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X iajs-2284 7 3 introduction introduction NOUN iajs-2284 7 4 the the DET iajs-2284 7 5 power power NOUN iajs-2284 7 6 function function NOUN iajs-2284 7 7 distribution distribution NOUN iajs-2284 7 8 represents represent VERB iajs-2284 7 9 one one NUM iajs-2284 7 10 of of ADP iajs-2284 7 11 the the DET iajs-2284 7 12 most most ADV iajs-2284 7 13 important important ADJ iajs-2284 7 14 distribution distribution NOUN iajs-2284 7 15 approach approach NOUN iajs-2284 7 16 in in ADP iajs-2284 7 17 statistical statistical ADJ iajs-2284 7 18 process process NOUN iajs-2284 7 19 . . PUNCT iajs-2284 8 1 it it PRON iajs-2284 8 2 can can AUX iajs-2284 8 3 be be AUX iajs-2284 8 4 expressed express VERB iajs-2284 8 5 by by ADP iajs-2284 8 6 π‘₯~π‘π‘œπ‘€(π‘₯ π‘₯~π‘π‘œπ‘€(π‘₯ NOUN iajs-2284 8 7 , , PUNCT iajs-2284 8 8 𝛼 𝛼 NOUN iajs-2284 8 9 ) ) PUNCT iajs-2284 8 10 . . 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PUNCT iajs-2284 10 1 this this DET iajs-2284 10 2 distribution distribution NOUN iajs-2284 10 3 has have AUX iajs-2284 10 4 been be AUX iajs-2284 10 5 introduced introduce VERB iajs-2284 10 6 in in ADP iajs-2284 10 7 ( ( PUNCT iajs-2284 10 8 1967 1967 NUM iajs-2284 10 9 ) ) PUNCT iajs-2284 10 10 by by ADP iajs-2284 10 11 malik malik PROPN iajs-2284 10 12 h.j h.j PROPN iajs-2284 10 13 throughout throughout ADP iajs-2284 10 14 studying study VERB iajs-2284 10 15 the the DET iajs-2284 10 16 exact exact ADJ iajs-2284 10 17 moment moment NOUN iajs-2284 10 18 of of ADP iajs-2284 10 19 power power NOUN iajs-2284 10 20 function function NOUN iajs-2284 10 21 distribution distribution NOUN iajs-2284 10 22 and and CCONJ iajs-2284 10 23 found find VERB iajs-2284 10 24 a a DET iajs-2284 10 25 precise precise ADJ iajs-2284 10 26 expression expression NOUN iajs-2284 10 27 for for ADP iajs-2284 10 28 moment moment NOUN iajs-2284 10 29 of of ADP iajs-2284 10 30 power power NOUN iajs-2284 10 31 function function NOUN iajs-2284 10 32 distribution distribution NOUN iajs-2284 10 33 [ [ X iajs-2284 10 34 2 2 NUM iajs-2284 10 35 ] ] PUNCT iajs-2284 10 36 . . PUNCT iajs-2284 11 1 although although SCONJ iajs-2284 11 2 bayesian bayesian NOUN iajs-2284 11 3 estimation estimation NOUN iajs-2284 11 4 method method NOUN iajs-2284 11 5 of of ADP iajs-2284 11 6 parameters parameter NOUN iajs-2284 11 7 have have AUX iajs-2284 11 8 been be AUX iajs-2284 11 9 used use VERB iajs-2284 11 10 by by ADP iajs-2284 11 11 several several ADJ iajs-2284 11 12 statisticians statistician NOUN iajs-2284 11 13 and and CCONJ iajs-2284 11 14 mathematical mathematical ADJ iajs-2284 11 15 analysts analyst NOUN iajs-2284 11 16 , , PUNCT iajs-2284 11 17 but but CCONJ iajs-2284 11 18 many many ADJ iajs-2284 11 19 researchers researcher NOUN iajs-2284 11 20 considered consider VERB iajs-2284 11 21 the the DET iajs-2284 11 22 power power NOUN iajs-2284 11 23 function function NOUN iajs-2284 11 24 distribution distribution NOUN iajs-2284 11 25 is be AUX iajs-2284 11 26 better well ADJ iajs-2284 11 27 than than ADP iajs-2284 11 28 a a DET iajs-2284 11 29 lot lot NOUN iajs-2284 11 30 of of ADP iajs-2284 11 31 distributions distribution NOUN iajs-2284 11 32 such such ADJ iajs-2284 11 33 as as ADP iajs-2284 11 34 lognormal lognormal ADJ iajs-2284 11 35 distribution distribution NOUN iajs-2284 11 36 , , PUNCT iajs-2284 11 37 exponential exponential ADJ iajs-2284 11 38 distribution distribution NOUN iajs-2284 11 39 and and CCONJ iajs-2284 11 40 weibull weibull NOUN iajs-2284 11 41 distribution distribution NOUN iajs-2284 11 42 . . PUNCT iajs-2284 12 1 the the DET iajs-2284 12 2 power power NOUN iajs-2284 12 3 function function NOUN iajs-2284 12 4 distribution distribution NOUN iajs-2284 12 5 is be AUX iajs-2284 12 6 as as ADP iajs-2284 12 7 a a DET iajs-2284 12 8 special special ADJ iajs-2284 12 9 case case NOUN iajs-2284 12 10 for for ADP iajs-2284 12 11 person person NOUN iajs-2284 12 12 first first ADJ iajs-2284 12 13 kind kind ADJ iajs-2284 12 14 distribution distribution NOUN iajs-2284 12 15 that that PRON iajs-2284 12 16 represents represent VERB iajs-2284 12 17 the the DET iajs-2284 12 18 simplicity simplicity NOUN iajs-2284 12 19 of of ADP iajs-2284 12 20 the the DET iajs-2284 12 21 moments moment NOUN iajs-2284 12 22 for for ADP iajs-2284 12 23 power power NOUN iajs-2284 12 24 function function NOUN iajs-2284 12 25 distribution distribution NOUN iajs-2284 12 26 [ [ X iajs-2284 12 27 3 3 NUM iajs-2284 12 28 ] ] PUNCT iajs-2284 12 29 . . PUNCT iajs-2284 13 1 in in ADP iajs-2284 13 2 fact fact NOUN iajs-2284 13 3 blue blue ADJ iajs-2284 13 4 estimation estimation NOUN iajs-2284 13 5 method method NOUN iajs-2284 13 6 has have AUX iajs-2284 13 7 been be AUX iajs-2284 13 8 introduced introduce VERB iajs-2284 13 9 for for ADP iajs-2284 13 10 the the DET iajs-2284 13 11 estimation estimation NOUN iajs-2284 13 12 of of ADP iajs-2284 13 13 the the DET iajs-2284 13 14 scale scale NOUN iajs-2284 13 15 and and CCONJ iajs-2284 13 16 location location NOUN iajs-2284 13 17 parameter parameter NOUN iajs-2284 13 18 from from ADP iajs-2284 13 19 the the DET iajs-2284 13 20 log log NOUN iajs-2284 13 21 - - PUNCT iajs-2284 13 22 gamma gamma NOUN iajs-2284 13 23 distribution distribution NOUN iajs-2284 13 24 . . PUNCT iajs-2284 14 1 many many ADJ iajs-2284 14 2 of of ADP iajs-2284 14 3 others other NOUN iajs-2284 14 4 researchers researcher NOUN iajs-2284 14 5 were be AUX iajs-2284 14 6 presented present VERB iajs-2284 14 7 estimations estimation NOUN iajs-2284 14 8 of of ADP iajs-2284 14 9 normal normal ADJ iajs-2284 14 10 distribution distribution NOUN iajs-2284 14 11 parameters parameter NOUN iajs-2284 14 12 by by ADP iajs-2284 14 13 using use VERB iajs-2284 14 14 likelihood likelihood NOUN iajs-2284 14 15 function function NOUN iajs-2284 14 16 [ [ X iajs-2284 14 17 4 4 NUM iajs-2284 14 18 - - SYM iajs-2284 14 19 6 6 NUM iajs-2284 14 20 ] ] PUNCT iajs-2284 14 21 . . PUNCT iajs-2284 15 1 the the DET iajs-2284 15 2 aim aim NOUN iajs-2284 15 3 of of ADP iajs-2284 15 4 this this DET iajs-2284 15 5 work work NOUN iajs-2284 15 6 is be AUX iajs-2284 15 7 to to PART iajs-2284 15 8 estimate estimate VERB iajs-2284 15 9 the the DET iajs-2284 15 10 reliability reliability NOUN iajs-2284 15 11 system system NOUN iajs-2284 15 12 in in ADP iajs-2284 15 13 the the DET iajs-2284 15 14 stressstrength stressstrength NOUN iajs-2284 15 15 model model NOUN iajs-2284 15 16 of of ADP iajs-2284 15 17 power power NOUN iajs-2284 15 18 function function NOUN iajs-2284 15 19 distribution distribution NOUN iajs-2284 15 20 . . PUNCT iajs-2284 16 1 ibn ibn PROPN iajs-2284 16 2 al al PROPN iajs-2284 16 3 haitham haitham PROPN iajs-2284 16 4 journal journal PROPN iajs-2284 16 5 for for ADP iajs-2284 16 6 pure pure ADJ iajs-2284 16 7 and and CCONJ iajs-2284 16 8 applied apply VERB iajs-2284 16 9 science science NOUN iajs-2284 16 10 journal journal PROPN iajs-2284 16 11 homepage homepage NOUN iajs-2284 16 12 : : PUNCT iajs-2284 16 13 http://jih.uobaghdad.edu.iq/index.php/j/index http://jih.uobaghdad.edu.iq/index.php/j/index PROPN iajs-2284 16 14 doi:10.30526/32.3.2284 doi:10.30526/32.3.2284 PROPN iajs-2284 16 15 article article NOUN iajs-2284 16 16 history history NOUN iajs-2284 16 17 : : PUNCT iajs-2284 16 18 received receive VERB iajs-2284 16 19 24 24 NUM iajs-2284 16 20 february february PROPN iajs-2284 16 21 2019 2019 NUM iajs-2284 16 22 , , PUNCT iajs-2284 16 23 accepted accept VERB iajs-2284 16 24 14 14 NUM iajs-2284 16 25 april april PROPN iajs-2284 16 26 2019 2019 NUM iajs-2284 16 27 , , PUNCT iajs-2284 16 28 publish publish VERB iajs-2284 16 29 september september PROPN iajs-2284 16 30 2019 2019 NUM iajs-2284 16 31 . . 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PUNCT iajs-2284 26 1 in in ADP iajs-2284 26 2 special special ADJ iajs-2284 26 3 case case NOUN iajs-2284 26 4 , , PUNCT iajs-2284 26 5 if if SCONJ iajs-2284 26 6 πœƒ πœƒ NUM iajs-2284 26 7 = = NOUN iajs-2284 26 8 1 1 NUM iajs-2284 26 9 then then ADV iajs-2284 26 10 ( ( PUNCT iajs-2284 26 11 c. c. PROPN iajs-2284 26 12 d. d. PROPN iajs-2284 26 13 f f PROPN iajs-2284 26 14 ) ) PUNCT iajs-2284 26 15 will will AUX iajs-2284 26 16 be be AUX iajs-2284 26 17 as as SCONJ iajs-2284 26 18 follows follow VERB iajs-2284 26 19 : : PUNCT iajs-2284 26 20 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-2284 26 21 , , PUNCT iajs-2284 26 22 𝛼 𝛼 NOUN iajs-2284 26 23 ) ) PUNCT iajs-2284 26 24 = = PUNCT iajs-2284 27 1 π‘₯𝛼 π‘₯𝛼 ADP iajs-2284 27 2 0 0 NUM iajs-2284 27 3 < < X iajs-2284 27 4 π‘₯ π‘₯ X iajs-2284 27 5 < < X iajs-2284 27 6 1 1 NUM iajs-2284 27 7 ( ( PUNCT iajs-2284 27 8 3 3 NUM iajs-2284 27 9 ) ) PUNCT iajs-2284 27 10 and and CCONJ iajs-2284 27 11 consequently consequently ADV iajs-2284 27 12 , , PUNCT iajs-2284 27 13 the the PRON iajs-2284 27 14 ( ( PUNCT iajs-2284 27 15 p. p. NOUN iajs-2284 27 16 d. d. PROPN iajs-2284 27 17 f f PROPN iajs-2284 27 18 ) ) PUNCT iajs-2284 27 19 of of ADP iajs-2284 27 20 power power NOUN iajs-2284 27 21 function function NOUN iajs-2284 27 22 distribution distribution NOUN iajs-2284 27 23 will will AUX iajs-2284 27 24 be be AUX iajs-2284 27 25 : : PUNCT iajs-2284 27 26 𝑓(π‘₯ 𝑓(π‘₯ NOUN iajs-2284 27 27 , , PUNCT iajs-2284 27 28 𝛼 𝛼 NOUN iajs-2284 27 29 ) ) PUNCT iajs-2284 27 30 = = PUNCT iajs-2284 28 1 𝛼π‘₯π›Όβˆ’1 𝛼π‘₯π›Όβˆ’1 NOUN iajs-2284 28 2 0 0 NUM iajs-2284 28 3 < < X iajs-2284 28 4 π‘₯ π‘₯ X iajs-2284 28 5 < < X iajs-2284 28 6 1 1 NUM iajs-2284 28 7 ( ( PUNCT iajs-2284 28 8 4 4 NUM iajs-2284 28 9 ) ) PUNCT iajs-2284 28 10 the the DET iajs-2284 28 11 two two NUM iajs-2284 28 12 random random ADJ iajs-2284 28 13 variable variable NOUN iajs-2284 28 14 x x PUNCT iajs-2284 28 15 and and CCONJ iajs-2284 28 16 y y PROPN iajs-2284 28 17 are be AUX iajs-2284 28 18 following follow VERB iajs-2284 28 19 the the DET iajs-2284 28 20 power power NOUN iajs-2284 28 21 function function NOUN iajs-2284 28 22 distribution distribution NOUN iajs-2284 28 23 with with ADP iajs-2284 28 24 parameters parameter NOUN iajs-2284 28 25 ( ( PUNCT iajs-2284 28 26 Ξ±1 Ξ±1 PROPN iajs-2284 28 27 , , PUNCT iajs-2284 28 28 1 1 NUM iajs-2284 28 29 ) ) PUNCT iajs-2284 28 30 and and CCONJ iajs-2284 28 31 ( ( PUNCT iajs-2284 28 32 𝛼2 𝛼2 PROPN iajs-2284 28 33 , , PUNCT iajs-2284 28 34 1 1 NUM iajs-2284 28 35 ) ) PUNCT iajs-2284 28 36 respectively respectively ADV iajs-2284 28 37 and and CCONJ iajs-2284 28 38 according accord VERB iajs-2284 28 39 to to ADP iajs-2284 28 40 strength strength NOUN iajs-2284 28 41 – – PUNCT iajs-2284 28 42 stress stress NOUN iajs-2284 28 43 ( ( PUNCT iajs-2284 28 44 s s NOUN iajs-2284 28 45 - - PUNCT iajs-2284 28 46 s s NOUN iajs-2284 28 47 ) ) PUNCT iajs-2284 28 48 model model NOUN iajs-2284 28 49 . . PUNCT iajs-2284 29 1 hence hence ADV iajs-2284 29 2 , , PUNCT iajs-2284 29 3 the the DET iajs-2284 29 4 π‘₯~π‘π‘œπ‘€(π‘₯ π‘₯~π‘π‘œπ‘€(π‘₯ NOUN iajs-2284 29 5 , , PUNCT iajs-2284 29 6 𝛼1 𝛼1 NOUN iajs-2284 29 7 ) ) PUNCT iajs-2284 29 8 and and CCONJ iajs-2284 29 9 𝑦~π‘π‘œπ‘€(𝑦 𝑦~π‘π‘œπ‘€(𝑦 NOUN iajs-2284 29 10 , , PUNCT iajs-2284 29 11 𝛼2)in 𝛼2)in VERB iajs-2284 29 12 the the DET iajs-2284 29 13 strength strength NOUN iajs-2284 29 14 – – PUNCT iajs-2284 29 15 stress stress NOUN iajs-2284 29 16 model model NOUN iajs-2284 29 17 can can AUX iajs-2284 29 18 be be AUX iajs-2284 29 19 defined define VERB iajs-2284 29 20 as as ADP iajs-2284 29 21 in in ADP iajs-2284 29 22 the the DET iajs-2284 29 23 following following NOUN iajs-2284 29 24 : : PUNCT iajs-2284 29 25 𝑅 𝑅 PROPN iajs-2284 29 26 = = SYM iajs-2284 29 27 𝑃(𝑦 𝑃(𝑦 X iajs-2284 29 28 < < X iajs-2284 29 29 π‘₯ π‘₯ NOUN iajs-2284 29 30 ) ) PUNCT iajs-2284 29 31 ∫ ∫ PROPN iajs-2284 29 32 ∫ ∫ PROPN iajs-2284 29 33 𝑓(π‘₯ 𝑓(π‘₯ NOUN iajs-2284 29 34 ) ) PUNCT iajs-2284 29 35 𝑓(𝑦 𝑓(𝑦 ADV iajs-2284 29 36 ) ) PUNCT iajs-2284 29 37 𝑑𝑦 𝑑𝑦 ADP iajs-2284 29 38 𝑑π‘₯ 𝑑π‘₯ ADP iajs-2284 29 39 𝑋 𝑋 NOUN iajs-2284 29 40 𝑂 𝑂 PROPN iajs-2284 29 41 1 1 NUM iajs-2284 29 42 0 0 NUM iajs-2284 29 43 = = SYM iajs-2284 30 1 ∫ ∫ PROPN iajs-2284 30 2 ∫ ∫ PROPN iajs-2284 30 3 𝛼1π‘₯𝛼1βˆ’1𝛼2𝑦𝛼2βˆ’1𝑑𝑦 𝛼1π‘₯𝛼1βˆ’1𝛼2𝑦𝛼2βˆ’1𝑑𝑦 PROPN iajs-2284 30 4 𝑑π‘₯ 𝑑π‘₯ VERB iajs-2284 30 5 π‘₯ π‘₯ NOUN iajs-2284 30 6 0 0 NUM iajs-2284 30 7 1 1 NUM iajs-2284 30 8 0 0 NUM iajs-2284 30 9 where where SCONJ iajs-2284 30 10 𝑝(𝑦 𝑝(𝑦 PROPN iajs-2284 30 11 < < X iajs-2284 30 12 π‘₯ π‘₯ PROPN iajs-2284 30 13 ) ) PUNCT iajs-2284 30 14 = = SYM iajs-2284 30 15 𝑅 𝑅 PROPN iajs-2284 30 16 = = PROPN iajs-2284 30 17 𝛼1 𝛼1 PROPN iajs-2284 30 18 𝛼1+𝛼2 𝛼1+𝛼2 NOUN iajs-2284 30 19 ( ( PUNCT iajs-2284 30 20 5 5 NUM iajs-2284 30 21 ) ) SYM iajs-2284 30 22 2 2 NUM iajs-2284 30 23 . . PUNCT iajs-2284 30 24 estimation estimation NOUN iajs-2284 30 25 methods method NOUN iajs-2284 30 26 2.1 2.1 NUM iajs-2284 30 27 maximum maximum ADJ iajs-2284 30 28 likelihood likelihood NOUN iajs-2284 30 29 estimator estimator NOUN iajs-2284 30 30 ( ( PUNCT iajs-2284 30 31 mle mle PROPN iajs-2284 30 32 ) ) PUNCT iajs-2284 30 33 the the DET iajs-2284 30 34 maximum maximum ADJ iajs-2284 30 35 likelihood likelihood NOUN iajs-2284 30 36 estimator estimator NOUN iajs-2284 30 37 is be AUX iajs-2284 30 38 most most ADV iajs-2284 30 39 popular popular ADJ iajs-2284 30 40 method method NOUN iajs-2284 30 41 because because SCONJ iajs-2284 30 42 it it PRON iajs-2284 30 43 is be AUX iajs-2284 30 44 approximates approximate VERB iajs-2284 30 45 the the DET iajs-2284 30 46 minimum minimum ADJ iajs-2284 30 47 variance variance NOUN iajs-2284 30 48 unbiased unbiased ADJ iajs-2284 31 1 [ [ X iajs-2284 31 2 12 12 NUM iajs-2284 31 3 ] ] PUNCT iajs-2284 31 4 . . PUNCT iajs-2284 32 1 letπ‘₯1 letπ‘₯1 ADJ iajs-2284 32 2 , , PUNCT iajs-2284 32 3 π‘₯2 π‘₯2 NOUN iajs-2284 32 4 … … PUNCT iajs-2284 32 5 … … PUNCT iajs-2284 32 6 π‘₯𝑛 π‘₯𝑛 AUX iajs-2284 32 7 be be AUX iajs-2284 32 8 a a DET iajs-2284 32 9 random random ADJ iajs-2284 32 10 sample sample NOUN iajs-2284 32 11 ofπ‘π‘œπ‘€(𝛼1 ofπ‘π‘œπ‘€(𝛼1 NOUN iajs-2284 32 12 , , PUNCT iajs-2284 32 13 1 1 NUM iajs-2284 32 14 ) ) PUNCT iajs-2284 32 15 and𝑦1 and𝑦1 PROPN iajs-2284 32 16 , , PUNCT iajs-2284 32 17 𝑦2 𝑦2 NOUN iajs-2284 32 18 … … PUNCT iajs-2284 32 19 … … PUNCT iajs-2284 32 20 π‘¦π‘š π‘¦π‘š AUX iajs-2284 32 21 be be AUX iajs-2284 32 22 a a DET iajs-2284 32 23 random random ADJ iajs-2284 32 24 sample sample NOUN iajs-2284 32 25 of of ADP iajs-2284 32 26 π‘π‘œπ‘€(𝛼2 π‘π‘œπ‘€(𝛼2 PROPN iajs-2284 32 27 , , PUNCT iajs-2284 32 28 1 1 NUM iajs-2284 32 29 ) ) PUNCT iajs-2284 32 30 then then ADV iajs-2284 32 31 , , PUNCT iajs-2284 32 32 the the DET iajs-2284 32 33 maximum maximum ADJ iajs-2284 32 34 likelihood likelihood NOUN iajs-2284 32 35 for𝛼1 for𝛼1 PROPN iajs-2284 32 36 and𝛼2 and𝛼2 PROPN iajs-2284 32 37 will will AUX iajs-2284 32 38 be be AUX iajs-2284 32 39 : : PUNCT iajs-2284 32 40 𝐿 𝐿 NOUN iajs-2284 32 41 = = NOUN iajs-2284 32 42 𝐿(𝛼𝑖 𝐿(𝛼𝑖 NOUN iajs-2284 32 43 , , PUNCT iajs-2284 32 44 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 32 45 , , PUNCT iajs-2284 32 46 𝑦𝑖 𝑦𝑖 PROPN iajs-2284 32 47 ) ) PUNCT iajs-2284 32 48 = = SYM iajs-2284 32 49 ∏ ∏ PROPN iajs-2284 32 50 𝑓(π‘₯𝑖 𝑓(π‘₯𝑖 PROPN iajs-2284 32 51 ) ) PUNCT iajs-2284 32 52 𝑛 𝑛 PRON iajs-2284 32 53 𝑖=1 𝑖=1 PROPN iajs-2284 32 54 ∏ ∏ PROPN iajs-2284 32 55 𝑔(𝑦𝑖 𝑔(𝑦𝑖 ADV iajs-2284 32 56 ) ) PUNCT iajs-2284 32 57 π‘š π‘š X iajs-2284 32 58 𝑖=1 𝑖=1 PUNCT iajs-2284 32 59 𝐿 𝐿 PROPN iajs-2284 32 60 = = SYM iajs-2284 32 61 ∏ ∏ PROPN iajs-2284 32 62 𝛼1 𝛼1 NOUN iajs-2284 32 63 𝑛 𝑛 ADP iajs-2284 32 64 𝑛 𝑛 PROPN iajs-2284 32 65 𝑖=1 𝑖=1 PROPN iajs-2284 32 66 π‘₯𝑖 π‘₯𝑖 ADP iajs-2284 32 67 𝛼1βˆ’1 𝛼1βˆ’1 PROPN iajs-2284 32 68 ∏ ∏ PROPN iajs-2284 32 69 𝛼2 𝛼2 PROPN iajs-2284 32 70 π‘š π‘š ADP iajs-2284 32 71 π‘š π‘š PROPN iajs-2284 32 72 𝑖=1 𝑖=1 PROPN iajs-2284 32 73 𝑦𝑖 𝑦𝑖 PROPN iajs-2284 32 74 𝛼2βˆ’1 𝛼2βˆ’1 NOUN iajs-2284 32 75 taking take VERB iajs-2284 32 76 the the DET iajs-2284 32 77 logarithm logarithm NOUN iajs-2284 32 78 of of ADP iajs-2284 32 79 both both DET iajs-2284 32 80 sides side NOUN iajs-2284 32 81 , , PUNCT iajs-2284 32 82 then then ADV iajs-2284 32 83 : : PUNCT iajs-2284 32 84 𝐿𝑛 𝐿𝑛 PROPN iajs-2284 32 85 𝐿 𝐿 PROPN iajs-2284 32 86 = = SYM iajs-2284 32 87 𝑛 𝑛 PRON iajs-2284 32 88 ln ln NOUN iajs-2284 32 89 𝛼1 𝛼1 NOUN iajs-2284 32 90 + + CCONJ iajs-2284 32 91 ( ( PUNCT iajs-2284 32 92 𝛼1 𝛼1 NOUN iajs-2284 32 93 + + CCONJ iajs-2284 32 94 1 1 X iajs-2284 32 95 ) ) PUNCT iajs-2284 32 96 ln ln ADV iajs-2284 32 97 βˆ‘ βˆ‘ PROPN iajs-2284 32 98 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 32 99 𝑛 𝑛 PRON iajs-2284 32 100 𝑖=1 𝑖=1 PUNCT iajs-2284 33 1 + + CCONJ iajs-2284 33 2 π‘š π‘š X iajs-2284 33 3 ln ln ADJ iajs-2284 33 4 𝛼2 𝛼2 NOUN iajs-2284 33 5 + + CCONJ iajs-2284 33 6 ( ( PUNCT iajs-2284 33 7 𝛼2 𝛼2 VERB iajs-2284 33 8 + + NOUN iajs-2284 33 9 1 1 X iajs-2284 33 10 ) ) PUNCT iajs-2284 33 11 ln ln ADV iajs-2284 33 12 βˆ‘ βˆ‘ PROPN iajs-2284 33 13 𝑦𝑖 𝑦𝑖 ADP iajs-2284 33 14 π‘š π‘š ADP iajs-2284 33 15 𝑖=1 𝑖=1 PUNCT iajs-2284 33 16 taking take VERB iajs-2284 33 17 the the DET iajs-2284 33 18 partial partial ADJ iajs-2284 33 19 derivation derivation NOUN iajs-2284 33 20 for for ADP iajs-2284 33 21 the the DET iajs-2284 33 22 above above ADJ iajs-2284 33 23 equations equation NOUN iajs-2284 33 24 with with ADP iajs-2284 33 25 respect respect NOUN iajs-2284 33 26 to to ADP iajs-2284 33 27 the the DET iajs-2284 33 28 shape shape NOUN iajs-2284 33 29 parameter parameter NOUN iajs-2284 33 30 and and CCONJ iajs-2284 33 31 then then ADV iajs-2284 33 32 equating equate VERB iajs-2284 33 33 the the DET iajs-2284 33 34 results result NOUN iajs-2284 33 35 to to ADP iajs-2284 33 36 zero zero NUM iajs-2284 33 37 , , PUNCT iajs-2284 33 38 this this PRON iajs-2284 33 39 will will AUX iajs-2284 33 40 lead lead VERB iajs-2284 33 41 to to ADP iajs-2284 33 42 : : PUNCT iajs-2284 33 43 οΏ½ οΏ½ PROPN iajs-2284 33 44 Μ‚ Μ‚ NOUN iajs-2284 33 45 οΏ½ οΏ½ NOUN iajs-2284 33 46 1π‘šπ‘™π‘’ 1π‘šπ‘™π‘’ NUM iajs-2284 33 47 = = SYM iajs-2284 33 48 βˆ’π‘› βˆ’π‘› NOUN iajs-2284 33 49 ln ln ADV iajs-2284 33 50 βˆ‘ βˆ‘ PROPN iajs-2284 33 51 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 33 52 𝑛 𝑛 PRON iajs-2284 33 53 𝑖=1 𝑖=1 PROPN iajs-2284 33 54 ( ( PUNCT iajs-2284 33 55 6 6 NUM iajs-2284 33 56 ) ) PUNCT iajs-2284 33 57 οΏ½ οΏ½ NOUN iajs-2284 33 58 Μ‚ Μ‚ SYM iajs-2284 33 59 οΏ½ οΏ½ NOUN iajs-2284 33 60 2π‘šπ‘™π‘’ 2π‘šπ‘™π‘’ NUM iajs-2284 33 61 = = SYM iajs-2284 33 62 βˆ’π‘š βˆ’π‘š ADJ iajs-2284 33 63 𝑙𝑛 𝑙𝑛 NOUN iajs-2284 33 64 βˆ‘ βˆ‘ PROPN iajs-2284 33 65 𝑦𝑖 𝑦𝑖 X iajs-2284 33 66 π‘š π‘š ADP iajs-2284 33 67 𝑖=1 𝑖=1 PROPN iajs-2284 33 68 ( ( PUNCT iajs-2284 33 69 7 7 NUM iajs-2284 33 70 ) ) PUNCT iajs-2284 33 71 οΏ½ οΏ½ NOUN iajs-2284 33 72 Μ‚ Μ‚ VERB iajs-2284 33 73 οΏ½ οΏ½ NOUN iajs-2284 33 74 2π‘šπ‘™π‘’in 2π‘šπ‘™π‘’in NUM iajs-2284 33 75 equation equation NOUN iajs-2284 33 76 ( ( PUNCT iajs-2284 33 77 5 5 NUM iajs-2284 33 78 ) ) PUNCT iajs-2284 33 79 ; ; PUNCT iajs-2284 33 80 the the DET iajs-2284 33 81 reliability reliability NOUN iajs-2284 33 82 estimation estimation NOUN iajs-2284 33 83 of of ADP iajs-2284 33 84 stress stress NOUN iajs-2284 33 85 – – PUNCT iajs-2284 33 86 strength strength NOUN iajs-2284 33 87 model model NOUN iajs-2284 33 88 using use VERB iajs-2284 33 89 maximum maximum ADJ iajs-2284 33 90 likelihood likelihood NOUN iajs-2284 33 91 method method NOUN iajs-2284 33 92 will will AUX iajs-2284 33 93 become become VERB iajs-2284 33 94 : : PUNCT iajs-2284 33 95 οΏ½ οΏ½ PROPN iajs-2284 33 96 Μ‚ Μ‚ PROPN iajs-2284 33 97 οΏ½ οΏ½ PROPN iajs-2284 33 98 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 33 99 = = SYM iajs-2284 33 100 οΏ½ οΏ½ PROPN iajs-2284 33 101 Μ‚ Μ‚ PROPN iajs-2284 33 102 οΏ½ οΏ½ PROPN iajs-2284 33 103 1π‘šπ‘™π‘’ 1π‘šπ‘™π‘’ NUM iajs-2284 33 104 οΏ½ οΏ½ PROPN iajs-2284 33 105 Μ‚ Μ‚ NOUN iajs-2284 33 106 οΏ½ οΏ½ PROPN iajs-2284 33 107 1π‘šπ‘™π‘’ 1π‘šπ‘™π‘’ NUM iajs-2284 33 108 + + PROPN iajs-2284 33 109 οΏ½ οΏ½ PROPN iajs-2284 33 110 Μ‚ Μ‚ NOUN iajs-2284 33 111 οΏ½ οΏ½ NOUN iajs-2284 33 112 2π‘šπ‘™π‘’ 2π‘šπ‘™π‘’ NUM iajs-2284 33 113 ( ( PUNCT iajs-2284 33 114 8) 8) NUM iajs-2284 33 115 72 72 NUM iajs-2284 33 116 ibn ibn PROPN iajs-2284 33 117 al al PROPN iajs-2284 33 118 - - PUNCT iajs-2284 33 119 haitham haitham PROPN iajs-2284 33 120 jour jour X iajs-2284 33 121 . . PROPN iajs-2284 34 1 for for ADP iajs-2284 34 2 pure pure ADJ iajs-2284 34 3 & & CCONJ iajs-2284 34 4 appl appl PROPN iajs-2284 34 5 . . PUNCT iajs-2284 35 1 sci sci PROPN iajs-2284 35 2 . . PROPN iajs-2284 35 3 32 32 NUM iajs-2284 35 4 ( ( PUNCT iajs-2284 35 5 3 3 NUM iajs-2284 35 6 ) ) PUNCT iajs-2284 35 7 2019 2019 NUM iajs-2284 35 8 2.2 2.2 NUM iajs-2284 35 9 . . PUNCT iajs-2284 36 1 moment moment NOUN iajs-2284 36 2 method method NOUN iajs-2284 36 3 ( ( PUNCT iajs-2284 36 4 mom mom NOUN iajs-2284 36 5 ) ) PUNCT iajs-2284 36 6 the the DET iajs-2284 36 7 moment moment NOUN iajs-2284 36 8 method method NOUN iajs-2284 36 9 can can AUX iajs-2284 36 10 be be AUX iajs-2284 36 11 considered consider VERB iajs-2284 36 12 as as ADP iajs-2284 36 13 the the DET iajs-2284 36 14 most most ADV iajs-2284 36 15 common common ADJ iajs-2284 36 16 and and CCONJ iajs-2284 36 17 a a DET iajs-2284 36 18 simple simple ADJ iajs-2284 36 19 method method NOUN iajs-2284 36 20 that that PRON iajs-2284 36 21 have have AUX iajs-2284 36 22 been be AUX iajs-2284 36 23 used use VERB iajs-2284 36 24 in in ADP iajs-2284 36 25 estimation estimation NOUN iajs-2284 36 26 of of ADP iajs-2284 36 27 the the DET iajs-2284 36 28 parameters parameter NOUN iajs-2284 36 29 . . PUNCT iajs-2284 37 1 it it PRON iajs-2284 37 2 can can AUX iajs-2284 37 3 be be AUX iajs-2284 37 4 summarized summarize VERB iajs-2284 37 5 by by ADP iajs-2284 37 6 equating equate VERB iajs-2284 37 7 the the DET iajs-2284 37 8 population population NOUN iajs-2284 37 9 moments moment NOUN iajs-2284 37 10 π‘€π‘Ÿ π‘€π‘Ÿ PROPN iajs-2284 37 11 = = PUNCT iajs-2284 37 12 𝐸(π‘₯π‘Ÿ 𝐸(π‘₯π‘Ÿ NOUN iajs-2284 37 13 ) ) PUNCT iajs-2284 37 14 as as ADP iajs-2284 37 15 in in ADP iajs-2284 37 16 the the DET iajs-2284 37 17 following following NOUN iajs-2284 37 18 [ [ X iajs-2284 37 19 8 8 NUM iajs-2284 37 20 ] ] PUNCT iajs-2284 37 21 . . PUNCT iajs-2284 38 1 𝐸(π‘₯ 𝐸(π‘₯ NOUN iajs-2284 38 2 ) ) PUNCT iajs-2284 38 3 = = SYM iajs-2284 38 4 𝛼1 𝛼1 NOUN iajs-2284 38 5 𝛼1 𝛼1 NOUN iajs-2284 38 6 + + NOUN iajs-2284 38 7 1 1 NUM iajs-2284 38 8 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ ADJ iajs-2284 38 9 𝐸(𝑦 𝐸(𝑦 NOUN iajs-2284 38 10 ) ) PUNCT iajs-2284 38 11 = = PUNCT iajs-2284 38 12 𝛼2 𝛼2 PROPN iajs-2284 38 13 𝛼2 𝛼2 VERB iajs-2284 38 14 + + PROPN iajs-2284 38 15 1 1 NUM iajs-2284 38 16 when when SCONJ iajs-2284 38 17 equating equate VERB iajs-2284 38 18 the the DET iajs-2284 38 19 sample sample NOUN iajs-2284 38 20 mean mean VERB iajs-2284 38 21 e(x e(x NUM iajs-2284 38 22 ) ) PUNCT iajs-2284 38 23 and and CCONJ iajs-2284 38 24 e(y e(y NOUN iajs-2284 38 25 ) ) PUNCT iajs-2284 38 26 to to ADP iajs-2284 38 27 the the DET iajs-2284 38 28 corresponding correspond VERB iajs-2284 38 29 population population NOUN iajs-2284 38 30 mean mean VERB iajs-2284 38 31 , , PUNCT iajs-2284 38 32 then then ADV iajs-2284 38 33 𝛼1 𝛼1 VERB iajs-2284 38 34 𝛼1 𝛼1 NOUN iajs-2284 38 35 + + NOUN iajs-2284 38 36 1 1 NUM iajs-2284 38 37 = = SYM iajs-2284 38 38 βˆ‘ βˆ‘ PROPN iajs-2284 38 39 π‘₯𝑖 π‘₯𝑖 NUM iajs-2284 38 40 𝑛 𝑛 PRON iajs-2284 38 41 𝑖=1 𝑖=1 PUNCT iajs-2284 38 42 𝑛 𝑛 PROPN iajs-2284 38 43 ( ( PUNCT iajs-2284 38 44 9 9 NUM iajs-2284 38 45 ) ) PUNCT iajs-2284 38 46 𝛼2 𝛼2 PROPN iajs-2284 38 47 𝛼2 𝛼2 VERB iajs-2284 38 48 + + PROPN iajs-2284 38 49 1 1 NUM iajs-2284 38 50 = = SYM iajs-2284 38 51 βˆ‘ βˆ‘ PROPN iajs-2284 38 52 𝑦𝑖 𝑦𝑖 X iajs-2284 38 53 π‘š π‘š X iajs-2284 38 54 𝑖=1 𝑖=1 PROPN iajs-2284 38 55 π‘š π‘š X iajs-2284 38 56 ( ( PUNCT iajs-2284 38 57 10 10 NUM iajs-2284 38 58 ) ) PUNCT iajs-2284 38 59 from from ADP iajs-2284 38 60 equations equation NOUN iajs-2284 38 61 ( ( PUNCT iajs-2284 38 62 9 9 NUM iajs-2284 38 63 ) ) PUNCT iajs-2284 38 64 and and CCONJ iajs-2284 38 65 ( ( PUNCT iajs-2284 38 66 10 10 NUM iajs-2284 38 67 ) ) PUNCT iajs-2284 38 68 , , PUNCT iajs-2284 38 69 the the DET iajs-2284 38 70 estimation estimation NOUN iajs-2284 38 71 of of ADP iajs-2284 38 72 parameters parameter NOUN iajs-2284 38 73 𝛼1and 𝛼1and CCONJ iajs-2284 38 74 Ξ±2 Ξ±2 ADJ iajs-2284 38 75 using use VERB iajs-2284 38 76 moment moment NOUN iajs-2284 38 77 method method NOUN iajs-2284 38 78 will will AUX iajs-2284 38 79 be be AUX iajs-2284 38 80 written write VERB iajs-2284 38 81 as as ADP iajs-2284 38 82 in in ADP iajs-2284 38 83 the the DET iajs-2284 38 84 following following NOUN iajs-2284 38 85 : : PUNCT iajs-2284 38 86 οΏ½ οΏ½ PROPN iajs-2284 38 87 Μ‚ Μ‚ NOUN iajs-2284 38 88 οΏ½ οΏ½ NOUN iajs-2284 38 89 1π‘šπ‘œπ‘š 1π‘šπ‘œπ‘š NOUN iajs-2284 38 90 = = PUNCT iajs-2284 38 91 βˆ‘ βˆ‘ PUNCT iajs-2284 38 92 π‘₯𝑖𝑛 π‘₯𝑖𝑛 VERB iajs-2284 38 93 𝑖=1 𝑖=1 PROPN iajs-2284 38 94 π‘›βˆ’βˆ‘ π‘›βˆ’βˆ‘ PROPN iajs-2284 38 95 π‘₯𝑖𝑛 π‘₯𝑖𝑛 NOUN iajs-2284 38 96 𝑖=1 𝑖=1 PROPN iajs-2284 38 97 ( ( PUNCT iajs-2284 38 98 11 11 NUM iajs-2284 38 99 ) ) PUNCT iajs-2284 38 100 οΏ½ οΏ½ NOUN iajs-2284 38 101 Μ‚ Μ‚ SYM iajs-2284 38 102 οΏ½ οΏ½ NOUN iajs-2284 38 103 2π‘šπ‘œπ‘š 2π‘šπ‘œπ‘š NOUN iajs-2284 38 104 = = PUNCT iajs-2284 38 105 βˆ‘ βˆ‘ PUNCT iajs-2284 38 106 π‘¦π‘–π‘š π‘¦π‘–π‘š VERB iajs-2284 38 107 𝑖=1 𝑖=1 PUNCT iajs-2284 38 108 π‘šβˆ’βˆ‘ π‘šβˆ’βˆ‘ PRON iajs-2284 38 109 π‘¦π‘–π‘š π‘¦π‘–π‘š ADJ iajs-2284 38 110 𝑖=1 𝑖=1 PROPN iajs-2284 38 111 ( ( PUNCT iajs-2284 38 112 12 12 NUM iajs-2284 38 113 ) ) PUNCT iajs-2284 38 114 substituting substitute VERB iajs-2284 38 115 the the DET iajs-2284 38 116 equations equation NOUN iajs-2284 38 117 ( ( PUNCT iajs-2284 38 118 11 11 NUM iajs-2284 38 119 ) ) PUNCT iajs-2284 38 120 and and CCONJ iajs-2284 38 121 ( ( PUNCT iajs-2284 38 122 12 12 NUM iajs-2284 38 123 ) ) PUNCT iajs-2284 38 124 in in ADP iajs-2284 38 125 equation equation NOUN iajs-2284 38 126 ( ( PUNCT iajs-2284 38 127 5 5 NUM iajs-2284 38 128 ) ) PUNCT iajs-2284 38 129 , , PUNCT iajs-2284 38 130 then then ADV iajs-2284 38 131 the the DET iajs-2284 38 132 estimation estimation NOUN iajs-2284 38 133 of of ADP iajs-2284 38 134 stress stress NOUN iajs-2284 38 135 – – PUNCT iajs-2284 38 136 strength strength NOUN iajs-2284 38 137 reliability reliability NOUN iajs-2284 38 138 with with ADP iajs-2284 38 139 using use VERB iajs-2284 38 140 moment moment NOUN iajs-2284 38 141 method method NOUN iajs-2284 38 142 will will AUX iajs-2284 38 143 become become VERB iajs-2284 38 144 : : PUNCT iajs-2284 38 145 οΏ½ οΏ½ PROPN iajs-2284 38 146 Μ‚ Μ‚ SYM iajs-2284 38 147 οΏ½ οΏ½ NOUN iajs-2284 38 148 π‘šπ‘œπ‘š π‘šπ‘œπ‘š NOUN iajs-2284 38 149 = = SYM iajs-2284 38 150 οΏ½ οΏ½ PROPN iajs-2284 38 151 Μ‚ Μ‚ NOUN iajs-2284 38 152 οΏ½ οΏ½ PROPN iajs-2284 38 153 1π‘šπ‘œπ‘š 1π‘šπ‘œπ‘š NUM iajs-2284 38 154 οΏ½ οΏ½ PROPN iajs-2284 38 155 Μ‚ Μ‚ NOUN iajs-2284 38 156 οΏ½ οΏ½ NOUN iajs-2284 38 157 1π‘šπ‘œπ‘š+ 1π‘šπ‘œπ‘š+ NUM iajs-2284 38 158 οΏ½ οΏ½ NOUN iajs-2284 38 159 Μ‚ Μ‚ SYM iajs-2284 38 160 οΏ½ οΏ½ NOUN iajs-2284 38 161 2π‘šπ‘œπ‘š 2π‘šπ‘œπ‘š NOUN iajs-2284 38 162 ( ( PUNCT iajs-2284 38 163 13 13 NUM iajs-2284 38 164 ) ) PUNCT iajs-2284 38 165 2.3 2.3 NUM iajs-2284 38 166 least least ADJ iajs-2284 38 167 square square ADJ iajs-2284 38 168 method method NOUN iajs-2284 38 169 ( ( PUNCT iajs-2284 38 170 lsm lsm PROPN iajs-2284 38 171 ) ) PUNCT iajs-2284 39 1 [ [ X iajs-2284 39 2 5 5 X iajs-2284 39 3 ] ] X iajs-2284 39 4 [ [ X iajs-2284 39 5 9 9 NUM iajs-2284 39 6 ] ] X iajs-2284 39 7 letπ‘₯1 letπ‘₯1 ADJ iajs-2284 39 8 , , PUNCT iajs-2284 39 9 π‘₯2 π‘₯2 NOUN iajs-2284 39 10 … … PUNCT iajs-2284 39 11 … … PUNCT iajs-2284 39 12 π‘₯𝑛 π‘₯𝑛 AUX iajs-2284 39 13 be be AUX iajs-2284 39 14 a a DET iajs-2284 39 15 random random ADJ iajs-2284 39 16 sample sample NOUN iajs-2284 39 17 of of ADP iajs-2284 39 18 π‘π‘œπ‘€(𝛼1 π‘π‘œπ‘€(𝛼1 PROPN iajs-2284 39 19 , , PUNCT iajs-2284 39 20 1 1 NUM iajs-2284 39 21 ) ) PUNCT iajs-2284 39 22 and𝑦1 and𝑦1 PROPN iajs-2284 39 23 , , PUNCT iajs-2284 39 24 𝑦2 𝑦2 NOUN iajs-2284 39 25 … … PUNCT iajs-2284 39 26 … … PUNCT iajs-2284 39 27 π‘¦π‘š π‘¦π‘š AUX iajs-2284 39 28 be be AUX iajs-2284 39 29 a a DET iajs-2284 39 30 random random ADJ iajs-2284 39 31 sample sample NOUN iajs-2284 39 32 of of ADP iajs-2284 39 33 π‘π‘œπ‘€(𝛼2 π‘π‘œπ‘€(𝛼2 PROPN iajs-2284 39 34 , , PUNCT iajs-2284 39 35 1 1 NUM iajs-2284 39 36 ) ) PUNCT iajs-2284 39 37 , , PUNCT iajs-2284 39 38 then then ADV iajs-2284 39 39 : : PUNCT iajs-2284 39 40 𝐹(π‘₯1 𝐹(π‘₯1 X iajs-2284 39 41 ) ) PUNCT iajs-2284 39 42 = = SYM iajs-2284 39 43 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 39 44 𝛼1 𝛼1 NOUN iajs-2284 39 45 π‘₯𝑖 π‘₯𝑖 ADP iajs-2284 39 46 = = PUNCT iajs-2284 40 1 [ [ X iajs-2284 40 2 𝐹(π‘₯𝑖 𝐹(π‘₯𝑖 X iajs-2284 40 3 ) ) PUNCT iajs-2284 40 4 ] ] PUNCT iajs-2284 40 5 1 1 NUM iajs-2284 40 6 𝛼1 𝛼1 NOUN iajs-2284 40 7 taking take VERB iajs-2284 40 8 the the DET iajs-2284 40 9 logarithm logarithm NOUN iajs-2284 40 10 for for ADP iajs-2284 40 11 the the DET iajs-2284 40 12 both both DET iajs-2284 40 13 sides side NOUN iajs-2284 40 14 of of ADP iajs-2284 40 15 the the DET iajs-2284 40 16 above above ADJ iajs-2284 40 17 equation equation NOUN iajs-2284 40 18 , , PUNCT iajs-2284 40 19 then then ADV iajs-2284 40 20 : : PUNCT iajs-2284 40 21 ln(π‘₯𝑖 ln(π‘₯𝑖 PROPN iajs-2284 40 22 ) ) PUNCT iajs-2284 40 23 = = SYM iajs-2284 40 24 1 1 NUM iajs-2284 40 25 𝛼1 𝛼1 NOUN iajs-2284 40 26 ln[𝐹(π‘₯𝑖 ln[𝐹(π‘₯𝑖 PROPN iajs-2284 40 27 ) ) PUNCT iajs-2284 40 28 ] ] PUNCT iajs-2284 41 1 𝑦 𝑦 NOUN iajs-2284 41 2 = = SYM iajs-2284 41 3 π‘Žπ‘₯ π‘Žπ‘₯ NOUN iajs-2284 42 1 + + CCONJ iajs-2284 42 2 𝑏 𝑏 PROPN iajs-2284 42 3 𝑦 𝑦 X iajs-2284 42 4 = = SYM iajs-2284 42 5 ln ln PROPN iajs-2284 42 6 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 42 7 , , PUNCT iajs-2284 42 8 π‘Ž π‘Ž NOUN iajs-2284 42 9 = = SYM iajs-2284 42 10 1 1 NUM iajs-2284 42 11 𝛼𝑖 𝛼𝑖 PROPN iajs-2284 42 12 , , PUNCT iajs-2284 42 13 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 42 14 = = PUNCT iajs-2284 42 15 ln[𝐹(π‘₯𝑖 ln[𝐹(π‘₯𝑖 PROPN iajs-2284 42 16 ) ) PUNCT iajs-2284 42 17 ] ] PUNCT iajs-2284 42 18 , , PUNCT iajs-2284 42 19 𝑏 𝑏 NOUN iajs-2284 42 20 = = SYM iajs-2284 42 21 0 0 PUNCT iajs-2284 42 22 hence hence ADV iajs-2284 42 23 π‘Ž π‘Ž X iajs-2284 42 24 = = PUNCT iajs-2284 42 25 βˆ‘ βˆ‘ PUNCT iajs-2284 42 26 π‘₯𝑖𝑦𝑖 π‘₯𝑖𝑦𝑖 NOUN iajs-2284 42 27 𝑛 𝑛 PRON iajs-2284 42 28 𝑖=1 𝑖=1 PROPN iajs-2284 42 29 βˆ’ βˆ’ NOUN iajs-2284 42 30 βˆ‘ βˆ‘ PUNCT iajs-2284 42 31 π‘₯𝑖𝑦𝑖 π‘₯𝑖𝑦𝑖 PROPN iajs-2284 42 32 𝑛 𝑛 PRON iajs-2284 42 33 𝑖=1 𝑖=1 PUNCT iajs-2284 42 34 𝑛 𝑛 PRON iajs-2284 42 35 βˆ‘ βˆ‘ ADP iajs-2284 42 36 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 42 37 2𝑛 2𝑛 PROPN iajs-2284 42 38 𝑖=1 𝑖=1 PUNCT iajs-2284 43 1 βˆ’ βˆ’ PROPN iajs-2284 43 2 ( ( PUNCT iajs-2284 43 3 βˆ‘ βˆ‘ PROPN iajs-2284 43 4 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 43 5 𝑛 𝑛 PROPN iajs-2284 43 6 𝑖=1 𝑖=1 PROPN iajs-2284 43 7 ) ) PUNCT iajs-2284 43 8 2 2 NUM iajs-2284 43 9 𝑛 𝑛 DET iajs-2284 43 10 οΏ½ οΏ½ PROPN iajs-2284 43 11 Μ‚ Μ‚ SYM iajs-2284 43 12 οΏ½ οΏ½ NOUN iajs-2284 43 13 1𝐿𝑠 1𝐿𝑠 NUM iajs-2284 43 14 = = SYM iajs-2284 43 15 βˆ‘ βˆ‘ PUNCT iajs-2284 44 1 [ [ X iajs-2284 44 2 ln ln ADJ iajs-2284 44 3 𝐹(π‘₯𝑖)]2𝑛 𝐹(π‘₯𝑖)]2𝑛 NUM iajs-2284 44 4 𝑖=1 𝑖=1 PUNCT iajs-2284 44 5 βˆ’ βˆ’ PROPN iajs-2284 45 1 [ [ X iajs-2284 45 2 βˆ‘ βˆ‘ X iajs-2284 45 3 ln ln ADJ iajs-2284 45 4 𝐹(π‘₯𝑖)𝑛 𝐹(π‘₯𝑖)𝑛 NOUN iajs-2284 45 5 𝑖=1 𝑖=1 PUNCT iajs-2284 45 6 ] ] X iajs-2284 45 7 2 2 NUM iajs-2284 45 8 𝑛 𝑛 PROPN iajs-2284 45 9 βˆ‘ βˆ‘ PROPN iajs-2284 45 10 ln ln ADJ iajs-2284 45 11 𝐹(π‘₯𝑖 𝐹(π‘₯𝑖 NOUN iajs-2284 45 12 ) ) PUNCT iajs-2284 45 13 ln ln ADV iajs-2284 45 14 π‘₯π‘–βˆ’π‘› π‘₯π‘–βˆ’π‘› NOUN iajs-2284 45 15 𝑖=1 𝑖=1 PUNCT iajs-2284 45 16 βˆ‘ βˆ‘ PUNCT iajs-2284 45 17 ln ln PROPN iajs-2284 45 18 𝐹(π‘₯𝑖 𝐹(π‘₯𝑖 NOUN iajs-2284 45 19 ) ) PUNCT iajs-2284 45 20 ln ln NOUN iajs-2284 45 21 π‘₯𝑖 π‘₯𝑖 ADP iajs-2284 45 22 𝑛 𝑛 PRON iajs-2284 45 23 𝑖=1 𝑖=1 PUNCT iajs-2284 45 24 𝑛 𝑛 PROPN iajs-2284 45 25 ( ( PUNCT iajs-2284 45 26 14 14 NUM iajs-2284 45 27 ) ) PUNCT iajs-2284 45 28 οΏ½ οΏ½ PROPN iajs-2284 45 29 Μ‚ Μ‚ VERB iajs-2284 45 30 οΏ½ οΏ½ PROPN iajs-2284 45 31 2𝐿𝑠 2𝐿𝑠 NUM iajs-2284 45 32 = = SYM iajs-2284 45 33 βˆ‘ βˆ‘ PUNCT iajs-2284 45 34 [ [ X iajs-2284 45 35 ln ln ADJ iajs-2284 45 36 𝐺(𝑦𝑖)]2π‘š 𝐺(𝑦𝑖)]2π‘š NOUN iajs-2284 45 37 𝑖=1 𝑖=1 PUNCT iajs-2284 45 38 βˆ’ βˆ’ PROPN iajs-2284 46 1 [ [ X iajs-2284 46 2 βˆ‘ βˆ‘ X iajs-2284 46 3 ln ln VERB iajs-2284 46 4 𝐺(𝑦𝑖)π‘š 𝐺(𝑦𝑖)π‘š ADV iajs-2284 46 5 𝑖=1 𝑖=1 PROPN iajs-2284 46 6 ] ] X iajs-2284 46 7 2 2 NUM iajs-2284 46 8 π‘š π‘š NOUN iajs-2284 46 9 βˆ‘ βˆ‘ ADV iajs-2284 46 10 ln ln ADJ iajs-2284 46 11 𝐺(𝑦𝑖 𝐺(𝑦𝑖 NOUN iajs-2284 46 12 ) ) PUNCT iajs-2284 46 13 ln ln ADV iajs-2284 46 14 π‘¦π‘–βˆ’π‘š π‘¦π‘–βˆ’π‘š NOUN iajs-2284 46 15 𝑖=1 𝑖=1 PUNCT iajs-2284 46 16 βˆ‘ βˆ‘ PUNCT iajs-2284 46 17 ln ln ADJ iajs-2284 46 18 𝐺(𝑦𝑖 𝐺(𝑦𝑖 NOUN iajs-2284 46 19 ) ) PUNCT iajs-2284 47 1 ln ln ADV iajs-2284 47 2 𝑦𝑖 𝑦𝑖 ADP iajs-2284 47 3 π‘š π‘š PROPN iajs-2284 47 4 𝑖=1 𝑖=1 PROPN iajs-2284 47 5 π‘š π‘š X iajs-2284 47 6 ( ( PUNCT iajs-2284 47 7 15 15 NUM iajs-2284 47 8 ) ) PUNCT iajs-2284 47 9 for for ADP iajs-2284 47 10 stress stress NOUN iajs-2284 47 11 – – PUNCT iajs-2284 47 12 strength strength NOUN iajs-2284 47 13 reliability reliability NOUN iajs-2284 47 14 οΏ½ οΏ½ NOUN iajs-2284 47 15 Μ‚ Μ‚ NOUN iajs-2284 47 16 οΏ½ οΏ½ NOUN iajs-2284 47 17 𝐿𝑠using 𝐿𝑠using NOUN iajs-2284 47 18 least least ADJ iajs-2284 47 19 square square ADJ iajs-2284 47 20 method method NOUN iajs-2284 47 21 as as ADP iajs-2284 47 22 in in ADP iajs-2284 47 23 the the DET iajs-2284 47 24 following following NOUN iajs-2284 47 25 : : PUNCT iajs-2284 47 26 73 73 NUM iajs-2284 47 27 ibn ibn PROPN iajs-2284 47 28 al al PROPN iajs-2284 47 29 - - PUNCT iajs-2284 47 30 haitham haitham PROPN iajs-2284 47 31 jour jour X iajs-2284 47 32 . . PROPN iajs-2284 48 1 for for ADP iajs-2284 48 2 pure pure ADJ iajs-2284 48 3 & & CCONJ iajs-2284 48 4 appl appl PROPN iajs-2284 48 5 . . PUNCT iajs-2284 49 1 sci sci PROPN iajs-2284 49 2 . . PROPN iajs-2284 49 3 32 32 NUM iajs-2284 49 4 ( ( PUNCT iajs-2284 49 5 3 3 NUM iajs-2284 49 6 ) ) PUNCT iajs-2284 49 7 2019 2019 NUM iajs-2284 49 8 οΏ½ οΏ½ PROPN iajs-2284 49 9 Μ‚ Μ‚ SYM iajs-2284 49 10 οΏ½ οΏ½ PROPN iajs-2284 49 11 𝐿𝑠 𝐿𝑠 PROPN iajs-2284 49 12 = = PUNCT iajs-2284 49 13 οΏ½ οΏ½ PROPN iajs-2284 49 14 Μ‚ Μ‚ PROPN iajs-2284 49 15 οΏ½ οΏ½ PROPN iajs-2284 49 16 1𝐿𝑠 1𝐿𝑠 NUM iajs-2284 49 17 οΏ½ οΏ½ PROPN iajs-2284 49 18 Μ‚ Μ‚ SYM iajs-2284 49 19 οΏ½ οΏ½ PROPN iajs-2284 49 20 1𝐿𝑠 1𝐿𝑠 NUM iajs-2284 49 21 + + ADJ iajs-2284 49 22 οΏ½ οΏ½ PROPN iajs-2284 49 23 Μ‚ Μ‚ NOUN iajs-2284 49 24 οΏ½ οΏ½ PROPN iajs-2284 49 25 2𝐿𝑠 2𝐿𝑠 NUM iajs-2284 49 26 ( ( PUNCT iajs-2284 49 27 16 16 NUM iajs-2284 49 28 ) ) PUNCT iajs-2284 49 29 2.4 2.4 NUM iajs-2284 49 30 shrinkage shrinkage NOUN iajs-2284 49 31 estimation estimation NOUN iajs-2284 49 32 method method NOUN iajs-2284 49 33 ( ( PUNCT iajs-2284 49 34 sh sh PROPN iajs-2284 49 35 ) ) PUNCT iajs-2284 50 1 [ [ X iajs-2284 50 2 10][13 10][13 PROPN iajs-2284 50 3 ] ] X iajs-2284 50 4 . . PUNCT iajs-2284 51 1 the the DET iajs-2284 51 2 shrinkage shrinkage NOUN iajs-2284 51 3 estimation estimation NOUN iajs-2284 51 4 method method NOUN iajs-2284 51 5 can can AUX iajs-2284 51 6 be be AUX iajs-2284 51 7 considered consider VERB iajs-2284 51 8 as as ADP iajs-2284 51 9 the the DET iajs-2284 51 10 bayesian bayesian NOUN iajs-2284 51 11 approach approach NOUN iajs-2284 51 12 which which PRON iajs-2284 51 13 has have AUX iajs-2284 51 14 depended depend VERB iajs-2284 51 15 on on ADP iajs-2284 51 16 the the DET iajs-2284 51 17 prior prior ADJ iajs-2284 51 18 information information NOUN iajs-2284 51 19 . . PUNCT iajs-2284 52 1 the the DET iajs-2284 52 2 basic basic ADJ iajs-2284 52 3 reasons reason NOUN iajs-2284 52 4 for for ADP iajs-2284 52 5 using use VERB iajs-2284 52 6 the the DET iajs-2284 52 7 prior prior ADJ iajs-2284 52 8 estimation estimation NOUN iajs-2284 52 9 had have AUX iajs-2284 52 10 been be AUX iajs-2284 52 11 introduced introduce VERB iajs-2284 52 12 by by ADP iajs-2284 52 13 thompson thompson PROPN iajs-2284 52 14 in in ADP iajs-2284 52 15 1968.in 1968.in NOUN iajs-2284 52 16 the the DET iajs-2284 52 17 shrinkage shrinkage NOUN iajs-2284 52 18 estimation estimation NOUN iajs-2284 52 19 method method NOUN iajs-2284 52 20 the the DET iajs-2284 52 21 parameter parameter NOUN iajs-2284 52 22 was be AUX iajs-2284 52 23 used use VERB iajs-2284 52 24 as as ADP iajs-2284 52 25 initial initial ADJ iajs-2284 52 26 value value NOUN iajs-2284 52 27 𝛼0 𝛼0 PROPN iajs-2284 52 28 from from ADP iajs-2284 52 29 the the DET iajs-2284 52 30 past past ADJ iajs-2284 52 31 and and CCONJ iajs-2284 52 32 usual usual ADJ iajs-2284 52 33 estimator estimator NOUN iajs-2284 52 34 οΏ½ οΏ½ PROPN iajs-2284 52 35 Μ‚ Μ‚ VERB iajs-2284 52 36 οΏ½ οΏ½ PROPN iajs-2284 52 37 𝑒𝑏 𝑒𝑏 VERB iajs-2284 52 38 through through ADP iajs-2284 52 39 consideration consideration NOUN iajs-2284 52 40 them they PRON iajs-2284 52 41 by by ADP iajs-2284 52 42 shrinkage shrinkage NOUN iajs-2284 52 43 weight weight NOUN iajs-2284 52 44 factor factor NOUN iajs-2284 52 45 , , PUNCT iajs-2284 52 46 βˆ…( βˆ…( PROPN iajs-2284 52 47 οΏ½ οΏ½ PROPN iajs-2284 52 48 Μ‚ Μ‚ NUM iajs-2284 52 49 οΏ½ οΏ½ NOUN iajs-2284 52 50 ) ) PUNCT iajs-2284 52 51 , , PUNCT iajs-2284 52 52 0 0 NUM iajs-2284 52 53 < < X iajs-2284 52 54 βˆ…( βˆ…( PROPN iajs-2284 52 55 οΏ½ οΏ½ PROPN iajs-2284 52 56 Μ‚ Μ‚ NUM iajs-2284 52 57 οΏ½ οΏ½ NOUN iajs-2284 52 58 ) ) PUNCT iajs-2284 52 59 < < X iajs-2284 52 60 1 1 NUM iajs-2284 52 61 , , PUNCT iajs-2284 52 62 which which PRON iajs-2284 52 63 can can AUX iajs-2284 52 64 be be AUX iajs-2284 52 65 written write VERB iajs-2284 52 66 as as ADP iajs-2284 52 67 : : PUNCT iajs-2284 52 68 οΏ½ οΏ½ PROPN iajs-2284 52 69 Μ‚ Μ‚ NOUN iajs-2284 52 70 οΏ½ οΏ½ NOUN iajs-2284 52 71 π‘ β„Ž π‘ β„Ž NOUN iajs-2284 52 72 = = SYM iajs-2284 52 73 βˆ…( βˆ…( PROPN iajs-2284 52 74 οΏ½ οΏ½ PROPN iajs-2284 52 75 Μ‚ Μ‚ SYM iajs-2284 52 76 οΏ½ οΏ½ NOUN iajs-2284 52 77 ) ) PUNCT iajs-2284 52 78 οΏ½ οΏ½ PROPN iajs-2284 52 79 Μ‚ Μ‚ VERB iajs-2284 52 80 οΏ½ οΏ½ NOUN iajs-2284 52 81 𝑒𝑏 𝑒𝑏 VERB iajs-2284 52 82 + + CCONJ iajs-2284 52 83 ( ( PUNCT iajs-2284 52 84 1 1 NUM iajs-2284 52 85 βˆ’ βˆ’ PROPN iajs-2284 52 86 βˆ…( βˆ…( PROPN iajs-2284 52 87 οΏ½ οΏ½ PROPN iajs-2284 52 88 Μ‚ Μ‚ NOUN iajs-2284 52 89 οΏ½ οΏ½ NOUN iajs-2284 52 90 ))𝛼0 ))𝛼0 PUNCT iajs-2284 52 91 ( ( PUNCT iajs-2284 52 92 17 17 NUM iajs-2284 52 93 ) ) PUNCT iajs-2284 52 94 to to PART iajs-2284 52 95 find find VERB iajs-2284 52 96 Ξ±Μ‚ub Ξ±Μ‚ub ADV iajs-2284 52 97 from from ADP iajs-2284 52 98 οΏ½ οΏ½ PROPN iajs-2284 52 99 Μ‚ Μ‚ SYM iajs-2284 52 100 οΏ½ οΏ½ PROPN iajs-2284 52 101 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 52 102 οΏ½ οΏ½ PROPN iajs-2284 52 103 Μ‚ Μ‚ PROPN iajs-2284 52 104 οΏ½ οΏ½ PROPN iajs-2284 52 105 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 52 106 = = NOUN iajs-2284 52 107 βˆ’π‘› βˆ’π‘› NOUN iajs-2284 52 108 ln ln ADV iajs-2284 52 109 βˆ‘ βˆ‘ PROPN iajs-2284 52 110 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 52 111 𝑛 𝑛 PROPN iajs-2284 52 112 𝑖=1 𝑖=1 PUNCT iajs-2284 53 1 𝑛 𝑛 DET iajs-2284 53 2 𝑛 𝑛 PRON iajs-2284 53 3 βˆ’ βˆ’ PROPN iajs-2284 53 4 1 1 NUM iajs-2284 53 5 οΏ½ οΏ½ PROPN iajs-2284 53 6 Μ‚ Μ‚ NUM iajs-2284 53 7 οΏ½ οΏ½ PROPN iajs-2284 53 8 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 53 9 β‰  β‰  PROPN iajs-2284 53 10 οΏ½ οΏ½ PROPN iajs-2284 53 11 Μ‚ Μ‚ PROPN iajs-2284 53 12 οΏ½ οΏ½ PROPN iajs-2284 53 13 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 53 14 οΏ½ οΏ½ PROPN iajs-2284 53 15 Μ‚ Μ‚ VERB iajs-2284 53 16 οΏ½ οΏ½ PROPN iajs-2284 53 17 𝑒𝑏 𝑒𝑏 ADP iajs-2284 53 18 = = SYM iajs-2284 53 19 π‘›βˆ’1 π‘›βˆ’1 PROPN iajs-2284 53 20 𝑛 𝑛 DET iajs-2284 53 21 οΏ½ οΏ½ PROPN iajs-2284 53 22 Μ‚ Μ‚ NUM iajs-2284 53 23 οΏ½ οΏ½ PROPN iajs-2284 53 24 π‘šπ‘™π‘’ π‘šπ‘™π‘’ NUM iajs-2284 53 25 οΏ½ οΏ½ PROPN iajs-2284 53 26 Μ‚ Μ‚ VERB iajs-2284 53 27 οΏ½ οΏ½ PROPN iajs-2284 53 28 𝑒𝑏 𝑒𝑏 ADP iajs-2284 53 29 = = SYM iajs-2284 53 30 βˆ’(π‘›βˆ’1 βˆ’(π‘›βˆ’1 PROPN iajs-2284 53 31 ) ) PUNCT iajs-2284 53 32 βˆ‘ βˆ‘ PUNCT iajs-2284 53 33 ln ln ADV iajs-2284 53 34 π‘₯𝑖 π‘₯𝑖 X iajs-2284 53 35 𝑛 𝑛 PRON iajs-2284 53 36 𝑖=1 𝑖=1 PROPN iajs-2284 53 37 ( ( PUNCT iajs-2284 53 38 18 18 NUM iajs-2284 53 39 ) ) PUNCT iajs-2284 53 40 2.4.1 2.4.1 NUM iajs-2284 53 41 shrinkage shrinkage NOUN iajs-2284 53 42 weight weight NOUN iajs-2284 53 43 function function NOUN iajs-2284 53 44 ( ( PUNCT iajs-2284 53 45 π’”π’‰πŸ π’”π’‰πŸ X iajs-2284 53 46 ) ) PUNCT iajs-2284 54 1 [ [ X iajs-2284 54 2 11 11 NUM iajs-2284 54 3 ] ] PUNCT iajs-2284 54 4 . . PUNCT iajs-2284 55 1 in in ADP iajs-2284 55 2 this this DET iajs-2284 55 3 case case NOUN iajs-2284 55 4 , , PUNCT iajs-2284 55 5 the the DET iajs-2284 55 6 shrinkage shrinkage NOUN iajs-2284 55 7 weight weight NOUN iajs-2284 55 8 factor factor NOUN iajs-2284 55 9 has have AUX iajs-2284 55 10 used use VERB iajs-2284 55 11 as as ADP iajs-2284 55 12 a a DET iajs-2284 55 13 function function NOUN iajs-2284 55 14 of of ADP iajs-2284 55 15 n n CCONJ iajs-2284 55 16 , , PUNCT iajs-2284 55 17 in in ADP iajs-2284 55 18 which which PRON iajs-2284 55 19 : : PUNCT iajs-2284 55 20 βˆ…( βˆ…( PROPN iajs-2284 55 21 οΏ½ οΏ½ PROPN iajs-2284 55 22 Μ‚ Μ‚ NUM iajs-2284 55 23 οΏ½ οΏ½ NOUN iajs-2284 55 24 ) ) PUNCT iajs-2284 55 25 = = PUNCT iajs-2284 56 1 | | ADV iajs-2284 56 2 sin sin VERB iajs-2284 56 3 𝑛 𝑛 DET iajs-2284 56 4 𝑛 𝑛 NOUN iajs-2284 56 5 | | NOUN iajs-2284 56 6 , , PUNCT iajs-2284 56 7 οΏ½ οΏ½ PROPN iajs-2284 56 8 Μ‚ Μ‚ VERB iajs-2284 56 9 οΏ½ οΏ½ PROPN iajs-2284 56 10 𝑒𝑏 𝑒𝑏 ADP iajs-2284 56 11 = = SYM iajs-2284 56 12 βˆ’(π‘›βˆ’1 βˆ’(π‘›βˆ’1 PROPN iajs-2284 56 13 ) ) PUNCT iajs-2284 56 14 βˆ‘ βˆ‘ PUNCT iajs-2284 56 15 ln ln ADV iajs-2284 56 16 π‘₯𝑖 π‘₯𝑖 X iajs-2284 56 17 𝑛 𝑛 DET iajs-2284 56 18 𝑖=1 𝑖=1 PUNCT iajs-2284 56 19 substituting substitute VERB iajs-2284 56 20 in in ADP iajs-2284 56 21 equation equation NOUN iajs-2284 56 22 ( ( PUNCT iajs-2284 56 23 17 17 NUM iajs-2284 56 24 ) ) PUNCT iajs-2284 56 25 , , PUNCT iajs-2284 56 26 then then ADV iajs-2284 56 27 : : PUNCT iajs-2284 56 28 οΏ½ οΏ½ PROPN iajs-2284 56 29 Μ‚ Μ‚ SYM iajs-2284 56 30 οΏ½ οΏ½ NOUN iajs-2284 56 31 1π‘ β„Ž1 1π‘ β„Ž1 NUM iajs-2284 56 32 = = SYM iajs-2284 56 33 | | ADV iajs-2284 56 34 sin sin VERB iajs-2284 56 35 𝑛 𝑛 PRON iajs-2284 56 36 𝑛 𝑛 PROPN iajs-2284 56 37 | | ADV iajs-2284 56 38 οΏ½ οΏ½ PROPN iajs-2284 56 39 Μ‚ Μ‚ VERB iajs-2284 56 40 οΏ½ οΏ½ NOUN iajs-2284 56 41 𝑒𝑏 𝑒𝑏 VERB iajs-2284 56 42 + + CCONJ iajs-2284 56 43 ( ( PUNCT iajs-2284 56 44 1 1 NUM iajs-2284 56 45 βˆ’ βˆ’ NOUN iajs-2284 56 46 | | INTJ iajs-2284 56 47 sin sin VERB iajs-2284 56 48 𝑛 𝑛 DET iajs-2284 56 49 𝑛 𝑛 PRON iajs-2284 56 50 | | NOUN iajs-2284 56 51 ) ) PUNCT iajs-2284 56 52 𝛼0 𝛼0 PROPN iajs-2284 56 53 ( ( PUNCT iajs-2284 56 54 19 19 NUM iajs-2284 56 55 ) ) PUNCT iajs-2284 56 56 οΏ½ οΏ½ PROPN iajs-2284 56 57 Μ‚ Μ‚ VERB iajs-2284 56 58 οΏ½ οΏ½ NOUN iajs-2284 56 59 2π‘ β„Ž1 2π‘ β„Ž1 NUM iajs-2284 56 60 = = PUNCT iajs-2284 57 1 | | ADV iajs-2284 57 2 sin sin VERB iajs-2284 57 3 π‘š π‘š ADP iajs-2284 57 4 π‘š π‘š ADP iajs-2284 57 5 | | ADV iajs-2284 57 6 οΏ½ οΏ½ PROPN iajs-2284 57 7 Μ‚ Μ‚ NOUN iajs-2284 57 8 οΏ½ οΏ½ NOUN iajs-2284 57 9 𝑒𝑏 𝑒𝑏 VERB iajs-2284 57 10 + + CCONJ iajs-2284 57 11 ( ( PUNCT iajs-2284 57 12 1 1 NUM iajs-2284 57 13 βˆ’ βˆ’ NOUN iajs-2284 57 14 | | INTJ iajs-2284 57 15 sin sin VERB iajs-2284 57 16 π‘š π‘š ADP iajs-2284 57 17 π‘š π‘š NOUN iajs-2284 57 18 | | NOUN iajs-2284 57 19 ) ) PUNCT iajs-2284 57 20 𝛼0 𝛼0 PROPN iajs-2284 57 21 ( ( PUNCT iajs-2284 57 22 20 20 NUM iajs-2284 57 23 ) ) PUNCT iajs-2284 57 24 substituting substitute VERB iajs-2284 57 25 οΏ½ οΏ½ PROPN iajs-2284 57 26 Μ‚ Μ‚ SYM iajs-2284 57 27 οΏ½ οΏ½ NOUN iajs-2284 57 28 1π‘ β„Ž1 1π‘ β„Ž1 NUM iajs-2284 57 29 , , PUNCT iajs-2284 57 30 οΏ½ οΏ½ PROPN iajs-2284 57 31 Μ‚ Μ‚ NOUN iajs-2284 57 32 οΏ½ οΏ½ NOUN iajs-2284 57 33 2π‘ β„Ž1 2π‘ β„Ž1 NUM iajs-2284 57 34 in in ADP iajs-2284 57 35 equation equation NOUN iajs-2284 57 36 ( ( PUNCT iajs-2284 57 37 5 5 NUM iajs-2284 57 38 ) ) PUNCT iajs-2284 57 39 , , PUNCT iajs-2284 57 40 then then ADV iajs-2284 57 41 the the DET iajs-2284 57 42 reliability reliability NOUN iajs-2284 57 43 estimation estimation NOUN iajs-2284 57 44 of of ADP iajs-2284 57 45 stress stress NOUN iajs-2284 57 46 – – PUNCT iajs-2284 57 47 strength strength NOUN iajs-2284 57 48 model model NOUN iajs-2284 57 49 with with ADP iajs-2284 57 50 using use VERB iajs-2284 57 51 shrinkage shrinkage NOUN iajs-2284 57 52 weight weight NOUN iajs-2284 57 53 function function NOUN iajs-2284 57 54 will will AUX iajs-2284 57 55 become become VERB iajs-2284 57 56 : : PUNCT iajs-2284 57 57 οΏ½ οΏ½ PROPN iajs-2284 57 58 Μ‚ Μ‚ NOUN iajs-2284 57 59 οΏ½ οΏ½ NOUN iajs-2284 57 60 π‘ β„Ž1 π‘ β„Ž1 NOUN iajs-2284 57 61 = = SYM iajs-2284 57 62 οΏ½ οΏ½ PROPN iajs-2284 57 63 Μ‚ Μ‚ VERB iajs-2284 57 64 οΏ½ οΏ½ PROPN iajs-2284 57 65 1π‘ β„Ž1 1π‘ β„Ž1 NUM iajs-2284 57 66 οΏ½ οΏ½ NOUN iajs-2284 57 67 Μ‚ Μ‚ VERB iajs-2284 57 68 οΏ½ οΏ½ NOUN iajs-2284 57 69 1π‘ β„Ž1 1π‘ β„Ž1 NUM iajs-2284 57 70 + + ADJ iajs-2284 57 71 οΏ½ οΏ½ PROPN iajs-2284 57 72 Μ‚ Μ‚ SYM iajs-2284 57 73 οΏ½ οΏ½ NOUN iajs-2284 57 74 2π‘ β„Ž1 2π‘ β„Ž1 NUM iajs-2284 57 75 ( ( PUNCT iajs-2284 57 76 21 21 NUM iajs-2284 57 77 ) ) PUNCT iajs-2284 57 78 2.4.2 2.4.2 NUM iajs-2284 57 79 constant constant ADJ iajs-2284 57 80 shrinkage shrinkage NOUN iajs-2284 57 81 factor factor NOUN iajs-2284 57 82 ( ( PUNCT iajs-2284 57 83 π’”π’‰πŸ π’”π’‰πŸ ADV iajs-2284 57 84 ) ) PUNCT iajs-2284 58 1 [ [ X iajs-2284 58 2 11 11 NUM iajs-2284 58 3 ] ] PUNCT iajs-2284 58 4 . . PUNCT iajs-2284 59 1 in in ADP iajs-2284 59 2 constant constant ADJ iajs-2284 59 3 shrinkage shrinkage NOUN iajs-2284 59 4 factor factor NOUN iajs-2284 59 5 case case NOUN iajs-2284 59 6 , , PUNCT iajs-2284 59 7 it it PRON iajs-2284 59 8 can can AUX iajs-2284 59 9 be be AUX iajs-2284 59 10 assumed assume VERB iajs-2284 59 11 thatβˆ…( thatβˆ…( ADJ iajs-2284 59 12 οΏ½ οΏ½ PROPN iajs-2284 59 13 Μ‚ Μ‚ NOUN iajs-2284 59 14 οΏ½ οΏ½ NOUN iajs-2284 59 15 ) ) PUNCT iajs-2284 59 16 = = SYM iajs-2284 59 17 π‘˜ π‘˜ PROPN iajs-2284 59 18 , , PUNCT iajs-2284 59 19 k=0.001 k=0.001 PUNCT iajs-2284 59 20 which which PRON iajs-2284 59 21 represent represent VERB iajs-2284 59 22 the the DET iajs-2284 59 23 constant constant ADJ iajs-2284 59 24 shrinkage shrinkage NOUN iajs-2284 59 25 weight weight NOUN iajs-2284 59 26 factor factor NOUN iajs-2284 59 27 . . PUNCT iajs-2284 60 1 implying imply VERB iajs-2284 60 2 ( ( PUNCT iajs-2284 60 3 1 1 NUM iajs-2284 60 4 - - PUNCT iajs-2284 60 5 k=0.999 k=0.999 NOUN iajs-2284 60 6 ) ) PUNCT iajs-2284 60 7 , , PUNCT iajs-2284 60 8 then then ADV iajs-2284 60 9 : : PUNCT iajs-2284 60 10 οΏ½ οΏ½ PROPN iajs-2284 60 11 Μ‚ Μ‚ SYM iajs-2284 60 12 οΏ½ οΏ½ NOUN iajs-2284 60 13 1π‘ β„Ž2 1π‘ β„Ž2 NUM iajs-2284 60 14 = = SYM iajs-2284 60 15 π‘˜1 π‘˜1 PROPN iajs-2284 60 16 οΏ½ οΏ½ PROPN iajs-2284 60 17 Μ‚ Μ‚ NOUN iajs-2284 60 18 οΏ½ οΏ½ NOUN iajs-2284 60 19 𝑒𝑏 𝑒𝑏 VERB iajs-2284 60 20 + + CCONJ iajs-2284 60 21 ( ( PUNCT iajs-2284 60 22 1 1 NUM iajs-2284 60 23 βˆ’ βˆ’ NOUN iajs-2284 60 24 π‘˜1)𝛼0 π‘˜1)𝛼0 NOUN iajs-2284 60 25 ( ( PUNCT iajs-2284 60 26 22 22 NUM iajs-2284 60 27 ) ) PUNCT iajs-2284 60 28 οΏ½ οΏ½ PROPN iajs-2284 60 29 Μ‚ Μ‚ VERB iajs-2284 60 30 οΏ½ οΏ½ NOUN iajs-2284 60 31 2π‘ β„Ž2 2π‘ β„Ž2 NUM iajs-2284 60 32 = = SYM iajs-2284 60 33 π‘˜2 π‘˜2 PROPN iajs-2284 60 34 οΏ½ οΏ½ PROPN iajs-2284 60 35 Μ‚ Μ‚ VERB iajs-2284 60 36 οΏ½ οΏ½ NOUN iajs-2284 60 37 𝑒𝑏 𝑒𝑏 VERB iajs-2284 60 38 + + CCONJ iajs-2284 60 39 ( ( PUNCT iajs-2284 60 40 1 1 NUM iajs-2284 60 41 βˆ’ βˆ’ PROPN iajs-2284 60 42 π‘˜2)𝛼0 π‘˜2)𝛼0 NOUN iajs-2284 60 43 ( ( PUNCT iajs-2284 60 44 23 23 NUM iajs-2284 60 45 ) ) PUNCT iajs-2284 60 46 substituting substitute VERB iajs-2284 60 47 οΏ½ οΏ½ PROPN iajs-2284 60 48 Μ‚ Μ‚ SYM iajs-2284 60 49 οΏ½ οΏ½ NOUN iajs-2284 60 50 1π‘ β„Ž2 1π‘ β„Ž2 NUM iajs-2284 60 51 , , PUNCT iajs-2284 60 52 οΏ½ οΏ½ NOUN iajs-2284 60 53 Μ‚ Μ‚ NOUN iajs-2284 60 54 οΏ½ οΏ½ NOUN iajs-2284 60 55 2π‘ β„Ž2 2π‘ β„Ž2 NUM iajs-2284 60 56 in in ADP iajs-2284 60 57 equation equation NOUN iajs-2284 60 58 ( ( PUNCT iajs-2284 60 59 5 5 NUM iajs-2284 60 60 ) ) PUNCT iajs-2284 60 61 , , PUNCT iajs-2284 60 62 then then ADV iajs-2284 60 63 reliability reliability NOUN iajs-2284 60 64 estimation estimation NOUN iajs-2284 60 65 of of ADP iajs-2284 60 66 stress stress NOUN iajs-2284 60 67 – – PUNCT iajs-2284 60 68 strength strength NOUN iajs-2284 60 69 model model NOUN iajs-2284 60 70 with with ADP iajs-2284 60 71 using use VERB iajs-2284 60 72 constant constant ADJ iajs-2284 60 73 shrinkage shrinkage NOUN iajs-2284 60 74 factor factor NOUN iajs-2284 60 75 will will AUX iajs-2284 60 76 become become VERB iajs-2284 60 77 as as ADP iajs-2284 60 78 in in ADP iajs-2284 60 79 the the DET iajs-2284 60 80 following following NOUN iajs-2284 60 81 : : PUNCT iajs-2284 60 82 οΏ½ οΏ½ PROPN iajs-2284 60 83 Μ‚ Μ‚ VERB iajs-2284 60 84 οΏ½ οΏ½ PROPN iajs-2284 60 85 π‘ β„Ž2 π‘ β„Ž2 NOUN iajs-2284 60 86 = = SYM iajs-2284 60 87 οΏ½ οΏ½ PROPN iajs-2284 60 88 Μ‚ Μ‚ NOUN iajs-2284 60 89 οΏ½ οΏ½ PROPN iajs-2284 60 90 1π‘ β„Ž2 1π‘ β„Ž2 NUM iajs-2284 60 91 οΏ½ οΏ½ PROPN iajs-2284 60 92 Μ‚ Μ‚ SYM iajs-2284 60 93 οΏ½ οΏ½ NOUN iajs-2284 60 94 1π‘ β„Ž2 1π‘ β„Ž2 NUM iajs-2284 60 95 + + ADJ iajs-2284 60 96 οΏ½ οΏ½ NOUN iajs-2284 60 97 Μ‚ Μ‚ SYM iajs-2284 60 98 οΏ½ οΏ½ NOUN iajs-2284 60 99 2π‘ β„Ž2 2π‘ β„Ž2 NUM iajs-2284 60 100 ( ( PUNCT iajs-2284 60 101 24 24 NUM iajs-2284 60 102 ) ) PUNCT iajs-2284 60 103 74 74 NUM iajs-2284 60 104 ibn ibn PROPN iajs-2284 60 105 al al PROPN iajs-2284 60 106 - - PUNCT iajs-2284 60 107 haitham haitham PROPN iajs-2284 60 108 jour jour X iajs-2284 60 109 . . PROPN iajs-2284 61 1 for for ADP iajs-2284 61 2 pure pure ADJ iajs-2284 61 3 & & CCONJ iajs-2284 61 4 appl appl PROPN iajs-2284 61 5 . . PUNCT iajs-2284 62 1 sci sci PROPN iajs-2284 62 2 . . PROPN iajs-2284 62 3 32 32 NUM iajs-2284 62 4 ( ( PUNCT iajs-2284 62 5 3 3 NUM iajs-2284 62 6 ) ) PUNCT iajs-2284 62 7 2019 2019 NUM iajs-2284 62 8 2.4.3 2.4.3 NUM iajs-2284 62 9 beta beta NOUN iajs-2284 62 10 shrinkage shrinkage NOUN iajs-2284 62 11 factor factor NOUN iajs-2284 62 12 ( ( PUNCT iajs-2284 62 13 π’”π’‰πŸ‘ π’”π’‰πŸ‘ NOUN iajs-2284 62 14 ) ) PUNCT iajs-2284 63 1 [ [ X iajs-2284 63 2 11 11 NUM iajs-2284 63 3 ] ] PUNCT iajs-2284 63 4 . . PUNCT iajs-2284 64 1 in in ADP iajs-2284 64 2 this this DET iajs-2284 64 3 case case NOUN iajs-2284 64 4 , , PUNCT iajs-2284 64 5 the the DET iajs-2284 64 6 assumption assumption NOUN iajs-2284 64 7 ofβˆ…( ofβˆ…( PROPN iajs-2284 64 8 οΏ½ οΏ½ PROPN iajs-2284 64 9 Μ‚ Μ‚ NUM iajs-2284 64 10 οΏ½ οΏ½ NOUN iajs-2284 64 11 ) ) PUNCT iajs-2284 64 12 = = SYM iajs-2284 64 13 𝛽(1 𝛽(1 PROPN iajs-2284 64 14 , , PUNCT iajs-2284 64 15 𝑛 𝑛 PROPN iajs-2284 64 16 , , PUNCT iajs-2284 64 17 π‘š π‘š NOUN iajs-2284 64 18 ) ) PUNCT iajs-2284 64 19 for for ADP iajs-2284 64 20 the the DET iajs-2284 64 21 beta beta NOUN iajs-2284 64 22 shrinkage shrinkage NOUN iajs-2284 64 23 weight weight NOUN iajs-2284 64 24 factor factor NOUN iajs-2284 64 25 has have AUX iajs-2284 64 26 been be AUX iajs-2284 64 27 taken take VERB iajs-2284 64 28 asβˆ…( asβˆ…( NOUN iajs-2284 64 29 οΏ½ οΏ½ PROPN iajs-2284 64 30 Μ‚ Μ‚ VERB iajs-2284 64 31 οΏ½ οΏ½ NOUN iajs-2284 64 32 1 1 NUM iajs-2284 64 33 ) ) PUNCT iajs-2284 64 34 = = SYM iajs-2284 64 35 𝛽(1 𝛽(1 PROPN iajs-2284 64 36 , , PUNCT iajs-2284 64 37 𝑛 𝑛 NOUN iajs-2284 64 38 ) ) PUNCT iajs-2284 64 39 , , PUNCT iajs-2284 64 40 and and CCONJ iajs-2284 64 41 βˆ…( βˆ…( PROPN iajs-2284 64 42 οΏ½ οΏ½ PROPN iajs-2284 64 43 Μ‚ Μ‚ VERB iajs-2284 64 44 οΏ½ οΏ½ NOUN iajs-2284 64 45 2 2 NUM iajs-2284 64 46 ) ) PUNCT iajs-2284 64 47 = = SYM iajs-2284 64 48 𝛽(1 𝛽(1 PROPN iajs-2284 64 49 , , PUNCT iajs-2284 64 50 π‘š π‘š NOUN iajs-2284 64 51 ) ) PUNCT iajs-2284 64 52 and and CCONJ iajs-2284 64 53 this this PRON iajs-2284 64 54 implies imply VERB iajs-2284 64 55 to to ADP iajs-2284 64 56 the the DET iajs-2284 64 57 following follow VERB iajs-2284 64 58 shrinkage shrinkage NOUN iajs-2284 64 59 estimators estimator NOUN iajs-2284 64 60 : : PUNCT iajs-2284 64 61 οΏ½ οΏ½ PROPN iajs-2284 64 62 Μ‚ Μ‚ SYM iajs-2284 64 63 οΏ½ οΏ½ PROPN iajs-2284 64 64 1π‘ β„Ž3 1π‘ β„Ž3 NUM iajs-2284 64 65 = = SYM iajs-2284 64 66 𝛽(1 𝛽(1 PROPN iajs-2284 64 67 , , PUNCT iajs-2284 64 68 𝑛) 𝑛) NOUN iajs-2284 64 69 οΏ½ οΏ½ PROPN iajs-2284 64 70 Μ‚ Μ‚ VERB iajs-2284 64 71 οΏ½ οΏ½ NOUN iajs-2284 64 72 𝑒𝑏 𝑒𝑏 VERB iajs-2284 64 73 + + CCONJ iajs-2284 64 74 ( ( PUNCT iajs-2284 64 75 1 1 NUM iajs-2284 64 76 βˆ’ βˆ’ PROPN iajs-2284 64 77 𝛽(1 𝛽(1 PROPN iajs-2284 64 78 , , PUNCT iajs-2284 64 79 π‘š))𝛼0 π‘š))𝛼0 NUM iajs-2284 64 80 ( ( PUNCT iajs-2284 64 81 25 25 NUM iajs-2284 64 82 ) ) PUNCT iajs-2284 64 83 οΏ½ οΏ½ PROPN iajs-2284 64 84 Μ‚ Μ‚ VERB iajs-2284 64 85 οΏ½ οΏ½ NOUN iajs-2284 64 86 2π‘ β„Ž3 2π‘ β„Ž3 NUM iajs-2284 64 87 = = SYM iajs-2284 64 88 𝛽(1 𝛽(1 PROPN iajs-2284 64 89 , , PUNCT iajs-2284 64 90 𝑛) 𝑛) NOUN iajs-2284 64 91 οΏ½ οΏ½ PROPN iajs-2284 64 92 Μ‚ Μ‚ VERB iajs-2284 64 93 οΏ½ οΏ½ NOUN iajs-2284 64 94 𝑒𝑏 𝑒𝑏 VERB iajs-2284 64 95 + + CCONJ iajs-2284 64 96 ( ( PUNCT iajs-2284 64 97 1 1 NUM iajs-2284 64 98 βˆ’ βˆ’ PROPN iajs-2284 64 99 𝛽(1 𝛽(1 PROPN iajs-2284 64 100 , , PUNCT iajs-2284 64 101 π‘š))𝛼0 π‘š))𝛼0 NUM iajs-2284 64 102 ( ( PUNCT iajs-2284 64 103 26 26 NUM iajs-2284 64 104 ) ) PUNCT iajs-2284 64 105 substituting substitute VERB iajs-2284 64 106 οΏ½ οΏ½ PROPN iajs-2284 64 107 Μ‚ Μ‚ SYM iajs-2284 64 108 οΏ½ οΏ½ NOUN iajs-2284 64 109 1π‘ β„Ž3 1π‘ β„Ž3 NUM iajs-2284 64 110 , , PUNCT iajs-2284 64 111 οΏ½ οΏ½ PROPN iajs-2284 64 112 Μ‚ Μ‚ VERB iajs-2284 64 113 οΏ½ οΏ½ NOUN iajs-2284 64 114 2π‘ β„Ž3 2π‘ β„Ž3 NUM iajs-2284 64 115 in in ADP iajs-2284 64 116 equation equation NOUN iajs-2284 64 117 ( ( PUNCT iajs-2284 64 118 5 5 NUM iajs-2284 64 119 ) ) PUNCT iajs-2284 64 120 , , PUNCT iajs-2284 64 121 then then ADV iajs-2284 64 122 the the DET iajs-2284 64 123 reliability reliability NOUN iajs-2284 64 124 estimation estimation NOUN iajs-2284 64 125 of of ADP iajs-2284 64 126 stress stress NOUN iajs-2284 64 127 – – PUNCT iajs-2284 64 128 strength strength NOUN iajs-2284 64 129 model model NOUN iajs-2284 64 130 with with ADP iajs-2284 64 131 using use VERB iajs-2284 64 132 beta beta NOUN iajs-2284 64 133 shrinkage shrinkage NOUN iajs-2284 64 134 factor factor NOUN iajs-2284 64 135 will will AUX iajs-2284 64 136 become become VERB iajs-2284 64 137 as as ADP iajs-2284 64 138 in in ADP iajs-2284 64 139 the the DET iajs-2284 64 140 following following NOUN iajs-2284 64 141 : : PUNCT iajs-2284 64 142 οΏ½ οΏ½ PROPN iajs-2284 64 143 Μ‚ Μ‚ VERB iajs-2284 64 144 οΏ½ οΏ½ NOUN iajs-2284 64 145 π‘ β„Ž3 π‘ β„Ž3 NOUN iajs-2284 64 146 = = SYM iajs-2284 64 147 οΏ½ οΏ½ PROPN iajs-2284 64 148 Μ‚ Μ‚ PROPN iajs-2284 64 149 οΏ½ οΏ½ PROPN iajs-2284 64 150 1π‘ β„Ž3 1π‘ β„Ž3 NUM iajs-2284 64 151 οΏ½ οΏ½ PROPN iajs-2284 64 152 Μ‚ Μ‚ SYM iajs-2284 64 153 οΏ½ οΏ½ PROPN iajs-2284 64 154 1π‘ β„Ž3 1π‘ β„Ž3 NUM iajs-2284 64 155 + + NOUN iajs-2284 64 156 οΏ½ οΏ½ PROPN iajs-2284 64 157 Μ‚ Μ‚ SYM iajs-2284 64 158 οΏ½ οΏ½ NOUN iajs-2284 64 159 2π‘ β„Ž3 2π‘ β„Ž3 NUM iajs-2284 64 160 ( ( PUNCT iajs-2284 64 161 27 27 NUM iajs-2284 64 162 ) ) PUNCT iajs-2284 64 163 3simulation 3simulation PROPN iajs-2284 64 164 process process NOUN iajs-2284 64 165 the the DET iajs-2284 64 166 simulation simulation NOUN iajs-2284 64 167 process process NOUN iajs-2284 64 168 has have AUX iajs-2284 64 169 done do VERB iajs-2284 64 170 with with ADP iajs-2284 64 171 using use VERB iajs-2284 64 172 different different ADJ iajs-2284 64 173 sample sample NOUN iajs-2284 64 174 size size NOUN iajs-2284 64 175 such such ADJ iajs-2284 64 176 as as ADP iajs-2284 64 177 ( ( PUNCT iajs-2284 64 178 30 30 NUM iajs-2284 64 179 , , PUNCT iajs-2284 64 180 50 50 NUM iajs-2284 64 181 and and CCONJ iajs-2284 64 182 100 100 NUM iajs-2284 64 183 ) ) PUNCT iajs-2284 64 184 and and CCONJ iajs-2284 64 185 built build VERB iajs-2284 64 186 on on ADP iajs-2284 64 187 1000 1000 NUM iajs-2284 64 188 iteration iteration NOUN iajs-2284 64 189 and and CCONJ iajs-2284 64 190 using use VERB iajs-2284 64 191 the the DET iajs-2284 64 192 mean mean ADJ iajs-2284 64 193 square square NOUN iajs-2284 64 194 error error NOUN iajs-2284 64 195 ( ( PUNCT iajs-2284 64 196 mse mse NOUN iajs-2284 64 197 ) ) PUNCT iajs-2284 64 198 to to PART iajs-2284 64 199 measure measure VERB iajs-2284 64 200 and and CCONJ iajs-2284 64 201 check check VERB iajs-2284 64 202 the the DET iajs-2284 64 203 performance performance NOUN iajs-2284 64 204 as as ADP iajs-2284 64 205 in in ADP iajs-2284 64 206 the the DET iajs-2284 64 207 following follow VERB iajs-2284 64 208 steps step NOUN iajs-2284 64 209 : : PUNCT iajs-2284 64 210 step step NOUN iajs-2284 64 211 1 1 NUM iajs-2284 64 212 : : PUNCT iajs-2284 64 213 the the DET iajs-2284 64 214 random random ADJ iajs-2284 64 215 sample sample NOUN iajs-2284 64 216 generated generate VERB iajs-2284 64 217 for for ADP iajs-2284 64 218 x x PUNCT iajs-2284 64 219 according accord VERB iajs-2284 64 220 to to ADP iajs-2284 64 221 the the DET iajs-2284 64 222 uniform uniform ADJ iajs-2284 64 223 distribution distribution NOUN iajs-2284 64 224 over over ADP iajs-2284 64 225 the the DET iajs-2284 64 226 interval interval NOUN iajs-2284 64 227 ( ( PUNCT iajs-2284 64 228 0 0 NUM iajs-2284 64 229 , , PUNCT iajs-2284 64 230 1 1 X iajs-2284 64 231 ) ) PUNCT iajs-2284 64 232 asπ‘Ÿ1,π‘Ÿ2 asπ‘Ÿ1,π‘Ÿ2 PROPN iajs-2284 64 233 … … NUM iajs-2284 64 234 … … PUNCT iajs-2284 64 235 … … PUNCT iajs-2284 64 236 … … PUNCT iajs-2284 64 237 π‘Ÿπ‘› π‘Ÿπ‘› NOUN iajs-2284 64 238 and and CCONJ iajs-2284 64 239 the the DET iajs-2284 64 240 random random ADJ iajs-2284 64 241 sample sample NOUN iajs-2284 64 242 generated generate VERB iajs-2284 64 243 for for ADP iajs-2284 64 244 y y PROPN iajs-2284 64 245 according accord VERB iajs-2284 64 246 to to ADP iajs-2284 64 247 the the DET iajs-2284 64 248 uniform uniform ADJ iajs-2284 64 249 distribution distribution NOUN iajs-2284 64 250 over over ADP iajs-2284 64 251 the the DET iajs-2284 64 252 interval interval NOUN iajs-2284 64 253 ( ( PUNCT iajs-2284 64 254 0 0 NUM iajs-2284 64 255 , , PUNCT iajs-2284 64 256 1 1 NUM iajs-2284 64 257 ) ) PUNCT iajs-2284 64 258 , , PUNCT iajs-2284 64 259 as as ADP iajs-2284 64 260 𝑠1,𝑠2, 𝑠1,𝑠2, PROPN iajs-2284 64 261 … … SYM iajs-2284 64 262 … … PUNCT iajs-2284 64 263 … … PUNCT iajs-2284 64 264 … … PUNCT iajs-2284 64 265 π‘ π‘š π‘ π‘š ADP iajs-2284 64 266 step step NOUN iajs-2284 64 267 2 2 NUM iajs-2284 64 268 : : PUNCT iajs-2284 64 269 transforming transform VERB iajs-2284 64 270 the the DET iajs-2284 64 271 above above ADJ iajs-2284 64 272 power power NOUN iajs-2284 64 273 distribution distribution NOUN iajs-2284 64 274 with with ADP iajs-2284 64 275 using use VERB iajs-2284 64 276 reliability reliability NOUN iajs-2284 64 277 as as ADP iajs-2284 64 278 in in ADP iajs-2284 64 279 the the DET iajs-2284 64 280 following following NOUN iajs-2284 64 281 : : PUNCT iajs-2284 64 282 𝑅(π‘₯ 𝑅(π‘₯ NUM iajs-2284 64 283 ) ) PUNCT iajs-2284 64 284 = = SYM iajs-2284 64 285 1 1 NUM iajs-2284 64 286 βˆ’ βˆ’ NOUN iajs-2284 64 287 π‘₯𝛼 π‘₯𝛼 ADP iajs-2284 64 288 π‘₯𝑖 π‘₯𝑖 PROPN iajs-2284 64 289 = = PUNCT iajs-2284 64 290 ( ( PUNCT iajs-2284 64 291 1 1 NUM iajs-2284 64 292 βˆ’ βˆ’ NUM iajs-2284 64 293 π‘Ÿπ‘– π‘Ÿπ‘– NOUN iajs-2284 64 294 ) ) PUNCT iajs-2284 64 295 1 1 NUM iajs-2284 64 296 𝛼 𝛼 NOUN iajs-2284 64 297 i=1 i=1 PROPN iajs-2284 64 298 , , PUNCT iajs-2284 64 299 2 2 NUM iajs-2284 64 300 , , PUNCT iajs-2284 64 301 3 3 NUM iajs-2284 64 302 … … PUNCT iajs-2284 64 303 … … PUNCT iajs-2284 64 304 .. .. PUNCT iajs-2284 64 305 n n ADP iajs-2284 64 306 using use VERB iajs-2284 64 307 the the DET iajs-2284 64 308 same same ADJ iajs-2284 64 309 procedure procedure NOUN iajs-2284 64 310 .then .then X iajs-2284 65 1 𝑦𝑗 𝑦𝑗 NOUN iajs-2284 65 2 = = PUNCT iajs-2284 65 3 ( ( PUNCT iajs-2284 65 4 1 1 NUM iajs-2284 65 5 βˆ’ βˆ’ NOUN iajs-2284 65 6 𝑠𝑗 𝑠𝑗 NOUN iajs-2284 65 7 ) ) PUNCT iajs-2284 65 8 1 1 NUM iajs-2284 65 9 𝛼 𝛼 NOUN iajs-2284 65 10 j=1 j=1 NOUN iajs-2284 65 11 , , PUNCT iajs-2284 65 12 2 2 NUM iajs-2284 65 13 , , PUNCT iajs-2284 65 14 3 3 NUM iajs-2284 65 15 … … PUNCT iajs-2284 65 16 … … PUNCT iajs-2284 65 17 .. .. PUNCT iajs-2284 65 18 m m NOUN iajs-2284 65 19 step step VERB iajs-2284 65 20 3 3 NUM iajs-2284 65 21 : : PUNCT iajs-2284 65 22 calculating calculate VERB iajs-2284 65 23 οΏ½ οΏ½ PROPN iajs-2284 65 24 Μ‚ Μ‚ SYM iajs-2284 65 25 οΏ½ οΏ½ PROPN iajs-2284 65 26 1π‘šπ‘™π‘’ 1π‘šπ‘™π‘’ NUM iajs-2284 65 27 and and CCONJ iajs-2284 65 28 οΏ½ οΏ½ PROPN iajs-2284 65 29 Μ‚ Μ‚ NOUN iajs-2284 65 30 οΏ½ οΏ½ NOUN iajs-2284 65 31 2π‘šπ‘™π‘’ 2π‘šπ‘™π‘’ NOUN iajs-2284 65 32 using use VERB iajs-2284 65 33 equations equation NOUN iajs-2284 65 34 ( ( PUNCT iajs-2284 65 35 6 6 NUM iajs-2284 65 36 ) ) PUNCT iajs-2284 65 37 and and CCONJ iajs-2284 65 38 ( ( PUNCT iajs-2284 65 39 7 7 X iajs-2284 65 40 ) ) PUNCT iajs-2284 65 41 respectively respectively ADV iajs-2284 65 42 . . PUNCT iajs-2284 66 1 step step NOUN iajs-2284 66 2 4 4 NUM iajs-2284 66 3 : : PUNCT iajs-2284 66 4 calculating calculate VERB iajs-2284 66 5 οΏ½ οΏ½ PROPN iajs-2284 66 6 Μ‚ Μ‚ SYM iajs-2284 66 7 οΏ½ οΏ½ NOUN iajs-2284 66 8 1π‘šπ‘œπ‘š 1π‘šπ‘œπ‘š NOUN iajs-2284 66 9 and and CCONJ iajs-2284 66 10 οΏ½ οΏ½ PROPN iajs-2284 66 11 Μ‚ Μ‚ NOUN iajs-2284 66 12 οΏ½ οΏ½ NOUN iajs-2284 66 13 2π‘šπ‘œπ‘š 2π‘šπ‘œπ‘š NOUN iajs-2284 66 14 using use VERB iajs-2284 66 15 equations equation NOUN iajs-2284 66 16 ( ( PUNCT iajs-2284 66 17 9 9 NUM iajs-2284 66 18 ) ) PUNCT iajs-2284 66 19 and and CCONJ iajs-2284 66 20 ( ( PUNCT iajs-2284 66 21 10 10 NUM iajs-2284 66 22 ) ) PUNCT iajs-2284 66 23 respectively respectively ADV iajs-2284 66 24 . . PUNCT iajs-2284 67 1 step step NOUN iajs-2284 67 2 5 5 NUM iajs-2284 67 3 : : PUNCT iajs-2284 67 4 calculating calculate VERB iajs-2284 67 5 οΏ½ οΏ½ PROPN iajs-2284 67 6 Μ‚ Μ‚ SYM iajs-2284 67 7 οΏ½ οΏ½ PROPN iajs-2284 67 8 1𝐿𝑠 1𝐿𝑠 NUM iajs-2284 67 9 and and CCONJ iajs-2284 67 10 οΏ½ οΏ½ PROPN iajs-2284 67 11 Μ‚ Μ‚ NOUN iajs-2284 67 12 οΏ½ οΏ½ NOUN iajs-2284 67 13 2𝐿𝑠 2𝐿𝑠 NOUN iajs-2284 67 14 using use VERB iajs-2284 67 15 equations equation NOUN iajs-2284 67 16 ( ( PUNCT iajs-2284 67 17 14 14 NUM iajs-2284 67 18 ) ) PUNCT iajs-2284 67 19 and and CCONJ iajs-2284 67 20 ( ( PUNCT iajs-2284 67 21 15 15 NUM iajs-2284 67 22 ) ) PUNCT iajs-2284 67 23 respectively respectively ADV iajs-2284 67 24 . . PUNCT iajs-2284 68 1 step step NOUN iajs-2284 68 2 6 6 NUM iajs-2284 68 3 : : PUNCT iajs-2284 68 4 calculating calculate VERB iajs-2284 68 5 οΏ½ οΏ½ PROPN iajs-2284 68 6 Μ‚ Μ‚ PROPN iajs-2284 68 7 οΏ½ οΏ½ NOUN iajs-2284 68 8 1π‘ β„Žπ‘– 1π‘ β„Žπ‘– NUM iajs-2284 68 9 and and CCONJ iajs-2284 68 10 οΏ½ οΏ½ PROPN iajs-2284 68 11 Μ‚ Μ‚ NOUN iajs-2284 68 12 οΏ½ οΏ½ NOUN iajs-2284 68 13 2π‘ β„Žπ‘– 2π‘ β„Žπ‘– NUM iajs-2284 68 14 when when SCONJ iajs-2284 68 15 i=1 i=1 PROPN iajs-2284 68 16 , , PUNCT iajs-2284 68 17 2 2 NUM iajs-2284 68 18 , , PUNCT iajs-2284 68 19 3 3 NUM iajs-2284 68 20 using use VERB iajs-2284 68 21 equations equation NOUN iajs-2284 68 22 ( ( PUNCT iajs-2284 68 23 19 19 NUM iajs-2284 68 24 ) ) PUNCT iajs-2284 68 25 , , PUNCT iajs-2284 68 26 ( ( PUNCT iajs-2284 68 27 20 20 NUM iajs-2284 68 28 ) ) PUNCT iajs-2284 68 29 , , PUNCT iajs-2284 68 30 ( ( PUNCT iajs-2284 68 31 22 22 NUM iajs-2284 68 32 ) ) PUNCT iajs-2284 68 33 , , PUNCT iajs-2284 68 34 ( ( PUNCT iajs-2284 68 35 23 23 NUM iajs-2284 68 36 ) ) PUNCT iajs-2284 68 37 , , PUNCT iajs-2284 68 38 ( ( PUNCT iajs-2284 68 39 25 25 NUM iajs-2284 68 40 ) ) PUNCT iajs-2284 68 41 and and CCONJ iajs-2284 68 42 ( ( PUNCT iajs-2284 68 43 26 26 NUM iajs-2284 68 44 ) ) PUNCT iajs-2284 68 45 respectively respectively ADV iajs-2284 68 46 . . PUNCT iajs-2284 69 1 step step NOUN iajs-2284 69 2 7 7 NUM iajs-2284 69 3 : : PUNCT iajs-2284 69 4 calculating calculate VERB iajs-2284 69 5 οΏ½ οΏ½ PROPN iajs-2284 69 6 Μ‚ Μ‚ PROPN iajs-2284 69 7 οΏ½ οΏ½ PROPN iajs-2284 69 8 π‘šπ‘™π‘’ π‘šπ‘™π‘’ PROPN iajs-2284 69 9 , , PUNCT iajs-2284 69 10 οΏ½ οΏ½ PROPN iajs-2284 69 11 Μ‚ Μ‚ NOUN iajs-2284 69 12 οΏ½ οΏ½ NOUN iajs-2284 69 13 π‘šπ‘œπ‘š π‘šπ‘œπ‘š NOUN iajs-2284 69 14 , , PUNCT iajs-2284 69 15 οΏ½ οΏ½ NOUN iajs-2284 69 16 Μ‚ Μ‚ NOUN iajs-2284 69 17 οΏ½ οΏ½ PROPN iajs-2284 69 18 𝐿𝑠 𝐿𝑠 PROPN iajs-2284 69 19 , , PUNCT iajs-2284 69 20 οΏ½ οΏ½ PROPN iajs-2284 69 21 Μ‚ Μ‚ NOUN iajs-2284 69 22 οΏ½ οΏ½ NOUN iajs-2284 69 23 π‘ β„Ž1 π‘ β„Ž1 NOUN iajs-2284 69 24 , , PUNCT iajs-2284 69 25 οΏ½ οΏ½ PROPN iajs-2284 69 26 Μ‚ Μ‚ NOUN iajs-2284 69 27 οΏ½ οΏ½ NOUN iajs-2284 69 28 π‘ β„Ž2 π‘ β„Ž2 NOUN iajs-2284 69 29 and and CCONJ iajs-2284 69 30 οΏ½ οΏ½ PROPN iajs-2284 69 31 Μ‚ Μ‚ VERB iajs-2284 69 32 οΏ½ οΏ½ NOUN iajs-2284 69 33 π‘ β„Ž3 π‘ β„Ž3 NOUN iajs-2284 69 34 using use VERB iajs-2284 69 35 equations equation NOUN iajs-2284 69 36 ( ( PUNCT iajs-2284 69 37 8) 8) NUM iajs-2284 69 38 , , PUNCT iajs-2284 69 39 ( ( PUNCT iajs-2284 69 40 13 13 NUM iajs-2284 69 41 ) ) PUNCT iajs-2284 69 42 , , PUNCT iajs-2284 69 43 ( ( PUNCT iajs-2284 69 44 16 16 NUM iajs-2284 69 45 ) ) PUNCT iajs-2284 69 46 , , PUNCT iajs-2284 69 47 ( ( PUNCT iajs-2284 69 48 21 21 NUM iajs-2284 69 49 ) ) PUNCT iajs-2284 69 50 , , PUNCT iajs-2284 69 51 ( ( PUNCT iajs-2284 69 52 24 24 NUM iajs-2284 69 53 ) ) PUNCT iajs-2284 69 54 and and CCONJ iajs-2284 69 55 ( ( PUNCT iajs-2284 69 56 27 27 NUM iajs-2284 69 57 ) ) PUNCT iajs-2284 69 58 respectively respectively ADV iajs-2284 69 59 . . 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NOUN iajs-2284 70 12 the the DET iajs-2284 70 13 outcomes outcome NOUN iajs-2284 70 14 results result NOUN iajs-2284 70 15 are be AUX iajs-2284 70 16 listed list VERB iajs-2284 70 17 in in ADP iajs-2284 70 18 the the DET iajs-2284 70 19 tables table NOUN iajs-2284 70 20 1 1 NUM iajs-2284 70 21 , , PUNCT iajs-2284 70 22 3 3 NUM iajs-2284 70 23 , , PUNCT iajs-2284 70 24 5 5 NUM iajs-2284 70 25 , , PUNCT iajs-2284 70 26 7 7 NUM iajs-2284 70 27 , , PUNCT iajs-2284 70 28 9 9 NUM iajs-2284 70 29 , , PUNCT iajs-2284 70 30 11 11 NUM iajs-2284 70 31 , , PUNCT iajs-2284 70 32 13 13 NUM iajs-2284 70 33 , , PUNCT iajs-2284 70 34 15 15 NUM iajs-2284 70 35 , , PUNCT iajs-2284 70 36 17 17 NUM iajs-2284 70 37 . . PUNCT iajs-2284 70 38 respectively respectively ADV iajs-2284 70 39 . . PUNCT iajs-2284 71 1 4 4 X iajs-2284 71 2 . . X iajs-2284 71 3 numerical numerical ADJ iajs-2284 71 4 result result VERB iajs-2284 71 5 some some DET iajs-2284 71 6 methods method NOUN iajs-2284 71 7 of of ADP iajs-2284 71 8 goodness goodness NOUN iajs-2284 71 9 of of ADP iajs-2284 71 10 fit fit ADJ iajs-2284 71 11 analysis analysis NOUN iajs-2284 71 12 are be AUX iajs-2284 71 13 employed employ VERB iajs-2284 71 14 here here ADV iajs-2284 71 15 ; ; PUNCT iajs-2284 71 16 the the DET iajs-2284 71 17 measurement measurement NOUN iajs-2284 71 18 give give VERB iajs-2284 71 19 an an DET iajs-2284 71 20 indication indication NOUN iajs-2284 71 21 of of ADP iajs-2284 71 22 best good ADJ iajs-2284 71 23 method method NOUN iajs-2284 71 24 is be AUX iajs-2284 71 25 mean mean ADJ iajs-2284 71 26 square square ADJ iajs-2284 71 27 error error NOUN iajs-2284 71 28 ( ( PUNCT iajs-2284 71 29 mse mse NOUN iajs-2284 71 30 ) ) PUNCT iajs-2284 71 31 from from ADP iajs-2284 71 32 tables table NOUN iajs-2284 71 33 for for ADP iajs-2284 71 34 all all PRON iajs-2284 71 35 . . 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PUNCT iajs-2284 73 1 2 2 X iajs-2284 73 2 . . X iajs-2284 73 3 for for ADP iajs-2284 73 4 all all DET iajs-2284 73 5 n=(30,50,100 n=(30,50,100 NOUN iajs-2284 73 6 ) ) PUNCT iajs-2284 73 7 and and CCONJ iajs-2284 73 8 m=(30,50,100 m=(30,50,100 NOUN iajs-2284 73 9 ) ) PUNCT iajs-2284 73 10 the the DET iajs-2284 73 11 minimum minimum ADJ iajs-2284 73 12 mean mean NOUN iajs-2284 73 13 square square NOUN iajs-2284 73 14 error error NOUN iajs-2284 73 15 ( ( PUNCT iajs-2284 73 16 mse mse NOUN iajs-2284 73 17 ) ) PUNCT iajs-2284 73 18 for for ADP iajs-2284 73 19 the the DET iajs-2284 73 20 stressstrength stressstrength NOUN iajs-2284 73 21 reliability reliability NOUN iajs-2284 73 22 estimator estimator NOUN iajs-2284 73 23 of of ADP iajs-2284 73 24 power power NOUN iajs-2284 73 25 function function NOUN iajs-2284 73 26 distribution distribution NOUN iajs-2284 73 27 , , PUNCT iajs-2284 73 28 we we PRON iajs-2284 73 29 noticed notice VERB iajs-2284 73 30 that that SCONJ iajs-2284 73 31 the the DET iajs-2284 73 32 shrinkage shrinkage NOUN iajs-2284 73 33 estimator estimator NOUN iajs-2284 73 34 is be AUX iajs-2284 73 35 the the DET iajs-2284 73 36 best good ADJ iajs-2284 73 37 and and CCONJ iajs-2284 73 38 follows follow VERB iajs-2284 73 39 by by ADP iajs-2284 73 40 maximum maximum ADJ iajs-2284 73 41 likelihood likelihood NOUN iajs-2284 73 42 estimator estimator NOUN iajs-2284 73 43 ( ( PUNCT iajs-2284 73 44 mle mle PROPN iajs-2284 73 45 ) ) PUNCT iajs-2284 73 46 , , PUNCT iajs-2284 73 47 moment moment NOUN iajs-2284 73 48 estimator estimator NOUN iajs-2284 73 49 ( ( PUNCT iajs-2284 73 50 mom mom NOUN iajs-2284 73 51 ) ) PUNCT iajs-2284 73 52 and and CCONJ iajs-2284 73 53 least least ADJ iajs-2284 73 54 square square ADJ iajs-2284 73 55 estimator estimator NOUN iajs-2284 73 56 ( ( PUNCT iajs-2284 73 57 ls ls PROPN iajs-2284 73 58 ) ) PUNCT iajs-2284 73 59 . . PUNCT iajs-2284 74 1 3 3 X iajs-2284 74 2 . . X iajs-2284 74 3 for for ADP iajs-2284 74 4 the the DET iajs-2284 74 5 various various ADJ iajs-2284 74 6 cases case NOUN iajs-2284 74 7 when when SCONJ iajs-2284 74 8 ( ( PUNCT iajs-2284 74 9 n=30 n=30 NOUN iajs-2284 74 10 and and CCONJ iajs-2284 74 11 m=30 m=30 PROPN iajs-2284 74 12 ) ) PUNCT iajs-2284 74 13 , , PUNCT iajs-2284 74 14 ( ( PUNCT iajs-2284 74 15 𝛼1=1and 𝛼1=1and PROPN iajs-2284 74 16 Ξ±2=1 Ξ±2=1 PROPN iajs-2284 74 17 ) ) PUNCT iajs-2284 74 18 then then ADV iajs-2284 74 19 be be AUX iajs-2284 74 20 moment moment NOUN iajs-2284 74 21 75 75 NUM iajs-2284 74 22 ibn ibn PROPN iajs-2284 74 23 al al PROPN iajs-2284 74 24 - - PUNCT iajs-2284 74 25 haitham haitham PROPN iajs-2284 74 26 jour jour X iajs-2284 74 27 . . PROPN iajs-2284 75 1 for for ADP iajs-2284 75 2 pure pure ADJ iajs-2284 75 3 & & CCONJ iajs-2284 75 4 appl appl PROPN iajs-2284 75 5 . . PUNCT iajs-2284 76 1 sci sci PROPN iajs-2284 76 2 . . PROPN iajs-2284 76 3 32 32 NUM iajs-2284 76 4 ( ( PUNCT iajs-2284 76 5 3 3 NUM iajs-2284 76 6 ) ) SYM iajs-2284 76 7 2019 2019 NUM iajs-2284 76 8 estimator estimator NOUN iajs-2284 76 9 ( ( PUNCT iajs-2284 76 10 mom mom NOUN iajs-2284 76 11 ) ) PUNCT iajs-2284 76 12 batter batter NOUN iajs-2284 76 13 then then ADV iajs-2284 76 14 maximum maximum ADJ iajs-2284 76 15 likelihood likelihood NOUN iajs-2284 76 16 estimator estimator NOUN iajs-2284 76 17 ( ( PUNCT iajs-2284 76 18 mle mle PROPN iajs-2284 76 19 ) ) PUNCT iajs-2284 76 20 . . PUNCT iajs-2284 77 1 table table NOUN iajs-2284 77 2 1 1 NUM iajs-2284 77 3 . . PUNCT iajs-2284 78 1 the the DET iajs-2284 78 2 estimation estimation NOUN iajs-2284 78 3 when when SCONJ iajs-2284 78 4 r=0.5 r=0.5 NOUN iajs-2284 78 5 , , PUNCT iajs-2284 78 6 alpha1= alpha1= VERB iajs-2284 78 7 1 1 NUM iajs-2284 78 8 , , PUNCT iajs-2284 78 9 alpha2= alpha2= PROPN iajs-2284 78 10 1 1 NUM iajs-2284 78 11 . . PUNCT iajs-2284 78 12 table table NOUN iajs-2284 78 13 2 2 NUM iajs-2284 78 14 . . PUNCT iajs-2284 78 15 mse mse NOUN iajs-2284 78 16 values value NOUN iajs-2284 78 17 when when SCONJ iajs-2284 78 18 r r NOUN iajs-2284 78 19 = = SYM iajs-2284 78 20 0.5 0.5 NUM iajs-2284 78 21 , , PUNCT iajs-2284 78 22 alpha1= alpha1= VERB iajs-2284 78 23 1 1 NUM iajs-2284 78 24 , , PUNCT iajs-2284 78 25 alpha2= alpha2= PROPN iajs-2284 78 26 1 1 NUM iajs-2284 78 27 . . PUNCT iajs-2284 78 28 table table NOUN iajs-2284 78 29 3 3 NUM iajs-2284 78 30 . . PUNCT iajs-2284 79 1 the the DET iajs-2284 79 2 estimation estimation NOUN iajs-2284 79 3 when when SCONJ iajs-2284 79 4 r r NOUN iajs-2284 79 5 = = NOUN iajs-2284 79 6 0.333333 0.333333 NUM iajs-2284 79 7 , , PUNCT iajs-2284 79 8 alpha1= alpha1= VERB iajs-2284 79 9 1 1 NUM iajs-2284 79 10 , , PUNCT iajs-2284 79 11 alpha2= alpha2= NOUN iajs-2284 79 12 2 2 NUM iajs-2284 79 13 . . PUNCT iajs-2284 80 1 n n NUM iajs-2284 80 2 m m PROPN iajs-2284 80 3 οΏ½ οΏ½ NOUN iajs-2284 80 4 Μ‚ Μ‚ VERB iajs-2284 80 5 οΏ½ οΏ½ PROPN iajs-2284 80 6 mle mle PROPN iajs-2284 80 7 οΏ½ οΏ½ PROPN iajs-2284 80 8 Μ‚ Μ‚ PROPN iajs-2284 80 9 οΏ½ οΏ½ PROPN iajs-2284 80 10 mom mom NOUN iajs-2284 80 11 οΏ½ οΏ½ PROPN iajs-2284 80 12 Μ‚ Μ‚ PROPN iajs-2284 80 13 οΏ½ οΏ½ PROPN iajs-2284 80 14 sh1 sh1 PROPN iajs-2284 80 15 οΏ½ οΏ½ PROPN iajs-2284 80 16 Μ‚ Μ‚ PROPN iajs-2284 80 17 οΏ½ οΏ½ PROPN iajs-2284 80 18 sh2 sh2 PROPN iajs-2284 80 19 οΏ½ οΏ½ PROPN iajs-2284 80 20 Μ‚ Μ‚ PROPN iajs-2284 80 21 οΏ½ οΏ½ PROPN iajs-2284 80 22 sh3 sh3 PROPN iajs-2284 80 23 οΏ½ οΏ½ PROPN iajs-2284 80 24 Μ‚ Μ‚ PROPN iajs-2284 80 25 οΏ½ οΏ½ NOUN iajs-2284 80 26 ls ls ADJ iajs-2284 80 27 30 30 NUM iajs-2284 80 28 30 30 NUM iajs-2284 80 29 0.490139 0.490139 NUM iajs-2284 80 30 0.511770 0.511770 NUM iajs-2284 80 31 0.500105 0.500105 NUM iajs-2284 80 32 0.500003 0.500003 NUM iajs-2284 80 33 0.500106 0.500106 NUM iajs-2284 80 34 0.491397 0.491397 NUM iajs-2284 80 35 50 50 NUM iajs-2284 80 36 0.502377 0.502377 NUM iajs-2284 80 37 0.501424 0.501424 NUM iajs-2284 80 38 0.485568 0.485568 NUM iajs-2284 80 39 0.500000 0.500000 NUM iajs-2284 80 40 0.492930 0.492930 NUM iajs-2284 80 41 0.498530 0.498530 NUM iajs-2284 80 42 100 100 NUM iajs-2284 80 43 0.500411 0.500411 NUM iajs-2284 80 44 0.497019 0.497019 NUM iajs-2284 80 45 0.485535 0.485535 NUM iajs-2284 80 46 0.500002 0.500002 NUM iajs-2284 80 47 0.487835 0.487835 NUM iajs-2284 80 48 0.495937 0.495937 NUM iajs-2284 80 49 50 50 NUM iajs-2284 80 50 30 30 NUM iajs-2284 80 51 0.497673 0.497673 NUM iajs-2284 80 52 0.499256 0.499256 NUM iajs-2284 80 53 0.514426 0.514426 NUM iajs-2284 80 54 0.500001 0.500001 NUM iajs-2284 80 55 0.507071 0.507071 NUM iajs-2284 80 56 0.501789 0.501789 NUM iajs-2284 80 57 50 50 NUM iajs-2284 80 58 0.501290 0.501290 NUM iajs-2284 80 59 0.502633 0.502633 NUM iajs-2284 80 60 0.499992 0.499992 NUM iajs-2284 80 61 0.499999 0.499999 NUM iajs-2284 80 62 0.499969 0.499969 NUM iajs-2284 80 63 0.501975 0.501975 NUM iajs-2284 80 64 100 100 NUM iajs-2284 80 65 0.501921 0.501921 NUM iajs-2284 80 66 0.501610 0.501610 NUM iajs-2284 81 1 0.499903 0.499903 NUM iajs-2284 81 2 0.499999 0.499999 NUM iajs-2284 81 3 0.494837 0.494837 NUM iajs-2284 81 4 0.500422 0.500422 NUM iajs-2284 81 5 100 100 NUM iajs-2284 81 6 30 30 NUM iajs-2284 81 7 0.496428 0.496428 NUM iajs-2284 81 8 0.499589 0.499589 NUM iajs-2284 81 9 0.514526 0.514526 NUM iajs-2284 81 10 0.500001 0.500001 NUM iajs-2284 81 11 0.512236 0.512236 NUM iajs-2284 81 12 0.502114 0.502114 NUM iajs-2284 81 13 50 50 NUM iajs-2284 81 14 0.497654 0.497654 NUM iajs-2284 81 15 0.498059 0.498059 NUM iajs-2284 81 16 0.500099 0.500099 NUM iajs-2284 81 17 0.500001 0.500001 NUM iajs-2284 81 18 0.505168 0.505168 NUM iajs-2284 81 19 0.501268 0.501268 NUM iajs-2284 81 20 100 100 NUM iajs-2284 81 21 0.500210 0.500210 NUM iajs-2284 81 22 0.500975 0.500975 NUM iajs-2284 81 23 0.499999 0.499999 NUM 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PROPN iajs-2284 104 22 jour jour X iajs-2284 104 23 . . 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PUNCT iajs-2284 108 1 mse mse NOUN iajs-2284 108 2 values value NOUN iajs-2284 108 3 when when SCONJ iajs-2284 108 4 r r NOUN iajs-2284 108 5 = = SYM iajs-2284 108 6 0.5000000 0.5000000 NUM iajs-2284 108 7 , , PUNCT iajs-2284 108 8 alpha1= alpha1= VERB iajs-2284 108 9 2 2 NUM iajs-2284 108 10 , , PUNCT iajs-2284 108 11 alpha2= alpha2= ADJ iajs-2284 108 12 2 2 NUM iajs-2284 108 13 . . PUNCT iajs-2284 108 14 table table NOUN iajs-2284 108 15 11.the 11.the PROPN iajs-2284 108 16 estimation estimation NOUN iajs-2284 108 17 when when SCONJ iajs-2284 108 18 r r NOUN iajs-2284 108 19 = = NOUN iajs-2284 108 20 0.750000 0.750000 NUM iajs-2284 108 21 , , PUNCT iajs-2284 108 22 alpha1= alpha1= VERB iajs-2284 108 23 3 3 NUM iajs-2284 108 24 , , PUNCT iajs-2284 108 25 alpha2= alpha2= NOUN iajs-2284 108 26 1 1 NUM iajs-2284 108 27 . . PUNCT iajs-2284 109 1 n n PRON iajs-2284 109 2 m m PROPN iajs-2284 109 3 οΏ½ οΏ½ NOUN iajs-2284 109 4 Μ‚ Μ‚ VERB iajs-2284 109 5 οΏ½ οΏ½ PROPN iajs-2284 109 6 mle mle PROPN iajs-2284 109 7 οΏ½ οΏ½ PROPN iajs-2284 109 8 Μ‚ Μ‚ PROPN iajs-2284 109 9 οΏ½ οΏ½ PROPN iajs-2284 109 10 mom mom NOUN iajs-2284 109 11 οΏ½ οΏ½ PROPN iajs-2284 109 12 Μ‚ Μ‚ PROPN iajs-2284 109 13 οΏ½ οΏ½ PROPN iajs-2284 109 14 sh1 sh1 PROPN iajs-2284 109 15 οΏ½ οΏ½ PROPN iajs-2284 109 16 Μ‚ Μ‚ PROPN iajs-2284 109 17 οΏ½ οΏ½ PROPN iajs-2284 109 18 sh2 sh2 PROPN iajs-2284 109 19 οΏ½ οΏ½ PROPN iajs-2284 109 20 Μ‚ Μ‚ PROPN iajs-2284 109 21 οΏ½ οΏ½ PROPN iajs-2284 109 22 sh3 sh3 PROPN iajs-2284 109 23 οΏ½ οΏ½ PROPN iajs-2284 109 24 Μ‚ Μ‚ PROPN iajs-2284 109 25 οΏ½ οΏ½ NOUN iajs-2284 109 26 ls ls ADJ iajs-2284 109 27 30 30 NUM iajs-2284 109 28 30 30 NUM iajs-2284 109 29 0.500752 0.500752 NUM iajs-2284 109 30 0.500283 0.500283 NUM iajs-2284 109 31 0.499984 0.499984 NUM iajs-2284 109 32 0.500000 0.500000 NUM iajs-2284 109 33 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π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 111 6 50 50 NUM iajs-2284 111 7 0.003355245833 0.003355245833 NUM iajs-2284 111 8 0.003784728713 0.003784728713 NUM iajs-2284 111 9 0.000209383584 0.000209383584 NUM iajs-2284 111 10 0.000000003620 0.000000003620 NUM iajs-2284 111 11 0.000052863372 0.000052863372 NUM iajs-2284 111 12 0.006185754049 0.006185754049 NUM iajs-2284 111 13 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 111 14 100 100 NUM iajs-2284 111 15 0.002539072228 0.002539072228 NUM iajs-2284 111 16 0.002862493900 0.002862493900 NUM iajs-2284 111 17 0.000211322115 0.000211322115 NUM iajs-2284 111 18 0.000000002679 0.000000002679 NUM iajs-2284 111 19 0.000150482732 0.000150482732 NUM iajs-2284 111 20 0.004649858803 0.004649858803 NUM iajs-2284 111 21 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 111 22 50 50 NUM iajs-2284 111 23 30 30 NUM iajs-2284 111 24 0.003222287571 0.003222287571 NUM iajs-2284 111 25 0.003616390312 0.003616390312 NUM iajs-2284 111 26 0.0002112752765 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PROPN iajs-2284 114 19 for for ADP iajs-2284 114 20 pure pure ADJ iajs-2284 114 21 & & CCONJ iajs-2284 114 22 appl appl PROPN iajs-2284 114 23 . . PUNCT iajs-2284 115 1 sci sci PROPN iajs-2284 115 2 . . PROPN iajs-2284 115 3 32 32 NUM iajs-2284 115 4 ( ( PUNCT iajs-2284 115 5 3 3 NUM iajs-2284 115 6 ) ) SYM iajs-2284 115 7 2019 2019 NUM iajs-2284 115 8 table table NOUN iajs-2284 115 9 12 12 NUM iajs-2284 115 10 . . PUNCT iajs-2284 116 1 mse mse NOUN iajs-2284 116 2 values value NOUN iajs-2284 116 3 when when SCONJ iajs-2284 116 4 r r NOUN iajs-2284 116 5 = = SYM iajs-2284 116 6 0.750000 0.750000 NUM iajs-2284 116 7 , , PUNCT iajs-2284 116 8 alpha1= alpha1= VERB iajs-2284 116 9 3 3 NUM iajs-2284 116 10 , , PUNCT iajs-2284 116 11 alpha2= alpha2= PROPN iajs-2284 116 12 1 1 NUM iajs-2284 116 13 . . PUNCT iajs-2284 116 14 table table NOUN iajs-2284 116 15 13 13 NUM iajs-2284 116 16 . . PUNCT iajs-2284 117 1 the the DET iajs-2284 117 2 estimation estimation NOUN iajs-2284 117 3 when when SCONJ iajs-2284 117 4 r r NOUN iajs-2284 117 5 = = NOUN iajs-2284 117 6 0.400000 0.400000 NUM iajs-2284 117 7 , , PUNCT iajs-2284 117 8 alpha1= alpha1= VERB iajs-2284 117 9 2 2 NUM iajs-2284 117 10 , , PUNCT iajs-2284 117 11 alpha2= alpha2= ADJ iajs-2284 117 12 3 3 NUM iajs-2284 117 13 . . PUNCT iajs-2284 117 14 table table NOUN iajs-2284 117 15 14 14 NUM iajs-2284 117 16 . . PUNCT iajs-2284 118 1 mse mse NOUN iajs-2284 118 2 values value NOUN iajs-2284 118 3 when when SCONJ iajs-2284 118 4 r r NOUN iajs-2284 118 5 = = SYM iajs-2284 118 6 0.400000 0.400000 NUM iajs-2284 118 7 , , PUNCT iajs-2284 118 8 alpha1= alpha1= VERB iajs-2284 118 9 2 2 NUM iajs-2284 118 10 , , PUNCT iajs-2284 118 11 alpha2= alpha2= NOUN iajs-2284 118 12 3 3 NUM iajs-2284 118 13 . . PUNCT iajs-2284 119 1 n n PRON iajs-2284 119 2 m m PROPN iajs-2284 119 3 π’Žπ’”π’†mle π’Žπ’”π’†mle NOUN iajs-2284 119 4 π’Žπ’”π’†mom π’Žπ’”π’†mom PROPN iajs-2284 119 5 π’Žπ’”π’†sh1 π’Žπ’”π’†sh1 PROPN iajs-2284 119 6 π’Žπ’”π’†sh2 π’Žπ’”π’†sh2 PROPN iajs-2284 119 7 π’Žπ’”π’†sh3 π’Žπ’”π’†sh3 PROPN iajs-2284 119 8 π’Žπ’”π’†ls π’Žπ’”π’†ls NOUN iajs-2284 119 9 best well ADV iajs-2284 119 10 30 30 NUM iajs-2284 119 11 30 30 NUM iajs-2284 119 12 0.002384459481 0.002384459481 NUM iajs-2284 120 1 0.002851628898 0.002851628898 NUM iajs-2284 120 2 0.000003192342 0.000003192342 NUM iajs-2284 120 3 0.000000002563 0.000000002563 NUM iajs-2284 120 4 0.000003275999 0.000003275999 NUM iajs-2284 120 5 0.004521397784 0.004521397784 NUM iajs-2284 120 6 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 120 7 50 50 NUM iajs-2284 120 8 0.001948985166 0.001948985166 NUM iajs-2284 120 9 0.002244248987 0.002244248987 NUM iajs-2284 120 10 0.000121340373 0.000121340373 NUM 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π‘šπ‘ π‘’sh2 NOUN iajs-2284 120 32 50 50 NUM iajs-2284 120 33 0.001497007264 0.001497007264 NUM iajs-2284 120 34 0.001814282137 0.001814282137 NUM iajs-2284 120 35 0.000000043673 0.000000043673 NUM iajs-2284 120 36 0.000000001558 0.000000001558 NUM iajs-2284 120 37 0.000000675002 0.000000675002 NUM iajs-2284 120 38 0.003051262077 0.003051262077 NUM iajs-2284 120 39 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 120 40 100 100 NUM iajs-2284 121 1 0.001020052304 0.001020052304 NUM iajs-2284 121 2 0.001169978602 0.001169978602 NUM iajs-2284 121 3 0.000000034777 0.000000034777 NUM iajs-2284 121 4 0.000000001064 0.000000001064 NUM iajs-2284 121 5 0.000015586022 0.000015586022 NUM iajs-2284 121 6 0.002017961664 0.002017961664 NUM iajs-2284 121 7 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 121 8 100 100 NUM iajs-2284 121 9 30 30 NUM iajs-2284 121 10 0.001547120432 0.001547120432 NUM iajs-2284 121 11 0.001996286322 0.001996286322 NUM iajs-2284 121 12 0.000115999905 0.000115999905 NUM iajs-2284 121 13 0.000000001544 0.000000001544 NUM iajs-2284 121 14 0.000083023582 0.000083023582 NUM iajs-2284 121 15 0.002746512587 0.002746512587 NUM iajs-2284 121 16 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 121 17 50 50 NUM iajs-2284 121 18 0.001026872629 0.001026872629 NUM iajs-2284 121 19 0.001229979595 0.001229979595 NUM iajs-2284 121 20 0.000000032430 0.000000032430 NUM iajs-2284 121 21 0.000000001027 0.000000001027 NUM iajs-2284 121 22 0.000014956803 0.000014956803 NUM iajs-2284 121 23 0.001827470288 0.001827470288 NUM iajs-2284 121 24 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 121 25 100 100 NUM iajs-2284 121 26 0.000702148814 0.000702148814 NUM iajs-2284 121 27 0.000841172097 0.000841172097 NUM iajs-2284 121 28 0.000000018293 0.000000018293 NUM iajs-2284 121 29 0.000000000701 0.000000000701 NUM iajs-2284 121 30 0.000000072800 0.000000072800 NUM iajs-2284 121 31 0.001371989596 0.001371989596 NUM iajs-2284 121 32 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 121 33 n n PRON iajs-2284 121 34 m m PROPN iajs-2284 121 35 οΏ½ οΏ½ NOUN iajs-2284 121 36 Μ‚ Μ‚ VERB iajs-2284 121 37 οΏ½ οΏ½ PROPN iajs-2284 121 38 mle mle PROPN iajs-2284 121 39 οΏ½ οΏ½ PROPN iajs-2284 121 40 Μ‚ Μ‚ PROPN iajs-2284 121 41 οΏ½ οΏ½ PROPN iajs-2284 121 42 mom mom NOUN iajs-2284 121 43 οΏ½ οΏ½ PROPN iajs-2284 121 44 Μ‚ Μ‚ PROPN iajs-2284 121 45 οΏ½ οΏ½ PROPN iajs-2284 121 46 sh1 sh1 PROPN iajs-2284 121 47 οΏ½ οΏ½ PROPN iajs-2284 121 48 Μ‚ Μ‚ PROPN iajs-2284 121 49 οΏ½ οΏ½ PROPN iajs-2284 121 50 sh2 sh2 PROPN iajs-2284 121 51 οΏ½ οΏ½ PROPN iajs-2284 121 52 Μ‚ Μ‚ PROPN iajs-2284 121 53 οΏ½ οΏ½ PROPN iajs-2284 121 54 sh3 sh3 PROPN iajs-2284 121 55 οΏ½ οΏ½ PROPN iajs-2284 121 56 Μ‚ Μ‚ PROPN iajs-2284 121 57 οΏ½ οΏ½ NOUN iajs-2284 121 58 ls ls ADJ iajs-2284 122 1 30 30 NUM iajs-2284 122 2 30 30 NUM iajs-2284 122 3 0.404506 0.404506 NUM iajs-2284 122 4 0.403784 0.403784 NUM iajs-2284 122 5 0.399881 0.399881 NUM iajs-2284 122 6 0.399997 0.399997 NUM iajs-2284 122 7 0.399879 0.399879 NUM iajs-2284 122 8 0.403496 0.403496 NUM iajs-2284 122 9 50 50 NUM iajs-2284 122 10 0.404397 0.404397 NUM iajs-2284 122 11 0.402729 0.402729 NUM iajs-2284 122 12 0.386249 0.386249 NUM iajs-2284 122 13 0.399998 0.399998 NUM iajs-2284 122 14 0.393222 0.393222 NUM iajs-2284 122 15 0.399588 0.399588 NUM iajs-2284 122 16 100 100 NUM iajs-2284 122 17 0.402856 0.402856 NUM iajs-2284 122 18 0.400909 0.400909 NUM iajs-2284 122 19 0.386181 0.386181 NUM iajs-2284 122 20 0.400001 0.400001 NUM iajs-2284 122 21 0.388360 0.388360 NUM iajs-2284 122 22 0.398094 0.398094 NUM iajs-2284 122 23 50 50 NUM iajs-2284 122 24 30 30 NUM iajs-2284 122 25 0.398661 0.398661 NUM iajs-2284 122 26 0.399451 0.399451 NUM iajs-2284 122 27 0.413926 0.413926 NUM iajs-2284 122 28 0.400001 0.400001 NUM iajs-2284 122 29 0.406817 0.406817 NUM iajs-2284 122 30 0.406414 0.406414 NUM iajs-2284 122 31 50 50 NUM iajs-2284 122 32 0.403676 0.403676 NUM iajs-2284 122 33 0.403770 0.403770 NUM iajs-2284 122 34 0.399987 0.399987 NUM iajs-2284 122 35 0.399997 0.399997 NUM iajs-2284 122 36 0.399947 0.399947 NUM iajs-2284 122 37 0.407139 0.407139 NUM iajs-2284 122 38 100 100 NUM iajs-2284 122 39 0.401190 0.401190 NUM iajs-2284 122 40 0.400025 0.400025 NUM iajs-2284 122 41 0.399914 0.399914 NUM iajs-2284 122 42 0.400001 0.400001 NUM iajs-2284 122 43 0.395066 0.395066 NUM iajs-2284 122 44 0.403155 0.403155 NUM iajs-2284 122 45 100 100 NUM iajs-2284 122 46 30 30 NUM iajs-2284 122 47 0.397284 0.397284 NUM iajs-2284 122 48 0.397751 0.397751 NUM iajs-2284 123 1 0.414066 0.414066 NUM iajs-2284 123 2 0.400001 0.400001 NUM iajs-2284 123 3 0.411838 0.411838 NUM iajs-2284 123 4 0.402213 0.402213 NUM iajs-2284 123 5 50 50 NUM iajs-2284 123 6 0.401166 0.401166 NUM iajs-2284 123 7 0.401576 0.401576 NUM iajs-2284 123 8 0.400081 0.400081 NUM iajs-2284 123 9 0.399998 0.399998 NUM iajs-2284 123 10 0.404928 0.404928 NUM iajs-2284 123 11 0.402906 0.402906 NUM iajs-2284 123 12 100 100 NUM iajs-2284 123 13 0.401270 0.401270 NUM iajs-2284 123 14 0.401548 0.401548 NUM iajs-2284 124 1 0.399996 0.399996 NUM iajs-2284 124 2 0.399999 0.399999 NUM iajs-2284 124 3 0.399992 0.399992 NUM iajs-2284 124 4 0.403123 0.403123 NUM iajs-2284 124 5 n n NUM iajs-2284 124 6 m m NOUN iajs-2284 124 7 π’Žπ’”π’†mle π’Žπ’”π’†mle NOUN iajs-2284 124 8 π’Žπ’”π’†mom π’Žπ’”π’†mom PROPN iajs-2284 124 9 π’Žπ’”π’†sh1 π’Žπ’”π’†sh1 PROPN iajs-2284 124 10 π’Žπ’”π’†sh2 π’Žπ’”π’†sh2 PROPN iajs-2284 124 11 π’Žπ’”π’†sh3 π’Žπ’”π’†sh3 PROPN iajs-2284 124 12 π’Žπ’”π’†ls π’Žπ’”π’†ls NOUN iajs-2284 124 13 best well ADV iajs-2284 124 14 30 30 NUM iajs-2284 124 15 30 30 NUM iajs-2284 124 16 0.003968719837 0.003968719837 NUM iajs-2284 124 17 0.004339244098 0.004339244098 NUM iajs-2284 124 18 0.000005400944 0.000005400944 NUM iajs-2284 124 19 0.000000004337 0.000000004337 NUM iajs-2284 124 20 0.000005542471 0.000005542471 NUM iajs-2284 124 21 0.007343458817 0.007343458817 NUM iajs-2284 124 22 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 1 50 50 NUM iajs-2284 125 2 0.002871054638 0.002871054638 NUM iajs-2284 125 3 0.003168491061 0.003168491061 NUM iajs-2284 125 4 0.000191532791 0.000191532791 NUM iajs-2284 125 5 0.000000003008 0.000000003008 NUM iajs-2284 125 6 0.000048857539 0.000048857539 NUM iajs-2284 125 7 0.005249976869 0.005249976869 NUM iajs-2284 125 8 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 9 100 100 NUM iajs-2284 125 10 0.002560059256 0.002560059256 NUM iajs-2284 125 11 0.002759431582 0.002759431582 NUM iajs-2284 125 12 0.000193533534 0.000193533534 NUM iajs-2284 125 13 0.000000002729 0.000000002729 NUM iajs-2284 125 14 0.000138181811 0.000138181811 NUM iajs-2284 125 15 0.004430761642 0.004430761642 NUM iajs-2284 125 16 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 17 50 50 NUM iajs-2284 125 18 30 30 NUM iajs-2284 125 19 0.003057266048 0.003057266048 NUM iajs-2284 125 20 0.003368884673 0.003368884673 NUM iajs-2284 125 21 0.000196646030 0.000196646030 NUM iajs-2284 125 22 0.000000003292 0.000000003292 NUM iajs-2284 125 23 0.000049708350 0.000049708350 NUM iajs-2284 125 24 0.005687576189 0.005687576189 NUM iajs-2284 125 25 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 26 50 50 NUM iajs-2284 125 27 0.002354827003 0.002354827003 NUM iajs-2284 125 28 0.002572130065 0.002572130065 NUM iajs-2284 125 29 0.000000068179 0.000000068179 NUM iajs-2284 125 30 0.000000002433 0.000000002433 NUM iajs-2284 125 31 0.000001053332 0.000001053332 NUM iajs-2284 125 32 0.004695426152 0.004695426152 NUM iajs-2284 125 33 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 34 100 100 NUM iajs-2284 125 35 0.001758583317 0.001758583317 NUM iajs-2284 125 36 0.001851572994 0.001851572994 NUM iajs-2284 125 37 0.000000057177 0.000000057177 NUM iajs-2284 125 38 0.000000001821 0.000000001821 NUM iajs-2284 125 39 0.000024931773 0.000024931773 NUM iajs-2284 125 40 0.003154647116 0.003154647116 NUM iajs-2284 125 41 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 42 100 100 NUM iajs-2284 125 43 30 30 NUM iajs-2284 125 44 0.002509204252 0.002509204252 NUM iajs-2284 125 45 0.002634167448 0.002634167448 NUM iajs-2284 125 46 0.000200568619 0.000200568619 NUM iajs-2284 125 47 0.000000002757 0.000000002757 NUM iajs-2284 125 48 0.000142971140 0.000142971140 NUM iajs-2284 125 49 0.004464657451 0.004464657451 NUM iajs-2284 125 50 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 51 50 50 NUM iajs-2284 125 52 0.001776285618 0.001776285618 NUM iajs-2284 125 53 0.001939439022 0.001939439022 NUM iajs-2284 125 54 0.000000056642 0.000000056642 NUM iajs-2284 125 55 0.000000001834 0.000000001834 NUM iajs-2284 125 56 0.000024872335 0.000024872335 NUM iajs-2284 125 57 0.003451614797 0.003451614797 NUM iajs-2284 125 58 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 59 100 100 NUM iajs-2284 125 60 0.001103485740 0.001103485740 NUM iajs-2284 125 61 0.001185957806 0.001185957806 NUM iajs-2284 125 62 0.000000029215 0.000000029215 NUM iajs-2284 125 63 0.000000001120 0.000000001120 NUM iajs-2284 125 64 0.000000116266 0.000000116266 NUM iajs-2284 125 65 0.002211734727 0.002211734727 NUM iajs-2284 125 66 π‘šπ‘ π‘’sh2 π‘šπ‘ π‘’sh2 NOUN iajs-2284 125 67 80 80 NUM iajs-2284 126 1 ibn ibn PROPN iajs-2284 126 2 al al PROPN iajs-2284 126 3 - - PUNCT iajs-2284 126 4 haitham haitham PROPN iajs-2284 126 5 jour jour X iajs-2284 126 6 . . PROPN iajs-2284 126 7 for for ADP iajs-2284 126 8 pure pure ADJ iajs-2284 126 9 & & CCONJ iajs-2284 126 10 appl appl PROPN iajs-2284 126 11 . . PUNCT iajs-2284 127 1 sci sci PROPN iajs-2284 127 2 . . PROPN iajs-2284 127 3 32 32 NUM iajs-2284 127 4 ( ( PUNCT iajs-2284 127 5 3 3 NUM iajs-2284 127 6 ) ) SYM iajs-2284 127 7 2019 2019 NUM iajs-2284 127 8 table table NOUN iajs-2284 127 9 15 15 NUM iajs-2284 127 10 . . PUNCT iajs-2284 128 1 the the DET iajs-2284 128 2 estimation estimation NOUN iajs-2284 128 3 when when SCONJ iajs-2284 128 4 r r NOUN iajs-2284 128 5 = = NOUN iajs-2284 128 6 0.600000 0.600000 NUM iajs-2284 128 7 , , PUNCT iajs-2284 128 8 alpha1= alpha1= VERB iajs-2284 128 9 3 3 NUM iajs-2284 128 10 , , PUNCT iajs-2284 128 11 alpha2= alpha2= PROPN iajs-2284 128 12 2 2 NUM iajs-2284 128 13 . . PUNCT iajs-2284 128 14 table table NOUN iajs-2284 128 15 16 16 NUM iajs-2284 128 16 . . PUNCT iajs-2284 129 1 mse mse NOUN iajs-2284 129 2 values value NOUN iajs-2284 129 3 when when SCONJ iajs-2284 129 4 r r NOUN iajs-2284 129 5 = = SYM iajs-2284 129 6 0.600000 0.600000 NUM iajs-2284 129 7 , , PUNCT iajs-2284 129 8 alpha1= alpha1= VERB iajs-2284 129 9 3 3 NUM iajs-2284 129 10 , , PUNCT iajs-2284 129 11 alpha2= alpha2= PROPN iajs-2284 129 12 2 2 NUM iajs-2284 129 13 . . PUNCT iajs-2284 129 14 table table NOUN iajs-2284 129 15 17 17 NUM iajs-2284 129 16 . . PUNCT iajs-2284 130 1 the the DET iajs-2284 130 2 estimation estimation NOUN iajs-2284 130 3 when when SCONJ iajs-2284 130 4 r r NOUN iajs-2284 130 5 = = NOUN iajs-2284 130 6 0.500000 0.500000 NUM iajs-2284 130 7 , , PUNCT iajs-2284 130 8 alpha1= alpha1= VERB iajs-2284 130 9 3 3 NUM iajs-2284 130 10 , , PUNCT iajs-2284 130 11 alpha2= alpha2= NOUN iajs-2284 130 12 3 3 NUM iajs-2284 130 13 . . PUNCT iajs-2284 131 1 n n NUM iajs-2284 131 2 m m PROPN iajs-2284 131 3 οΏ½ οΏ½ NOUN iajs-2284 131 4 Μ‚ Μ‚ VERB iajs-2284 131 5 οΏ½ οΏ½ PROPN iajs-2284 131 6 mle mle PROPN iajs-2284 131 7 οΏ½ οΏ½ PROPN iajs-2284 131 8 Μ‚ Μ‚ PROPN iajs-2284 131 9 οΏ½ οΏ½ PROPN iajs-2284 131 10 mom mom NOUN iajs-2284 131 11 οΏ½ οΏ½ PROPN iajs-2284 131 12 Μ‚ Μ‚ PROPN iajs-2284 131 13 οΏ½ οΏ½ PROPN iajs-2284 131 14 sh1 sh1 PROPN iajs-2284 131 15 οΏ½ οΏ½ PROPN iajs-2284 131 16 Μ‚ Μ‚ PROPN iajs-2284 131 17 οΏ½ οΏ½ PROPN iajs-2284 131 18 sh2 sh2 PROPN iajs-2284 131 19 οΏ½ οΏ½ PROPN iajs-2284 131 20 Μ‚ Μ‚ PROPN iajs-2284 131 21 οΏ½ οΏ½ PROPN iajs-2284 131 22 sh3 sh3 PROPN iajs-2284 131 23 οΏ½ οΏ½ PROPN iajs-2284 131 24 Μ‚ Μ‚ PROPN iajs-2284 131 25 οΏ½ οΏ½ NOUN iajs-2284 131 26 ls ls ADJ iajs-2284 131 27 30 30 NUM iajs-2284 131 28 30 30 NUM iajs-2284 131 29 0.598078 0.598078 NUM iajs-2284 131 30 0.599079 0.599079 NUM iajs-2284 131 31 0.600008 0.600008 NUM iajs-2284 131 32 0.600000 0.600000 NUM iajs-2284 131 33 0.600008 0.600008 NUM iajs-2284 131 34 0.597839 0.597839 NUM iajs-2284 131 35 50 50 NUM iajs-2284 131 36 0.599919 0.599919 NUM iajs-2284 131 37 0.598806 0.598806 NUM iajs-2284 131 38 0.586143 0.586143 NUM iajs-2284 131 39 0.600000 0.600000 NUM iajs-2284 131 40 0.593246 0.593246 NUM iajs-2284 132 1 0.594149 0.594149 NUM iajs-2284 132 2 100 100 NUM iajs-2284 132 3 0.602922 0.602922 NUM iajs-2284 132 4 0.601586 0.601586 NUM iajs-2284 132 5 0.585963 0.585963 NUM iajs-2284 132 6 0.599999 0.599999 NUM iajs-2284 132 7 0.588188 0.588188 NUM iajs-2284 132 8 0.597739 0.597739 NUM iajs-2284 132 9 50 50 NUM iajs-2284 132 10 30 30 NUM iajs-2284 132 11 0.597608 0.597608 NUM iajs-2284 132 12 0.597803 0.597803 NUM iajs-2284 132 13 0.613749 0.613749 NUM iajs-2284 132 14 0.600000 0.600000 NUM iajs-2284 132 15 0.606745 0.606745 NUM iajs-2284 132 16 0.594849 0.594849 NUM iajs-2284 132 17 50 50 NUM iajs-2284 132 18 0.598873 0.598873 NUM iajs-2284 132 19 0.599349 0.599349 NUM iajs-2284 132 20 0.600002 0.600002 NUM iajs-2284 132 21 0.600000 0.600000 NUM iajs-2284 132 22 0.600008 0.600008 NUM iajs-2284 132 23 0.598037 0.598037 NUM iajs-2284 132 24 100 100 NUM iajs-2284 132 25 0.599726 0.599726 NUM iajs-2284 132 26 0.598941 0.598941 NUM iajs-2284 132 27 0.599914 0.599914 NUM iajs-2284 132 28 0.600001 0.600001 NUM iajs-2284 132 29 0.595049 0.595049 NUM iajs-2284 132 30 0.596674 0.596674 NUM iajs-2284 132 31 100 100 NUM iajs-2284 132 32 30 30 NUM iajs-2284 132 33 0.595986 0.595986 NUM iajs-2284 132 34 0.597631 0.597631 NUM iajs-2284 132 35 0.613846 0.613846 NUM iajs-2284 132 36 0.600000 0.600000 NUM iajs-2284 132 37 0.611669 0.611669 NUM iajs-2284 132 38 0.598814 0.598814 NUM iajs-2284 132 39 50 50 NUM iajs-2284 132 40 0.600409 0.600409 NUM iajs-2284 132 41 0.601163 0.601163 NUM iajs-2284 132 42 0.600076 0.600076 NUM iajs-2284 132 43 0.599998 0.599998 NUM iajs-2284 132 44 0.604884 0.604884 NUM iajs-2284 132 45 0.602419 0.602419 NUM iajs-2284 132 46 100 100 NUM iajs-2284 132 47 0.598798 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