iajs-2006 48 63 moderate moderate ADJ iajs-2006 48 64 , , PUNCT iajs-2006 48 65 large large ADJ iajs-2006 48 66 and and CCONJ iajs-2006 48 67 very very ADV iajs-2006 48 68 large large ADJ iajs-2006 48 69 sample sample NOUN iajs-2006 48 70 sizes size NOUN iajs-2006 48 71 from from ADP iajs-2006 48 72 the the DET iajs-2006 48 73 one one NUM iajs-2006 48 74 parameter parameter NOUN iajs-2006 48 75 exponential exponential ADJ iajs-2006 48 76 distribution distribution NOUN iajs-2006 48 77 .the .the ADP iajs-2006 48 78 postulated postulate VERB iajs-2006 48 79 values value NOUN iajs-2006 48 80 of of ADP iajs-2006 48 81 the the DET iajs-2006 48 82 unique unique ADJ iajs-2006 48 83 parameter parameter NOUN iajs-2006 48 84 Ι΅ Ι΅ PART iajs-2006 48 85 were be AUX iajs-2006 48 86 Ι΅=0.5,1.5 Ι΅=0.5,1.5 PROPN iajs-2006 48 87 and and CCONJ iajs-2006 48 88 the the DET iajs-2006 48 89 values value NOUN iajs-2006 48 90 of of ADP iajs-2006 48 91 the the DET iajs-2006 48 92 parameters parameter NOUN iajs-2006 48 93 for for ADP iajs-2006 48 94 gamma gamma PROPN iajs-2006 48 95 prior prior ADV iajs-2006 48 96 were be AUX iajs-2006 48 97 Ξ±=0.3,1 Ξ±=0.3,1 NOUN iajs-2006 48 98 and and CCONJ iajs-2006 48 99 Ξ²=1.2,3 Ξ²=1.2,3 X iajs-2006 48 100 . . PUNCT iajs-2006 49 1 the the DET iajs-2006 49 2 results result NOUN iajs-2006 49 3 are be AUX iajs-2006 49 4 presented present VERB iajs-2006 49 5 in in ADP iajs-2006 49 6 tables table NOUN iajs-2006 49 7 below below ADV iajs-2006 49 8 : : PUNCT iajs-2006 49 9 mathematics mathematic NOUN iajs-2006 49 10 | | ADV iajs-2006 49 11 141 141 NUM iajs-2006 49 12 ibn ibn PROPN iajs-2006 49 13 al al PROPN iajs-2006 49 14 - - PUNCT iajs-2006 49 15 haitham haitham PROPN iajs-2006 49 16 jour jour X iajs-2006 49 17 . . PROPN iajs-2006 50 1 for for ADP iajs-2006 50 2 pure pure ADJ iajs-2006 50 3 & & CCONJ iajs-2006 50 4 appl appl PROPN iajs-2006 50 5 . . PUNCT iajs-2006 51 1 sci sci PROPN iajs-2006 51 2 . . PROPN iajs-2006 51 3 ihjpas ihjpa VERB iajs-2006 51 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 51 5 vol vol NOUN iajs-2006 51 6 . . PROPN iajs-2006 51 7 31 31 NUM iajs-2006 52 1 ( ( PUNCT iajs-2006 52 2 3 3 NUM iajs-2006 52 3 ) ) SYM iajs-2006 52 4 2018 2018 NUM iajs-2006 52 5 table table NOUN iajs-2006 52 6 1 1 NUM iajs-2006 52 7 . . PUNCT iajs-2006 53 1 ( ( PUNCT iajs-2006 53 2 imse imse PROPN iajs-2006 53 3 ’s ’s PART iajs-2006 53 4 ) ) PUNCT iajs-2006 53 5 values value NOUN iajs-2006 53 6 of of ADP iajs-2006 53 7 the the DET iajs-2006 53 8 reliability reliability NOUN iajs-2006 53 9 function function NOUN iajs-2006 53 10 estimators estimator NOUN iajs-2006 53 11 by by ADP iajs-2006 53 12 using use VERB iajs-2006 53 13 jeffrey jeffrey PROPN iajs-2006 53 14 's 's PART iajs-2006 53 15 prior prior ADJ iajs-2006 53 16 information information NOUN iajs-2006 53 17 at at ADP iajs-2006 53 18 Ι΅=0.5 Ι΅=0.5 VERB iajs-2006 53 19 200 200 NUM iajs-2006 53 20 100 100 NUM iajs-2006 53 21 50 50 NUM iajs-2006 53 22 10 10 NUM iajs-2006 53 23 n n NOUN iajs-2006 53 24 estimator estimator NOUN iajs-2006 53 25 0.002635 0.002635 NUM iajs-2006 53 26 0.004064 0.004064 NUM iajs-2006 53 27 0.004635 0.004635 NUM iajs-2006 53 28 0.000524 0.000524 NUM iajs-2006 53 29 jsqu jsqu NOUN iajs-2006 54 1 0.002632 0.002632 NUM iajs-2006 54 2 0.004041 0.004041 NUM iajs-2006 54 3 0.004524 0.004524 NUM iajs-2006 54 4 0.000484 0.000484 NUM iajs-2006 54 5 jpre jpre VERB iajs-2006 54 6 0.002981 0.002981 NUM iajs-2006 54 7 0.005875 0.005875 NUM iajs-2006 54 8 0.010603 0.010603 NUM iajs-2006 54 9 0.027725 0.027725 NUM iajs-2006 54 10 jlin jlin PROPN iajs-2006 54 11 table table NOUN iajs-2006 54 12 2 2 NUM iajs-2006 54 13 . . PUNCT iajs-2006 55 1 ( ( PUNCT iajs-2006 55 2 imse imse ADJ iajs-2006 55 3 ) ) PUNCT iajs-2006 55 4 values value NOUN iajs-2006 55 5 of of ADP iajs-2006 55 6 the the DET iajs-2006 55 7 reliability reliability NOUN iajs-2006 55 8 function function NOUN iajs-2006 55 9 estimators estimator NOUN iajs-2006 55 10 by by ADP iajs-2006 55 11 using use VERB iajs-2006 55 12 jeffrey jeffrey PROPN iajs-2006 55 13 's 's PART iajs-2006 55 14 prior prior ADJ iajs-2006 55 15 information information NOUN iajs-2006 55 16 at at ADP iajs-2006 55 17 Ι΅=1.5 Ι΅=1.5 NOUN iajs-2006 55 18 200 200 NUM iajs-2006 55 19 100 100 NUM iajs-2006 55 20 50 50 NUM iajs-2006 55 21 10 10 NUM iajs-2006 55 22 n n NOUN iajs-2006 55 23 estimator estimator NOUN iajs-2006 55 24 0.001260 0.001260 NUM iajs-2006 55 25 0.002309 0.002309 NUM iajs-2006 55 26 0.003425 0.003425 NUM iajs-2006 55 27 0.000963 0.000963 NUM iajs-2006 55 28 jsqu jsqu NOUN iajs-2006 55 29 0.001259 0.001259 NUM iajs-2006 55 30 0.002301 0.002301 NUM iajs-2006 55 31 0.003376 0.003376 NUM iajs-2006 55 32 0.000932 0.000932 NUM iajs-2006 55 33 jpre jpre NOUN iajs-2006 55 34 0.001279 0.001279 NUM iajs-2006 55 35 0.002565 0.002565 NUM iajs-2006 55 36 0.005140 0.005140 NUM iajs-2006 55 37 0.019773 0.019773 NUM iajs-2006 55 38 jlin jlin PROPN iajs-2006 55 39 table table NOUN iajs-2006 55 40 3 3 NUM iajs-2006 55 41 . . 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PROPN iajs-2006 60 1 for for ADP iajs-2006 60 2 pure pure ADJ iajs-2006 60 3 & & CCONJ iajs-2006 60 4 appl appl PROPN iajs-2006 60 5 . . PUNCT iajs-2006 61 1 sci sci PROPN iajs-2006 61 2 . . PROPN iajs-2006 61 3 ihjpas ihjpa VERB iajs-2006 61 4 https://doi.org/10.30526/31.3.2006 https://doi.org/10.30526/31.3.2006 ADJ iajs-2006 61 5 vol vol NOUN iajs-2006 61 6 . . PROPN iajs-2006 61 7 31 31 NUM iajs-2006 61 8 ( ( PUNCT iajs-2006 61 9 3 3 NUM iajs-2006 61 10 ) ) PUNCT iajs-2006 61 11 2018 2018 NUM iajs-2006 61 12 0.001279 0.001279 NUM iajs-2006 61 13 0.002564 0.002564 NUM iajs-2006 61 14 0.005081 0.005081 NUM iajs-2006 61 15 0.017556 0.017556 NUM iajs-2006 61 16 Ξ²=3 Ξ²=3 PUNCT iajs-2006 61 17 glin glin NOUN iajs-2006 61 18 0.001279 0.001279 NUM iajs-2006 61 19 0.002565 0.002565 NUM iajs-2006 61 20 0.005127 0.005127 NUM iajs-2006 61 21 0.019206 0.019206 NUM iajs-2006 61 22 Ξ²=1.2 Ξ²=1.2 NOUN iajs-2006 61 23 Ξ±=1 Ξ±=1 SYM iajs-2006 61 24 0.001279 0.001279 NUM iajs-2006 61 25 0.002564 0.002564 NUM iajs-2006 61 26 0.005087 0.005087 NUM iajs-2006 61 27 0.017887 0.017887 NUM iajs-2006 61 28 Ξ²=3 Ξ²=3 SYM iajs-2006 61 29 simulation simulation NOUN iajs-2006 61 30 results result NOUN iajs-2006 61 31 and and CCONJ iajs-2006 61 32 conclusions conclusion NOUN iajs-2006 61 33 9 9 NUM iajs-2006 61 34 . . PUNCT iajs-2006 62 1 from from ADP iajs-2006 62 2 our our PRON iajs-2006 62 3 simulation simulation NOUN iajs-2006 62 4 study study NOUN iajs-2006 62 5 , , PUNCT iajs-2006 62 6 the the DET iajs-2006 62 7 following follow VERB iajs-2006 62 8 results result NOUN iajs-2006 62 9 are be AUX iajs-2006 62 10 clear clear ADJ iajs-2006 62 11 ο‚· ο‚· NOUN iajs-2006 62 12 from from ADP iajs-2006 62 13 table table NOUN iajs-2006 62 14 1 1 NUM iajs-2006 62 15 . . PUNCT iajs-2006 62 16 and and CCONJ iajs-2006 62 17 table table NOUN iajs-2006 62 18 2 2 NUM iajs-2006 62 19 . . PUNCT iajs-2006 62 20 : : PUNCT iajs-2006 62 21 the the DET iajs-2006 62 22 bayes bayes PROPN iajs-2006 62 23 estimator estimator NOUN iajs-2006 62 24 under under ADP iajs-2006 62 25 ο‚· ο‚· NOUN iajs-2006 62 26 precautionary precautionary ADJ iajs-2006 62 27 error error NOUN iajs-2006 62 28 loss loss NOUN iajs-2006 62 29 function function NOUN iajs-2006 62 30 with with ADP iajs-2006 62 31 jeffrey jeffrey PROPN iajs-2006 62 32 's 's PART iajs-2006 62 33 prior prior NOUN iajs-2006 62 34 is be AUX iajs-2006 62 35 the the DET iajs-2006 62 36 best good ADJ iajs-2006 62 37 comparing comparing NOUN iajs-2006 62 38 to to ADP iajs-2006 62 39 other other ADJ iajs-2006 62 40 estimators estimator NOUN iajs-2006 62 41 for for ADP iajs-2006 62 42 all all DET iajs-2006 62 43 sample sample NOUN iajs-2006 62 44 sizes size NOUN iajs-2006 62 45 . . PUNCT iajs-2006 63 1 ο‚· ο‚· NOUN iajs-2006 63 2 from from ADP iajs-2006 63 3 table table NOUN iajs-2006 63 4 3 3 NUM iajs-2006 63 5 . . PUNCT iajs-2006 63 6 : : PUNCT iajs-2006 64 1 the the DET iajs-2006 64 2 bayes bayes PROPN iajs-2006 64 3 estimator estimator NOUN iajs-2006 64 4 under under ADP iajs-2006 64 5 precautionary precautionary ADJ iajs-2006 64 6 error error NOUN iajs-2006 64 7 loss loss NOUN iajs-2006 64 8 function function NOUN iajs-2006 64 9 with with ADP iajs-2006 64 10 gamma gamma PROPN iajs-2006 64 11 prior prior ADV iajs-2006 64 12 ( ( PUNCT iajs-2006 64 13 Ξ±=0.3 Ξ±=0.3 ADV iajs-2006 64 14 , , PUNCT iajs-2006 64 15 Ξ²=3 Ξ²=3 PUNCT iajs-2006 64 16 ) ) PUNCT iajs-2006 64 17 is be AUX iajs-2006 64 18 the the DET iajs-2006 64 19 best good ADJ iajs-2006 64 20 comparing comparing NOUN iajs-2006 64 21 to to ADP iajs-2006 64 22 other other ADJ iajs-2006 64 23 estimators estimator NOUN iajs-2006 64 24 for for ADP iajs-2006 64 25 all all DET iajs-2006 64 26 sample sample NOUN iajs-2006 64 27 sizes size NOUN iajs-2006 64 28 . . PUNCT iajs-2006 65 1 ο‚· ο‚· NOUN iajs-2006 65 2 from from ADP iajs-2006 65 3 table table NOUN iajs-2006 65 4 4 4 NUM iajs-2006 65 5 . . PUNCT iajs-2006 65 6 : : PUNCT iajs-2006 65 7 for for ADP iajs-2006 65 8 ( ( PUNCT iajs-2006 65 9 n=10 n=10 NOUN iajs-2006 65 10 ) ) PUNCT iajs-2006 65 11 the the DET iajs-2006 65 12 performance performance NOUN iajs-2006 65 13 of of ADP iajs-2006 65 14 bayes bayes PROPN iajs-2006 65 15 estimator estimator NOUN iajs-2006 65 16 under under ADP iajs-2006 65 17 squared square VERB iajs-2006 65 18 error error NOUN iajs-2006 65 19 loss loss NOUN iajs-2006 65 20 function function NOUN iajs-2006 65 21 with with ADP iajs-2006 65 22 gamma gamma PROPN iajs-2006 65 23 prior prior ADV iajs-2006 65 24 ( ( PUNCT iajs-2006 65 25 Ξ±=1 Ξ±=1 NOUN iajs-2006 65 26 , , PUNCT iajs-2006 65 27 Ξ²=1.2 Ξ²=1.2 NOUN iajs-2006 65 28 ) ) PUNCT iajs-2006 65 29 is be AUX iajs-2006 65 30 the the DET iajs-2006 65 31 best good ADJ iajs-2006 65 32 , , PUNCT iajs-2006 65 33 and and CCONJ iajs-2006 65 34 for for ADP iajs-2006 65 35 ( ( PUNCT iajs-2006 65 36 n=50,100 n=50,100 NOUN iajs-2006 65 37 ) ) PUNCT iajs-2006 65 38 the the DET iajs-2006 65 39 performance performance NOUN iajs-2006 65 40 of of ADP iajs-2006 65 41 bayes bayes PROPN iajs-2006 65 42 estimator estimator NOUN iajs-2006 65 43 under under ADP iajs-2006 65 44 precautionary precautionary ADJ iajs-2006 65 45 error error NOUN iajs-2006 65 46 loss loss NOUN iajs-2006 65 47 function function NOUN iajs-2006 65 48 with with ADP iajs-2006 65 49 gamma gamma PROPN iajs-2006 65 50 prior prior ADV iajs-2006 65 51 ( ( PUNCT iajs-2006 65 52 Ξ±=0.3 Ξ±=0.3 ADV iajs-2006 65 53 , , PUNCT iajs-2006 65 54 Ξ²=3 Ξ²=3 PUNCT iajs-2006 65 55 ) ) PUNCT iajs-2006 65 56 is be AUX iajs-2006 65 57 the the DET iajs-2006 65 58 best good ADJ iajs-2006 65 59 and and CCONJ iajs-2006 65 60 for for ADP iajs-2006 65 61 ( ( PUNCT iajs-2006 65 62 n=200 n=200 PROPN iajs-2006 65 63 ) ) PUNCT iajs-2006 65 64 the the DET iajs-2006 65 65 performance performance NOUN iajs-2006 65 66 of of ADP iajs-2006 65 67 bayes bayes PROPN iajs-2006 65 68 estimator estimator NOUN iajs-2006 65 69 under under ADP iajs-2006 65 70 precautionary precautionary ADJ iajs-2006 65 71 error error NOUN iajs-2006 65 72 loss loss NOUN iajs-2006 65 73 function function NOUN iajs-2006 65 74 with with ADP iajs-2006 65 75 gamma gamma PROPN iajs-2006 65 76 prior prior ADV iajs-2006 65 77 ( ( PUNCT iajs-2006 65 78 Ξ±=1 Ξ±=1 X iajs-2006 65 79 , , PUNCT iajs-2006 65 80 Ξ²=3 Ξ²=3 NUM iajs-2006 65 81 ) ) PUNCT iajs-2006 65 82 is be AUX iajs-2006 65 83 the the DET iajs-2006 65 84 best good ADJ iajs-2006 65 85 . . PUNCT iajs-2006 66 1 ο‚· ο‚· NOUN iajs-2006 66 2 that that PRON iajs-2006 66 3 is be AUX iajs-2006 66 4 the the DET iajs-2006 66 5 performance performance NOUN iajs-2006 66 6 of of ADP iajs-2006 66 7 bayes bayes PROPN iajs-2006 66 8 estimator estimator NOUN iajs-2006 66 9 under under ADP iajs-2006 66 10 precautionary precautionary ADJ iajs-2006 66 11 error error NOUN iajs-2006 66 12 loss loss NOUN iajs-2006 66 13 function function NOUN iajs-2006 66 14 is be AUX iajs-2006 66 15 superior superior ADJ iajs-2006 66 16 to to ADP iajs-2006 66 17 the the DET iajs-2006 66 18 performance performance NOUN iajs-2006 66 19 of of ADP iajs-2006 66 20 other other ADJ iajs-2006 66 21 estimators estimator NOUN iajs-2006 66 22 in in ADP iajs-2006 66 23 almost almost ADV iajs-2006 66 24 cases case NOUN iajs-2006 66 25 that that PRON iajs-2006 66 26 are be AUX iajs-2006 66 27 studied study VERB iajs-2006 66 28 in in ADP iajs-2006 66 29 this this DET iajs-2006 66 30 paper paper NOUN iajs-2006 66 31 , , PUNCT iajs-2006 66 32 where where SCONJ iajs-2006 66 33 the the DET iajs-2006 66 34 integrated integrate VERB iajs-2006 66 35 mean mean NOUN iajs-2006 66 36 squared square VERB iajs-2006 66 37 error error NOUN iajs-2006 66 38 ( ( PUNCT iajs-2006 66 39 imse imse NOUN iajs-2006 66 40 ) ) PUNCT iajs-2006 66 41 is be AUX iajs-2006 66 42 employed employ VERB iajs-2006 66 43 as as ADP iajs-2006 66 44 a a DET iajs-2006 66 45 criterion criterion NOUN iajs-2006 66 46 to to PART iajs-2006 66 47 assess assess VERB iajs-2006 66 48 the the DET iajs-2006 66 49 performance performance NOUN iajs-2006 66 50 of of ADP iajs-2006 66 51 such such ADJ iajs-2006 66 52 estimators estimator NOUN iajs-2006 66 53 . . PUNCT iajs-2006 67 1 references reference NOUN iajs-2006 67 2 1 1 NUM iajs-2006 67 3 . . PUNCT iajs-2006 68 1 meeker meeker PROPN iajs-2006 68 2 , , PUNCT iajs-2006 68 3 w.q w.q PROPN iajs-2006 68 4 . . PUNCT iajs-2006 68 5 ; ; PUNCT iajs-2006 69 1 escobar escobar PROPN iajs-2006 69 2 , , PUNCT iajs-2006 69 3 l.u l.u PROPN iajs-2006 69 4 .statistical .statistical PRON iajs-2006 69 5 methods method NOUN iajs-2006 69 6 for for ADP iajs-2006 69 7 reliability reliability NOUN iajs-2006 69 8 data datum NOUN iajs-2006 69 9 . . PUNCT iajs-2006 70 1 john john PROPN iajs-2006 70 2 wiley wiley PROPN iajs-2006 70 3 & & CCONJ iajs-2006 70 4 sons sons PROPN iajs-2006 70 5 . . PUNCT iajs-2006 70 6 inc inc PROPN iajs-2006 70 7 , , PUNCT iajs-2006 70 8 canada canada PROPN iajs-2006 70 9 . . PUNCT iajs-2006 71 1 1998 1998 NUM iajs-2006 71 2 . . PUNCT iajs-2006 72 1 2 2 X iajs-2006 72 2 . . X iajs-2006 72 3 pugh pugh PROPN iajs-2006 72 4 , , PUNCT iajs-2006 72 5 e.l e.l PROPN iajs-2006 72 6 . . PUNCT iajs-2006 73 1 the the DET iajs-2006 73 2 best good ADJ iajs-2006 73 3 estimation estimation NOUN iajs-2006 73 4 of of ADP iajs-2006 73 5 reliability reliability NOUN iajs-2006 73 6 in in ADP iajs-2006 73 7 the the DET iajs-2006 73 8 exponential exponential ADJ iajs-2006 73 9 case case NOUN iajs-2006 73 10 . . PUNCT iajs-2006 74 1 journal journal PROPN iajs-2006 74 2 of of ADP iajs-2006 74 3 operation operation NOUN iajs-2006 74 4 research research NOUN iajs-2006 74 5 . . PUNCT iajs-2006 75 1 1993 1993 NUM iajs-2006 75 2 , , PUNCT iajs-2006 75 3 ii ii PROPN iajs-2006 75 4 . . PROPN iajs-2006 76 1 3 3 X iajs-2006 76 2 . . X iajs-2006 76 3 hogg hogg PROPN iajs-2006 76 4 , , PUNCT iajs-2006 76 5 r.v r.v PROPN iajs-2006 76 6 . . PROPN iajs-2006 76 7 ; ; PUNCT iajs-2006 76 8 graig graig PROPN iajs-2006 76 9 , , PUNCT iajs-2006 76 10 a.t a.t PROPN iajs-2006 76 11 . . PROPN iajs-2006 76 12 introduction introduction NOUN iajs-2006 76 13 to to ADP iajs-2006 76 14 mathematical mathematical ADJ iajs-2006 76 15 statistics statistic NOUN iajs-2006 76 16 . . PUNCT iajs-2006 77 1 4 4 NUM iajs-2006 77 2 edition edition NOUN iajs-2006 77 3 . . PUNCT iajs-2006 78 1 mocmillan mocmillan PROPN iajs-2006 78 2 pub pub NOUN iajs-2006 78 3 . . PUNCT iajs-2006 79 1 co. co. PROPN iajs-2006 79 2 new new PROPN iajs-2006 79 3 york york PROPN iajs-2006 79 4 . . PUNCT iajs-2006 80 1 1978 1978 NUM iajs-2006 80 2 . . PUNCT iajs-2006 81 1 4 4 X iajs-2006 81 2 . . X iajs-2006 81 3 dey dey PROPN iajs-2006 81 4 , , PUNCT iajs-2006 81 5 s. s. PROPN iajs-2006 81 6 bayesian bayesian NOUN iajs-2006 81 7 estimation estimation NOUN iajs-2006 81 8 of of ADP iajs-2006 81 9 the the DET iajs-2006 81 10 parameter parameter NOUN iajs-2006 81 11 and and CCONJ iajs-2006 81 12 reliability reliability NOUN iajs-2006 81 13 function function NOUN iajs-2006 81 14 of of ADP iajs-2006 81 15 inverse inverse NOUN iajs-2006 81 16 rayleigh rayleigh NOUN iajs-2006 81 17 distribution distribution NOUN iajs-2006 81 18 . . PUNCT iajs-2006 82 1 malaysian malaysian ADJ iajs-2006 82 2 journal journal PROPN iajs-2006 82 3 of of ADP iajs-2006 82 4 mathematical mathematical ADJ iajs-2006 82 5 science science NOUN iajs-2006 82 6 . . PUNCT iajs-2006 83 1 2012 2012 NUM iajs-2006 83 2 , , PUNCT iajs-2006 83 3 6 6 NUM iajs-2006 83 4 , , PUNCT iajs-2006 83 5 1,113 1,113 NUM iajs-2006 83 6 - - SYM iajs-2006 83 7 124 124 NUM iajs-2006 83 8 . . PUNCT iajs-2006 84 1 5.rasheed 5.rasheed NUM iajs-2006 84 2 , , PUNCT iajs-2006 84 3 h.a h.a PROPN iajs-2006 84 4 . . PROPN iajs-2006 84 5 ; ; PUNCT iajs-2006 84 6 al al PROPN iajs-2006 84 7 - - PUNCT iajs-2006 84 8 gazi gazi PROPN iajs-2006 84 9 , , PUNCT iajs-2006 84 10 n.a.a n.a.a PROPN iajs-2006 84 11 . . PUNCT iajs-2006 84 12 bayesian bayesian NOUN iajs-2006 84 13 estimation estimation NOUN iajs-2006 84 14 for for ADP iajs-2006 84 15 the the DET iajs-2006 84 16 reliability reliability NOUN iajs-2006 84 17 function function NOUN iajs-2006 84 18 of of ADP iajs-2006 84 19 pareto pareto ADJ iajs-2006 84 20 type type NOUN iajs-2006 84 21 ΞΉ ΞΉ PRON iajs-2006 84 22 distribution distribution NOUN iajs-2006 84 23 under under ADP iajs-2006 84 24 generalized generalized ADJ iajs-2006 84 25 square square ADJ iajs-2006 84 26 error error NOUN iajs-2006 84 27 loss loss NOUN iajs-2006 84 28 function function NOUN iajs-2006 84 29 . . PUNCT iajs-2006 85 1 international international ADJ iajs-2006 85 2 journal journal NOUN iajs-2006 85 3 of of ADP iajs-2006 85 4 engineering engineering NOUN iajs-2006 85 5 and and CCONJ iajs-2006 85 6 innovative innovative ADJ iajs-2006 85 7 technology technology NOUN iajs-2006 85 8 ( ( PUNCT iajs-2006 85 9 ijeit ijeit ADJ iajs-2006 85 10 ) ) PUNCT iajs-2006 85 11 .2014 .2014 PROPN iajs-2006 85 12 , , PUNCT iajs-2006 85 13 4 4 NUM iajs-2006 85 14 , , PUNCT iajs-2006 85 15 6 6 NUM iajs-2006 85 16 , , PUNCT iajs-2006 85 17 105 105 NUM iajs-2006 85 18 - - SYM iajs-2006 85 19 112 112 NUM iajs-2006 85 20 . . PUNCT iajs-2006 86 1 6 6 NUM iajs-2006 86 2 . . X iajs-2006 87 1 kuo kuo PROPN iajs-2006 87 2 , , PUNCT iajs-2006 87 3 w. w. PROPN iajs-2006 87 4 ; ; PUNCT iajs-2006 87 5 zuo zuo PROPN iajs-2006 87 6 , , PUNCT iajs-2006 87 7 m.j m.j PROPN iajs-2006 87 8 . . PROPN iajs-2006 87 9 optimal optimal ADJ iajs-2006 87 10 reliability reliability NOUN iajs-2006 87 11 modeling model VERB iajs-2006 87 12 principles principle NOUN iajs-2006 87 13 and and CCONJ iajs-2006 87 14 applications application NOUN iajs-2006 87 15 . . PUNCT iajs-2006 88 1 john john PROPN iajs-2006 88 2 wiley wiley PROPN iajs-2006 88 3 & & CCONJ iajs-2006 88 4 sons sons PROPN iajs-2006 88 5 , , PUNCT iajs-2006 88 6 inc inc PROPN iajs-2006 88 7 , , PUNCT iajs-2006 88 8 hoboken hoboken PROPN iajs-2006 88 9 , , PUNCT iajs-2006 88 10 new new PROPN iajs-2006 88 11 jersey jersey PROPN iajs-2006 88 12 . . PUNCT iajs-2006 88 13 2003 2003 NUM iajs-2006 88 14 . . PUNCT