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PUNCT iajs-2375 19 1 bbsmh896@gmail.com bbsmh896@gmail.com X iajs-2375 20 1 hbama75@yahoo.com hbama75@yahoo.com X iajs-2375 21 1 abbasnajim66@yahoo.com abbasnajim66@yahoo.com X iajs-2375 21 2 on on ADP iajs-2375 21 3 estimation estimation NOUN iajs-2375 21 4 of of ADP iajs-2375 21 5 p(y p(y PROPN iajs-2375 21 6 < < X iajs-2375 21 7 x x X iajs-2375 21 8 ) ) PUNCT iajs-2375 21 9 in in ADP iajs-2375 21 10 case case NOUN iajs-2375 21 11 inverse inverse NOUN iajs-2375 21 12 kumaraswamy kumaraswamy NOUN iajs-2375 21 13 distribution distribution NOUN iajs-2375 21 14 article article NOUN iajs-2375 21 15 history history NOUN iajs-2375 21 16 : : PUNCT iajs-2375 21 17 received receive VERB iajs-2375 21 18 2 2 NUM iajs-2375 21 19 april april PROPN iajs-2375 21 20 2019 2019 NUM iajs-2375 21 21 , , PUNCT iajs-2375 21 22 accepted accept VERB iajs-2375 21 23 30 30 NUM iajs-2375 21 24 june june PROPN iajs-2375 21 25 2019 2019 NUM iajs-2375 21 26 , , PUNCT iajs-2375 21 27 publish publish VERB iajs-2375 21 28 january january PROPN iajs-2375 21 29 2020 2020 NUM iajs-2375 21 30 . . 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PUNCT iajs-2375 28 1 the the DET iajs-2375 28 2 term term NOUN iajs-2375 28 3 stress stress NOUN iajs-2375 28 4 - - PUNCT iajs-2375 28 5 strength strength NOUN iajs-2375 28 6 ( ( PUNCT iajs-2375 28 7 s s NOUN iajs-2375 28 8 - - PUNCT iajs-2375 28 9 s s NOUN iajs-2375 28 10 ) ) PUNCT iajs-2375 28 11 refers refer VERB iajs-2375 28 12 to to ADP iajs-2375 28 13 a a DET iajs-2375 28 14 component component NOUN iajs-2375 28 15 which which PRON iajs-2375 28 16 has have VERB iajs-2375 28 17 a a DET iajs-2375 28 18 random random ADJ iajs-2375 28 19 of of ADP iajs-2375 28 20 strength strength NOUN iajs-2375 28 21 𝑋 𝑋 NOUN iajs-2375 28 22 subject subject NOUN iajs-2375 28 23 to to ADP iajs-2375 28 24 a a DET iajs-2375 28 25 random random ADJ iajs-2375 28 26 stress stress NOUN iajs-2375 28 27 π‘Œ π‘Œ PROPN iajs-2375 28 28 to to PART iajs-2375 28 29 evaluate evaluate VERB iajs-2375 28 30 the the DET iajs-2375 28 31 reliability reliability NOUN iajs-2375 28 32 . . 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PUNCT iajs-2375 30 1 several several ADJ iajs-2375 30 2 researchers researcher NOUN iajs-2375 30 3 assuming assume VERB iajs-2375 30 4 various various ADJ iajs-2375 30 5 lifetime lifetime NOUN iajs-2375 30 6 distributions distribution NOUN iajs-2375 30 7 for for ADP iajs-2375 30 8 the the DET iajs-2375 30 9 stress stress NOUN iajs-2375 30 10 strength strength NOUN iajs-2375 30 11 random random ADJ iajs-2375 30 12 variates.[11 variates.[11 PROPN iajs-2375 30 13 - - SYM iajs-2375 30 14 14 14 NUM iajs-2375 30 15 ] ] PUNCT iajs-2375 30 16 . . PUNCT iajs-2375 31 1 accordingly accordingly ADV iajs-2375 31 2 , , PUNCT iajs-2375 31 3 𝑅 𝑅 PROPN iajs-2375 31 4 ( ( PUNCT iajs-2375 31 5 π‘Œ π‘Œ PROPN iajs-2375 31 6 𝑋 𝑋 PROPN iajs-2375 31 7 is be AUX iajs-2375 31 8 a a DET iajs-2375 31 9 measure measure NOUN iajs-2375 31 10 of of ADP iajs-2375 31 11 component component NOUN iajs-2375 31 12 reliability reliability NOUN iajs-2375 31 13 in in ADP iajs-2375 31 14 ( ( PUNCT iajs-2375 31 15 s s NOUN iajs-2375 31 16 - - PUNCT iajs-2375 31 17 s s NOUN iajs-2375 31 18 ) ) PUNCT iajs-2375 31 19 model model NOUN iajs-2375 31 20 . . PUNCT iajs-2375 32 1 consequently consequently ADV iajs-2375 32 2 , , PUNCT iajs-2375 32 3 this this DET iajs-2375 32 4 study study NOUN iajs-2375 32 5 estimates estimate VERB iajs-2375 32 6 the the DET iajs-2375 32 7 ( ( PUNCT iajs-2375 32 8 s s NOUN iajs-2375 32 9 - - PUNCT iajs-2375 32 10 s s NOUN iajs-2375 32 11 ) ) PUNCT iajs-2375 32 12 reliability reliability NOUN iajs-2375 32 13 when when SCONJ iajs-2375 32 14 the the DET iajs-2375 32 15 stress stress NOUN iajs-2375 32 16 and and CCONJ iajs-2375 32 17 strength strength NOUN iajs-2375 32 18 follows follow VERB iajs-2375 32 19 the the DET iajs-2375 32 20 two two NUM iajs-2375 32 21 parameters parameter NOUN iajs-2375 32 22 invers inver NOUN iajs-2375 32 23 kumaraswamy kumaraswamy ADJ iajs-2375 32 24 distribution distribution NOUN iajs-2375 32 25 ( ( PUNCT iajs-2375 32 26 ikumd ikumd NOUN iajs-2375 32 27 ) ) PUNCT iajs-2375 32 28 via via ADP iajs-2375 32 29 different different ADJ iajs-2375 32 30 estimation estimation NOUN iajs-2375 32 31 methods method NOUN iajs-2375 32 32 . . PUNCT iajs-2375 33 1 now now ADV iajs-2375 33 2 , , PUNCT iajs-2375 33 3 if if SCONJ iajs-2375 33 4 x x PRON iajs-2375 33 5 and and CCONJ iajs-2375 33 6 y y PROPN iajs-2375 33 7 are be AUX iajs-2375 33 8 two two NUM iajs-2375 33 9 random random ADJ iajs-2375 33 10 variables variable NOUN iajs-2375 33 11 follows follow VERB iajs-2375 33 12 the the DET iajs-2375 33 13 ikumd ikumd NOUN iajs-2375 33 14 with with ADP iajs-2375 33 15 parameters parameter NOUN iajs-2375 33 16 ( ( PUNCT iajs-2375 33 17 and and CCONJ iajs-2375 33 18 ( ( PUNCT iajs-2375 33 19 as as ADP iajs-2375 33 20 strength strength NOUN iajs-2375 33 21 and and CCONJ iajs-2375 33 22 stress stress NOUN iajs-2375 33 23 respectively respectively ADV iajs-2375 33 24 when when SCONJ iajs-2375 33 25 the the DET iajs-2375 33 26 parameter parameter NOUN iajs-2375 33 27 is be AUX iajs-2375 33 28 known know VERB iajs-2375 33 29 , , PUNCT iajs-2375 33 30 then then ADV iajs-2375 33 31 the the DET iajs-2375 33 32 ( ( PUNCT iajs-2375 33 33 s s NOUN iajs-2375 33 34 - - PUNCT iajs-2375 33 35 s s NOUN iajs-2375 33 36 ) ) PUNCT iajs-2375 33 37 reliability reliability NOUN iajs-2375 33 38 is be AUX iajs-2375 33 39 defined define VERB iajs-2375 33 40 as as ADP iajs-2375 33 41 below below ADV iajs-2375 33 42 ; ; PUNCT iajs-2375 34 1 𝑅 𝑅 PROPN iajs-2375 34 2 ( ( PUNCT iajs-2375 34 3 π‘Œ π‘Œ PROPN iajs-2375 34 4 𝑋 𝑋 PROPN iajs-2375 34 5 ∫ ∫ PROPN iajs-2375 34 6 ∫ ∫ PROPN iajs-2375 34 7 𝑓 𝑓 PROPN iajs-2375 34 8 ( ( PUNCT iajs-2375 34 9 ( ( PUNCT iajs-2375 34 10 ∫ ∫ PROPN iajs-2375 34 11 𝐹 𝐹 PROPN iajs-2375 34 12 ( ( PUNCT iajs-2375 34 13 𝑓 𝑓 PROPN iajs-2375 34 14 ( ( PUNCT iajs-2375 34 15 ∫ ∫ PROPN iajs-2375 34 16 ( ( PUNCT iajs-2375 34 17 ( ( PUNCT iajs-2375 34 18 ( ( PUNCT iajs-2375 34 19 ( ( PUNCT iajs-2375 34 20 ( ( PUNCT iajs-2375 34 21 ( ( PUNCT iajs-2375 34 22 ( ( PUNCT iajs-2375 34 23 3 3 X iajs-2375 34 24 ) ) PUNCT iajs-2375 34 25 the the DET iajs-2375 34 26 rest rest NOUN iajs-2375 34 27 of of ADP iajs-2375 34 28 this this DET iajs-2375 34 29 paper paper NOUN iajs-2375 34 30 organized organize VERB iajs-2375 34 31 as as SCONJ iajs-2375 34 32 follows follow VERB iajs-2375 34 33 : : PUNCT iajs-2375 34 34 section section NOUN iajs-2375 34 35 2 2 NUM iajs-2375 34 36 including include VERB iajs-2375 34 37 some some DET iajs-2375 34 38 estimation estimation NOUN iajs-2375 34 39 methods method NOUN iajs-2375 34 40 of of ADP iajs-2375 34 41 p(π‘Œ p(π‘Œ PROPN iajs-2375 34 42 𝑋 𝑋 PROPN iajs-2375 34 43 ) ) PUNCT iajs-2375 34 44 . . PUNCT iajs-2375 35 1 section section NOUN iajs-2375 35 2 3 3 NUM iajs-2375 35 3 offers offer VERB iajs-2375 35 4 simulation simulation NOUN iajs-2375 35 5 study study NOUN iajs-2375 35 6 . . PUNCT iajs-2375 36 1 section section NOUN iajs-2375 36 2 4 4 NUM iajs-2375 36 3 demonstrates demonstrate VERB iajs-2375 36 4 the the DET iajs-2375 36 5 effectiveness effectiveness NOUN iajs-2375 36 6 of of ADP iajs-2375 36 7 the the DET iajs-2375 36 8 proposed propose VERB iajs-2375 36 9 method method NOUN iajs-2375 36 10 through through ADP iajs-2375 36 11 results result NOUN iajs-2375 36 12 . . PUNCT iajs-2375 37 1 finally finally ADV iajs-2375 37 2 , , PUNCT iajs-2375 37 3 a a DET iajs-2375 37 4 conclusion conclusion NOUN iajs-2375 37 5 is be AUX iajs-2375 37 6 provided provide VERB iajs-2375 37 7 in in ADP iajs-2375 37 8 section5 section5 NOUN iajs-2375 37 9 . . PUNCT iajs-2375 38 1 2 2 X iajs-2375 38 2 . . X iajs-2375 38 3 estimation estimation NOUN iajs-2375 38 4 methods method NOUN iajs-2375 38 5 of of ADP iajs-2375 38 6 p p X iajs-2375 38 7 ( ( PUNCT iajs-2375 38 8 2 2 NUM iajs-2375 38 9 . . NOUN iajs-2375 38 10 1 1 NUM iajs-2375 38 11 . . X iajs-2375 38 12 maximum maximum ADJ iajs-2375 38 13 likelihood likelihood NOUN iajs-2375 38 14 estimation estimation NOUN iajs-2375 38 15 ( ( PUNCT iajs-2375 38 16 mle mle NOUN iajs-2375 38 17 ) ) PUNCT iajs-2375 38 18 let let AUX iajs-2375 38 19 be be AUX iajs-2375 38 20 a a DET iajs-2375 38 21 random random ADJ iajs-2375 38 22 sample sample NOUN iajs-2375 38 23 from from ADP iajs-2375 38 24 ikumd ikumd NOUN iajs-2375 38 25 ( ( PUNCT iajs-2375 38 26 and and CCONJ iajs-2375 38 27 be be AUX iajs-2375 38 28 a a DET iajs-2375 38 29 random random ADJ iajs-2375 38 30 sample sample NOUN iajs-2375 38 31 from from ADP iajs-2375 38 32 ikumd ikumd NOUN iajs-2375 38 33 ( ( PUNCT iajs-2375 38 34 , , PUNCT iajs-2375 38 35 then then ADV iajs-2375 38 36 the the DET iajs-2375 38 37 likelihood likelihood NOUN iajs-2375 38 38 function function NOUN iajs-2375 38 39 is be AUX iajs-2375 38 40 given give VERB iajs-2375 38 41 by by ADP iajs-2375 38 42 𝑙 𝑙 PROPN iajs-2375 38 43 ( ( PUNCT iajs-2375 38 44 ∏ ∏ PROPN iajs-2375 38 45 𝑓 𝑓 PROPN iajs-2375 38 46 ( ( PUNCT iajs-2375 38 47 ∏ ∏ PROPN iajs-2375 38 48 ( ( PUNCT iajs-2375 38 49 ) ) PUNCT iajs-2375 38 50 ∏ ∏ PROPN iajs-2375 38 51 ( ( PUNCT iajs-2375 38 52 ( ( PUNCT iajs-2375 38 53 ( ( PUNCT iajs-2375 38 54 ( ( PUNCT iajs-2375 38 55 ∏ ∏ X iajs-2375 38 56 ( ( PUNCT iajs-2375 38 57 ) ) PUNCT iajs-2375 38 58 ( ( PUNCT iajs-2375 38 59 ( ( PUNCT iajs-2375 38 60 ( ( PUNCT iajs-2375 38 61 ) ) PUNCT iajs-2375 38 62 ) ) PUNCT iajs-2375 38 63 ∏ ∏ PROPN iajs-2375 38 64 ( ( PUNCT iajs-2375 38 65 ( ( PUNCT iajs-2375 38 66 ∏ ∏ X iajs-2375 38 67 ( ( PUNCT iajs-2375 38 68 ) ) PUNCT iajs-2375 38 69 ( ( PUNCT iajs-2375 38 70 ∏ ∏ X iajs-2375 38 71 ( ( PUNCT iajs-2375 38 72 ( ( PUNCT iajs-2375 38 73 ∏ ∏ X iajs-2375 38 74 ( ( PUNCT iajs-2375 38 75 ( ( PUNCT iajs-2375 38 76 ) ) PUNCT iajs-2375 38 77 ) ) PUNCT iajs-2375 38 78 ( ( PUNCT iajs-2375 38 79 4 4 X iajs-2375 38 80 ) ) PUNCT iajs-2375 38 81 take take VERB iajs-2375 38 82 ln ln ADV iajs-2375 38 83 to to ADP iajs-2375 38 84 both both DET iajs-2375 38 85 sides side NOUN iajs-2375 38 86 and and CCONJ iajs-2375 38 87 the the DET iajs-2375 38 88 equation equation NOUN iajs-2375 38 89 ( ( PUNCT iajs-2375 38 90 4 4 X iajs-2375 38 91 ) ) PUNCT iajs-2375 38 92 will will AUX iajs-2375 38 93 be be AUX iajs-2375 38 94 𝑙 𝑙 DET iajs-2375 38 95 𝑙 𝑙 X iajs-2375 38 96 ( ( PUNCT iajs-2375 38 97 𝑙 𝑙 PROPN iajs-2375 38 98 ( ( PUNCT iajs-2375 38 99 βˆ‘ βˆ‘ PART iajs-2375 38 100 𝑙 𝑙 X iajs-2375 38 101 ( ( PUNCT iajs-2375 38 102 ( ( PUNCT iajs-2375 38 103 βˆ‘ βˆ‘ PART iajs-2375 38 104 𝑙 𝑙 PROPN iajs-2375 38 105 ( ( PUNCT iajs-2375 38 106 ) ) PUNCT iajs-2375 38 107 ( ( PUNCT iajs-2375 38 108 βˆ‘ βˆ‘ PUNCT iajs-2375 38 109 𝑙 𝑙 X iajs-2375 38 110 ( ( PUNCT iajs-2375 38 111 ( ( PUNCT iajs-2375 38 112 ( ( PUNCT iajs-2375 38 113 βˆ‘ βˆ‘ PART iajs-2375 38 114 𝑙 𝑙 X iajs-2375 38 115 ( ( PUNCT iajs-2375 38 116 ( ( PUNCT iajs-2375 38 117 ) ) PUNCT iajs-2375 38 118 ) ) PUNCT iajs-2375 38 119 the the DET iajs-2375 38 120 partial partial ADJ iajs-2375 38 121 derivative derivative NOUN iajs-2375 38 122 of of ADP iajs-2375 38 123 𝑙 𝑙 NOUN iajs-2375 38 124 with with ADP iajs-2375 38 125 respect respect NOUN iajs-2375 38 126 to to ADP iajs-2375 38 127 and and CCONJ iajs-2375 38 128 equate equate VERB iajs-2375 38 129 the the DET iajs-2375 38 130 result result NOUN iajs-2375 38 131 to to ADP iajs-2375 38 132 zero zero NUM iajs-2375 38 133 , , PUNCT iajs-2375 38 134 we we PRON iajs-2375 38 135 obtained obtain VERB iajs-2375 38 136 the the DET iajs-2375 38 137 following follow VERB iajs-2375 38 138 880 880 NUM iajs-2375 38 139 ibn ibn PROPN iajs-2375 38 140 al al PROPN iajs-2375 38 141 - - PUNCT iajs-2375 38 142 haitham haitham PROPN iajs-2375 38 143 jour jour X iajs-2375 38 144 . . PROPN iajs-2375 39 1 for for ADP iajs-2375 39 2 pure pure ADJ iajs-2375 39 3 & & CCONJ iajs-2375 39 4 appl appl PROPN iajs-2375 39 5 . . PUNCT iajs-2375 40 1 sci sci PROPN iajs-2375 40 2 . . PROPN iajs-2375 41 1 33 33 NUM iajs-2375 41 2 ( ( PUNCT iajs-2375 41 3 1 1 NUM iajs-2375 41 4 ) ) PUNCT iajs-2375 41 5 2020 2020 NUM iajs-2375 41 6 βˆ‘ βˆ‘ PUNCT iajs-2375 41 7 ( ( PUNCT iajs-2375 41 8 ( ( PUNCT iajs-2375 41 9 βˆ‘ βˆ‘ PUNCT iajs-2375 41 10 ( ( PUNCT iajs-2375 41 11 ( ( PUNCT iajs-2375 41 12 ) ) PUNCT iajs-2375 41 13 ) ) PUNCT iajs-2375 42 1 the the DET iajs-2375 42 2 mlΚΌs mlΚΌs PROPN iajs-2375 42 3 estimator estimator NOUN iajs-2375 42 4 for for ADP iajs-2375 42 5 the the DET iajs-2375 42 6 unknown unknown ADJ iajs-2375 42 7 shape shape NOUN iajs-2375 42 8 parameters parameter NOUN iajs-2375 42 9 ( ( PUNCT iajs-2375 42 10 is be AUX iajs-2375 42 11 given give VERB iajs-2375 42 12 by by ADP iajs-2375 42 13 Μ‚ Μ‚ PUNCT iajs-2375 42 14 βˆ‘ βˆ‘ INTJ iajs-2375 42 15 ( ( PUNCT iajs-2375 42 16 ( ( PUNCT iajs-2375 42 17 ( ( PUNCT iajs-2375 42 18 5 5 NUM iajs-2375 42 19 ) ) PUNCT iajs-2375 42 20 Μ‚ Μ‚ PUNCT iajs-2375 42 21 βˆ‘ βˆ‘ X iajs-2375 42 22 ( ( PUNCT iajs-2375 42 23 ( ( PUNCT iajs-2375 42 24 ) ) PUNCT iajs-2375 42 25 ) ) PUNCT iajs-2375 43 1 ( ( PUNCT iajs-2375 43 2 6 6 NUM iajs-2375 43 3 ) ) PUNCT iajs-2375 43 4 by by ADP iajs-2375 43 5 substituting substitute VERB iajs-2375 43 6 equation equation NOUN iajs-2375 43 7 ( ( PUNCT iajs-2375 43 8 5 5 NUM iajs-2375 43 9 ) ) PUNCT iajs-2375 43 10 and and CCONJ iajs-2375 43 11 ( ( PUNCT iajs-2375 43 12 6 6 NUM iajs-2375 43 13 ) ) PUNCT iajs-2375 43 14 in in ADP iajs-2375 43 15 equation equation NOUN iajs-2375 43 16 ( ( PUNCT iajs-2375 43 17 3 3 X iajs-2375 43 18 ) ) PUNCT iajs-2375 43 19 we we PRON iajs-2375 43 20 get get VERB iajs-2375 43 21 οΏ½ οΏ½ PROPN iajs-2375 43 22 Μ‚ Μ‚ VERB iajs-2375 43 23 οΏ½ οΏ½ NOUN iajs-2375 43 24 Μ‚ Μ‚ PUNCT iajs-2375 43 25 Μ‚ Μ‚ PUNCT iajs-2375 43 26 Μ‚ Μ‚ PUNCT iajs-2375 43 27 ( ( PUNCT iajs-2375 43 28 7 7 NUM iajs-2375 43 29 ) ) PUNCT iajs-2375 43 30 2 2 NUM iajs-2375 43 31 . . NOUN iajs-2375 44 1 2 2 NUM iajs-2375 44 2 . . PUNCT iajs-2375 44 3 moments moment NOUN iajs-2375 44 4 method method NOUN iajs-2375 44 5 ( ( PUNCT iajs-2375 44 6 mom mom NOUN iajs-2375 44 7 ) ) PUNCT iajs-2375 44 8 in in ADP iajs-2375 44 9 this this DET iajs-2375 44 10 section section NOUN iajs-2375 44 11 , , PUNCT iajs-2375 44 12 population population NOUN iajs-2375 44 13 moments moment NOUN iajs-2375 44 14 for for ADP iajs-2375 44 15 x x PROPN iajs-2375 44 16 and and CCONJ iajs-2375 44 17 π‘Œ π‘Œ PROPN iajs-2375 44 18 of of ADP iajs-2375 44 19 ikumd ikumd NOUN iajs-2375 44 20 were be AUX iajs-2375 44 21 needed need VERB iajs-2375 44 22 . . PUNCT iajs-2375 45 1 therefore therefore ADV iajs-2375 45 2 , , PUNCT iajs-2375 45 3 moments moment NOUN iajs-2375 45 4 method method NOUN iajs-2375 45 5 ( ( PUNCT iajs-2375 45 6 mom mom NOUN iajs-2375 45 7 ) ) PUNCT iajs-2375 45 8 was be AUX iajs-2375 45 9 considered consider VERB iajs-2375 45 10 to to PART iajs-2375 45 11 estimate estimate VERB iajs-2375 45 12 the the DET iajs-2375 45 13 parameter parameter NOUN iajs-2375 45 14 for for ADP iajs-2375 45 15 ikumd ikumd NOUN iajs-2375 45 16 when when SCONJ iajs-2375 45 17 the the DET iajs-2375 45 18 parameter parameter NOUN iajs-2375 45 19 is be AUX iajs-2375 45 20 known know VERB iajs-2375 45 21 . . PUNCT iajs-2375 46 1 e(𝑋 e(𝑋 PROPN iajs-2375 46 2 βˆ‘ βˆ‘ PROPN iajs-2375 46 3 ( ( PUNCT iajs-2375 46 4 ) ) PUNCT iajs-2375 46 5 ( ( PUNCT iajs-2375 46 6 ) ) PUNCT iajs-2375 46 7 π‘Ÿ π‘Ÿ NOUN iajs-2375 46 8 , , PUNCT iajs-2375 46 9 2 2 NUM iajs-2375 46 10 , , PUNCT iajs-2375 46 11 … … PUNCT iajs-2375 46 12 hence hence ADV iajs-2375 46 13 , , PUNCT iajs-2375 46 14 the the DET iajs-2375 46 15 population population NOUN iajs-2375 46 16 means mean VERB iajs-2375 46 17 of of ADP iajs-2375 46 18 x x PUNCT iajs-2375 46 19 and and CCONJ iajs-2375 46 20 y y PROPN iajs-2375 46 21 are be AUX iajs-2375 46 22 given give VERB iajs-2375 46 23 respectively respectively ADV iajs-2375 46 24 as as ADP iajs-2375 46 25 below below ADP iajs-2375 46 26 e(𝑋 e(𝑋 PROPN iajs-2375 46 27 ( ( PUNCT iajs-2375 46 28 ) ) PUNCT iajs-2375 46 29 , , PUNCT iajs-2375 46 30 e(π‘Œ e(π‘Œ NUM iajs-2375 46 31 ( ( PUNCT iajs-2375 46 32 ) ) PUNCT iajs-2375 46 33 , , PUNCT iajs-2375 46 34 where where SCONJ iajs-2375 46 35 ( ( PUNCT iajs-2375 46 36 refer refer VERB iajs-2375 46 37 to to ADP iajs-2375 46 38 beta beta ADJ iajs-2375 46 39 distribution distribution NOUN iajs-2375 46 40 . . PUNCT iajs-2375 47 1 and and CCONJ iajs-2375 47 2 when when SCONJ iajs-2375 47 3 equality equality NOUN iajs-2375 47 4 the the DET iajs-2375 47 5 sample sample NOUN iajs-2375 47 6 mean mean VERB iajs-2375 47 7 with with ADP iajs-2375 47 8 the the DET iajs-2375 47 9 corresponding correspond VERB iajs-2375 47 10 population population NOUN iajs-2375 47 11 mean mean VERB iajs-2375 47 12 , , PUNCT iajs-2375 47 13 we we PRON iajs-2375 47 14 get get VERB iajs-2375 47 15 οΏ½ οΏ½ NOUN iajs-2375 47 16 Μ… Μ… NOUN iajs-2375 47 17 οΏ½ οΏ½ NOUN iajs-2375 47 18 βˆ‘ βˆ‘ PUNCT iajs-2375 47 19 ( ( PUNCT iajs-2375 47 20 ) ) PUNCT iajs-2375 47 21 and and CCONJ iajs-2375 47 22 οΏ½ οΏ½ PROPN iajs-2375 47 23 Μ… Μ… NOUN iajs-2375 47 24 οΏ½ οΏ½ NOUN iajs-2375 47 25 βˆ‘ βˆ‘ PUNCT iajs-2375 47 26 ( ( PUNCT iajs-2375 47 27 ) ) PUNCT iajs-2375 47 28 as as ADP iajs-2375 47 29 a a DET iajs-2375 47 30 result result NOUN iajs-2375 47 31 , , PUNCT iajs-2375 47 32 we we PRON iajs-2375 47 33 obtained obtain VERB iajs-2375 47 34 Μ‚ Μ‚ PUNCT iajs-2375 47 35 βˆ‘ βˆ‘ PROPN iajs-2375 47 36 ( ( PUNCT iajs-2375 47 37 ) ) PUNCT iajs-2375 47 38 ( ( PUNCT iajs-2375 47 39 8) 8) NUM iajs-2375 47 40 and and CCONJ iajs-2375 47 41 , , PUNCT iajs-2375 47 42 Μ‚ Μ‚ PUNCT iajs-2375 47 43 βˆ‘ βˆ‘ X iajs-2375 47 44 ( ( PUNCT iajs-2375 47 45 ) ) PUNCT iajs-2375 47 46 ( ( PUNCT iajs-2375 47 47 9 9 X iajs-2375 47 48 ) ) PUNCT iajs-2375 47 49 where where SCONJ iajs-2375 47 50 is be AUX iajs-2375 47 51 an an DET iajs-2375 47 52 initial initial ADJ iajs-2375 47 53 value value NOUN iajs-2375 47 54 for for ADP iajs-2375 47 55 ( ( PUNCT iajs-2375 47 56 . . PUNCT iajs-2375 48 1 similarly similarly ADV iajs-2375 48 2 , , PUNCT iajs-2375 48 3 substitution substitution VERB iajs-2375 48 4 the the DET iajs-2375 48 5 equations equation NOUN iajs-2375 48 6 ( ( PUNCT iajs-2375 48 7 8) 8) NUM iajs-2375 48 8 and and CCONJ iajs-2375 48 9 ( ( PUNCT iajs-2375 48 10 9 9 NUM iajs-2375 48 11 ) ) PUNCT iajs-2375 48 12 in in ADP iajs-2375 48 13 the the DET iajs-2375 48 14 equation equation NOUN iajs-2375 48 15 ( ( PUNCT iajs-2375 48 16 3 3 X iajs-2375 48 17 ) ) PUNCT iajs-2375 48 18 we we PRON iajs-2375 48 19 get get VERB iajs-2375 48 20 οΏ½ οΏ½ PROPN iajs-2375 48 21 Μ‚ Μ‚ VERB iajs-2375 48 22 οΏ½ οΏ½ NOUN iajs-2375 48 23 Μ‚ Μ‚ PUNCT iajs-2375 48 24 Μ‚ Μ‚ PUNCT iajs-2375 48 25 Μ‚ Μ‚ PUNCT iajs-2375 48 26 ( ( PUNCT iajs-2375 48 27 10 10 NUM iajs-2375 48 28 ) ) PUNCT iajs-2375 48 29 2 2 NUM iajs-2375 48 30 . . NOUN iajs-2375 48 31 3 3 NUM iajs-2375 48 32 . . X iajs-2375 48 33 shrinkage shrinkage NOUN iajs-2375 48 34 estimation estimation NOUN iajs-2375 48 35 method method NOUN iajs-2375 48 36 in in ADP iajs-2375 48 37 1968 1968 NUM iajs-2375 48 38 , , PUNCT iajs-2375 48 39 thompson thompson PROPN iajs-2375 48 40 proposed propose VERB iajs-2375 48 41 the the DET iajs-2375 48 42 shrink shrink ADJ iajs-2375 48 43 usual usual ADJ iajs-2375 48 44 estimator estimator NOUN iajs-2375 48 45 Μ‚ Μ‚ PUNCT iajs-2375 48 46 ( ( PUNCT iajs-2375 48 47 ex ex PROPN iajs-2375 48 48 . . PROPN iajs-2375 48 49 mle mle PROPN iajs-2375 48 50 or or CCONJ iajs-2375 48 51 unbiased unbiased ADJ iajs-2375 48 52 estimator estimator NOUN iajs-2375 48 53 ) ) PUNCT iajs-2375 48 54 of of ADP iajs-2375 48 55 the the DET iajs-2375 48 56 parameter parameter NOUN iajs-2375 48 57 to to ADP iajs-2375 48 58 prior prior ADJ iajs-2375 48 59 information information NOUN iajs-2375 48 60 using use VERB iajs-2375 48 61 shrinkage shrinkage NOUN iajs-2375 48 62 weight weight NOUN iajs-2375 48 63 actor actor NOUN iajs-2375 48 64 ψ ψ X iajs-2375 48 65 ( ( PUNCT iajs-2375 48 66 Μ‚ Μ‚ NUM iajs-2375 48 67 ) ) PUNCT iajs-2375 48 68 , , PUNCT iajs-2375 48 69 such such ADJ iajs-2375 48 70 that that SCONJ iajs-2375 48 71 0 0 NUM iajs-2375 48 72 ψ ψ NOUN iajs-2375 48 73 ( ( PUNCT iajs-2375 48 74 Μ‚ Μ‚ PROPN iajs-2375 48 75 1 1 NUM iajs-2375 48 76 . . X iajs-2375 49 1 thompson thompson PROPN iajs-2375 49 2 say say VERB iajs-2375 49 3 that that SCONJ iajs-2375 49 4 " " PUNCT iajs-2375 49 5 we we PRON iajs-2375 49 6 are be AUX iajs-2375 49 7 estimating estimate VERB iajs-2375 49 8 and and CCONJ iajs-2375 49 9 we we PRON iajs-2375 49 10 believe believe VERB iajs-2375 49 11 is be AUX iajs-2375 49 12 closed close VERB iajs-2375 49 13 to to ADP iajs-2375 49 14 the the DET iajs-2375 49 15 888 888 NUM iajs-2375 49 16 ibn ibn PROPN iajs-2375 49 17 al al PROPN iajs-2375 49 18 - - PUNCT iajs-2375 49 19 haitham haitham PROPN iajs-2375 49 20 jour jour X iajs-2375 49 21 . . PROPN iajs-2375 50 1 for for ADP iajs-2375 50 2 pure pure ADJ iajs-2375 50 3 & & CCONJ iajs-2375 50 4 appl appl PROPN iajs-2375 50 5 . . PUNCT iajs-2375 51 1 sci sci PROPN iajs-2375 51 2 . . PROPN iajs-2375 52 1 33 33 NUM iajs-2375 52 2 ( ( PUNCT iajs-2375 52 3 1 1 NUM iajs-2375 52 4 ) ) PUNCT iajs-2375 52 5 2020 2020 NUM iajs-2375 52 6 true true ADJ iajs-2375 52 7 value value NOUN iajs-2375 52 8 of of ADP iajs-2375 52 9 and and CCONJ iajs-2375 52 10 something something PRON iajs-2375 52 11 bad bad ADJ iajs-2375 52 12 happens happen VERB iajs-2375 52 13 if if SCONJ iajs-2375 52 14 and and CCONJ iajs-2375 52 15 we we PRON iajs-2375 52 16 do do AUX iajs-2375 52 17 not not PART iajs-2375 52 18 use use VERB iajs-2375 52 19 " " PUNCT iajs-2375 52 20 . . PUNCT iajs-2375 53 1 thus thus ADV iajs-2375 53 2 , , PUNCT iajs-2375 53 3 thompson thompson PROPN iajs-2375 53 4 gave give VERB iajs-2375 53 5 the the DET iajs-2375 53 6 form form NOUN iajs-2375 53 7 of of ADP iajs-2375 53 8 shrinkage shrinkage NOUN iajs-2375 53 9 estimator estimator NOUN iajs-2375 53 10 of of ADP iajs-2375 53 11 say say PROPN iajs-2375 53 12 Μ‚ Μ‚ PUNCT iajs-2375 53 13 as as ADP iajs-2375 53 14 bellow bellow ADJ iajs-2375 53 15 : : PUNCT iajs-2375 53 16 Μ‚ Μ‚ PUNCT iajs-2375 53 17 ψ ψ X iajs-2375 53 18 ( ( PUNCT iajs-2375 53 19 Μ‚ Μ‚ PUNCT iajs-2375 53 20 Μ‚ Μ‚ X iajs-2375 53 21 ( ( PUNCT iajs-2375 53 22 ψ ψ X iajs-2375 53 23 ( ( PUNCT iajs-2375 53 24 Μ‚ Μ‚ PUNCT iajs-2375 53 25 ( ( PUNCT iajs-2375 53 26 11 11 NUM iajs-2375 53 27 ) ) PUNCT iajs-2375 53 28 where where SCONJ iajs-2375 53 29 Μ‚ Μ‚ PUNCT iajs-2375 53 30 was be AUX iajs-2375 53 31 an an DET iajs-2375 53 32 unbiased unbiased ADJ iajs-2375 53 33 estimator estimator NOUN iajs-2375 53 34 and and CCONJ iajs-2375 53 35 applied apply VERB iajs-2375 53 36 as as ADP iajs-2375 53 37 usual usual ADJ iajs-2375 53 38 estimator estimator NOUN iajs-2375 53 39 of of ADP iajs-2375 53 40 , , PUNCT iajs-2375 53 41 ψ ψ X iajs-2375 53 42 ( ( PUNCT iajs-2375 53 43 Μ‚ Μ‚ VERB iajs-2375 53 44 ) ) PUNCT iajs-2375 53 45 may may AUX iajs-2375 53 46 be be AUX iajs-2375 53 47 a a DET iajs-2375 53 48 function function NOUN iajs-2375 53 49 of of ADP iajs-2375 53 50 sample sample NOUN iajs-2375 53 51 size size NOUN iajs-2375 53 52 ( ( PUNCT iajs-2375 53 53 n n CCONJ iajs-2375 53 54 , , PUNCT iajs-2375 53 55 m m PROPN iajs-2375 53 56 ) ) PUNCT iajs-2375 53 57 , , PUNCT iajs-2375 53 58 a a DET iajs-2375 53 59 constant constant ADJ iajs-2375 53 60 , , PUNCT iajs-2375 53 61 or or CCONJ iajs-2375 53 62 found find VERB iajs-2375 53 63 through through ADP iajs-2375 53 64 minimizing minimize VERB iajs-2375 53 65 mean mean NOUN iajs-2375 53 66 square square ADJ iajs-2375 53 67 error error NOUN iajs-2375 53 68 of of ADP iajs-2375 53 69 Μ‚ Μ‚ PUNCT iajs-2375 53 70 ( ( PUNCT iajs-2375 53 71 ad ad X iajs-2375 53 72 hoc hoc X iajs-2375 53 73 basis basis NOUN iajs-2375 53 74 ) ) PUNCT iajs-2375 53 75 . . PUNCT iajs-2375 54 1 on on ADP iajs-2375 54 2 the the DET iajs-2375 54 3 other other ADJ iajs-2375 54 4 hand hand NOUN iajs-2375 54 5 , , PUNCT iajs-2375 54 6 is be AUX iajs-2375 54 7 a a DET iajs-2375 54 8 very very ADV iajs-2375 54 9 closed closed ADJ iajs-2375 54 10 value value NOUN iajs-2375 54 11 of of ADP iajs-2375 54 12 which which PRON iajs-2375 54 13 used use VERB iajs-2375 54 14 as as ADP iajs-2375 54 15 a a DET iajs-2375 54 16 prior prior ADJ iajs-2375 54 17 information information NOUN iajs-2375 54 18 . . PUNCT iajs-2375 55 1 [ [ X iajs-2375 55 2 15 15 NUM iajs-2375 55 3 , , PUNCT iajs-2375 55 4 16 16 NUM iajs-2375 55 5 , , PUNCT iajs-2375 55 6 17 17 NUM iajs-2375 55 7 , , PUNCT iajs-2375 55 8 18 18 NUM iajs-2375 55 9 ] ] PUNCT iajs-2375 55 10 . . PUNCT iajs-2375 56 1 there there PRON iajs-2375 56 2 is be VERB iajs-2375 56 3 no no DET iajs-2375 56 4 doubt doubt NOUN iajs-2375 56 5 , , PUNCT iajs-2375 56 6 if if SCONJ iajs-2375 56 7 our our PRON iajs-2375 56 8 assumption assumption NOUN iajs-2375 56 9 to to PART iajs-2375 56 10 take take VERB iajs-2375 56 11 [ [ PUNCT iajs-2375 56 12 .001 .001 NUM iajs-2375 56 13 ] ] X iajs-2375 56 14 , , PUNCT iajs-2375 56 15 as as ADP iajs-2375 56 16 a a DET iajs-2375 56 17 prior prior ADJ iajs-2375 56 18 information information NOUN iajs-2375 56 19 of of ADP iajs-2375 56 20 for for ADP iajs-2375 56 21 i i PROPN iajs-2375 56 22 = = NOUN iajs-2375 56 23 1 1 NUM iajs-2375 56 24 , , PUNCT iajs-2375 56 25 2 2 NUM iajs-2375 56 26 in in ADP iajs-2375 56 27 this this DET iajs-2375 56 28 work work NOUN iajs-2375 56 29 . . PUNCT iajs-2375 57 1 noted note VERB iajs-2375 57 2 that that PRON iajs-2375 57 3 is be AUX iajs-2375 57 4 biased biased ADJ iajs-2375 57 5 estimator estimator NOUN iajs-2375 57 6 , , PUNCT iajs-2375 57 7 since since SCONJ iajs-2375 57 8 e e PROPN iajs-2375 57 9 ( ( PUNCT iajs-2375 57 10 Μ‚ Μ‚ PROPN iajs-2375 57 11 ) ) PUNCT iajs-2375 57 12 , , PUNCT iajs-2375 57 13 refer refer VERB iajs-2375 57 14 to to ADP iajs-2375 57 15 or or CCONJ iajs-2375 57 16 . . PUNCT iajs-2375 58 1 thus thus ADV iajs-2375 58 2 Μ‚ Μ‚ PUNCT iajs-2375 58 3 Μ‚ Μ‚ VERB iajs-2375 58 4 become become VERB iajs-2375 58 5 unbiased unbiased ADJ iajs-2375 58 6 estimator estimator NOUN iajs-2375 58 7 of of ADP iajs-2375 58 8 whereas whereas SCONJ iajs-2375 58 9 ( ( PUNCT iajs-2375 58 10 Μ‚ Μ‚ PUNCT iajs-2375 58 11 ) ) PUNCT iajs-2375 58 12 . . PUNCT iajs-2375 59 1 likewise likewise ADV iajs-2375 59 2 , , PUNCT iajs-2375 59 3 var var NOUN iajs-2375 59 4 ( ( PUNCT iajs-2375 59 5 Μ‚ Μ‚ PROPN iajs-2375 59 6 ) ) PUNCT iajs-2375 59 7 ( ( PUNCT iajs-2375 59 8 ( ( PUNCT iajs-2375 59 9 and and CCONJ iajs-2375 59 10 var var NOUN iajs-2375 59 11 ( ( PUNCT iajs-2375 59 12 Μ‚ Μ‚ PROPN iajs-2375 59 13 ) ) PUNCT iajs-2375 59 14 ( ( PUNCT iajs-2375 59 15 ( ( PUNCT iajs-2375 59 16 i.e. i.e. X iajs-2375 59 17 ; ; PUNCT iajs-2375 59 18 Μ‚ Μ‚ PUNCT iajs-2375 59 19 βˆ‘ βˆ‘ X iajs-2375 59 20 ( ( PUNCT iajs-2375 59 21 ( ( PUNCT iajs-2375 59 22 ( ( PUNCT iajs-2375 59 23 12 12 NUM iajs-2375 59 24 ) ) PUNCT iajs-2375 59 25 and and CCONJ iajs-2375 60 1 Μ‚ Μ‚ VERB iajs-2375 60 2 βˆ‘ βˆ‘ INTJ iajs-2375 60 3 ( ( PUNCT iajs-2375 60 4 ( ( PUNCT iajs-2375 60 5 ) ) PUNCT iajs-2375 60 6 ) ) PUNCT iajs-2375 60 7 ( ( PUNCT iajs-2375 60 8 13 13 NUM iajs-2375 60 9 ) ) PUNCT iajs-2375 60 10 2 2 NUM iajs-2375 60 11 . . NOUN iajs-2375 60 12 3 3 NUM iajs-2375 60 13 . . NOUN iajs-2375 60 14 1 1 NUM iajs-2375 60 15 . . PUNCT iajs-2375 60 16 constant constant ADJ iajs-2375 60 17 shrinkage shrinkage NOUN iajs-2375 60 18 weight weight NOUN iajs-2375 60 19 factor factor NOUN iajs-2375 60 20 ( ( PUNCT iajs-2375 60 21 sh1 sh1 PROPN iajs-2375 60 22 ) ) PUNCT iajs-2375 60 23 in in ADP iajs-2375 60 24 this this DET iajs-2375 60 25 subsection subsection NOUN iajs-2375 60 26 , , PUNCT iajs-2375 60 27 the the DET iajs-2375 60 28 constant constant ADJ iajs-2375 60 29 shrinkage shrinkage NOUN iajs-2375 60 30 weight weight NOUN iajs-2375 60 31 factor factor NOUN iajs-2375 60 32 will will AUX iajs-2375 60 33 be be AUX iajs-2375 60 34 assumed assume VERB iajs-2375 60 35 as as ADP iajs-2375 60 36 ; ; PUNCT iajs-2375 60 37 𝛹 𝛹 X iajs-2375 60 38 ( ( PUNCT iajs-2375 60 39 Μ‚ Μ‚ X iajs-2375 60 40 ) ) PUNCT iajs-2375 60 41 = = PUNCT iajs-2375 61 1 = = PUNCT iajs-2375 61 2 0.01 0.01 NUM iajs-2375 61 3 , , PUNCT iajs-2375 61 4 and and CCONJ iajs-2375 61 5 𝛹 𝛹 PROPN iajs-2375 61 6 ( ( PUNCT iajs-2375 61 7 Μ‚ Μ‚ PROPN iajs-2375 61 8 ) ) PUNCT iajs-2375 61 9 = = NOUN iajs-2375 62 1 , , PUNCT iajs-2375 62 2 then then ADV iajs-2375 62 3 applying apply VERB iajs-2375 62 4 to to ADP iajs-2375 62 5 the the DET iajs-2375 62 6 following follow VERB iajs-2375 62 7 shrinkage shrinkage NOUN iajs-2375 62 8 estimators estimator NOUN iajs-2375 62 9 ; ; PUNCT iajs-2375 62 10 Μ‚ Μ‚ X iajs-2375 62 11 = = PUNCT iajs-2375 62 12 Μ‚ Μ‚ PUNCT iajs-2375 62 13 + + CCONJ iajs-2375 62 14 ( ( PUNCT iajs-2375 62 15 ( ( PUNCT iajs-2375 62 16 14 14 NUM iajs-2375 62 17 ) ) PUNCT iajs-2375 62 18 Μ‚ Μ‚ X iajs-2375 62 19 = = PUNCT iajs-2375 63 1 Μ‚ Μ‚ PUNCT iajs-2375 63 2 + + CCONJ iajs-2375 63 3 ( ( PUNCT iajs-2375 63 4 ( ( PUNCT iajs-2375 63 5 15 15 NUM iajs-2375 63 6 ) ) PUNCT iajs-2375 63 7 when when SCONJ iajs-2375 63 8 substitution substitution VERB iajs-2375 63 9 the the DET iajs-2375 63 10 equation equation NOUN iajs-2375 63 11 ( ( PUNCT iajs-2375 63 12 14 14 NUM iajs-2375 63 13 ) ) PUNCT iajs-2375 63 14 and and CCONJ iajs-2375 63 15 ( ( PUNCT iajs-2375 63 16 15 15 NUM iajs-2375 63 17 ) ) PUNCT iajs-2375 63 18 in in ADP iajs-2375 63 19 equation equation NOUN iajs-2375 63 20 ( ( PUNCT iajs-2375 63 21 3 3 NUM iajs-2375 63 22 ) ) PUNCT iajs-2375 63 23 , , PUNCT iajs-2375 63 24 lead lead VERB iajs-2375 63 25 to to ADP iajs-2375 63 26 the the DET iajs-2375 63 27 estimation estimation NOUN iajs-2375 63 28 of of ADP iajs-2375 63 29 s s NOUN iajs-2375 63 30 - - PUNCT iajs-2375 63 31 s s NOUN iajs-2375 63 32 reliability reliability NOUN iajs-2375 63 33 using use VERB iajs-2375 63 34 shrinkage shrinkage NOUN iajs-2375 63 35 estimator estimator NOUN iajs-2375 63 36 οΏ½ οΏ½ PROPN iajs-2375 63 37 Μ‚ Μ‚ PROPN iajs-2375 63 38 οΏ½ οΏ½ PROPN iajs-2375 63 39 as as ADP iajs-2375 63 40 below below ADP iajs-2375 63 41 οΏ½ οΏ½ PROPN iajs-2375 63 42 Μ‚ Μ‚ SYM iajs-2375 63 43 οΏ½ οΏ½ PROPN iajs-2375 63 44 Μ‚ Μ‚ PUNCT iajs-2375 63 45 Μ‚ Μ‚ PUNCT iajs-2375 63 46 Μ‚ Μ‚ PUNCT iajs-2375 63 47 ( ( PUNCT iajs-2375 63 48 16 16 NUM iajs-2375 63 49 ) ) PUNCT iajs-2375 63 50 2 2 NUM iajs-2375 63 51 . . NOUN iajs-2375 63 52 3 3 NUM iajs-2375 63 53 . . NOUN iajs-2375 63 54 2 2 NUM iajs-2375 63 55 . . X iajs-2375 63 56 shrinkage shrinkage NOUN iajs-2375 63 57 weight weight NOUN iajs-2375 63 58 function function NOUN iajs-2375 63 59 ( ( PUNCT iajs-2375 63 60 sh2 sh2 NOUN iajs-2375 63 61 ) ) PUNCT iajs-2375 63 62 in in ADP iajs-2375 63 63 this this DET iajs-2375 63 64 subsection subsection NOUN iajs-2375 63 65 , , PUNCT iajs-2375 63 66 we we PRON iajs-2375 63 67 considered consider VERB iajs-2375 63 68 the the DET iajs-2375 63 69 shrinkage shrinkage NOUN iajs-2375 63 70 weight weight NOUN iajs-2375 63 71 factor factor NOUN iajs-2375 63 72 as as ADP iajs-2375 63 73 a a DET iajs-2375 63 74 function function NOUN iajs-2375 63 75 of of ADP iajs-2375 63 76 n n PROPN iajs-2375 63 77 and and CCONJ iajs-2375 63 78 m m PROPN iajs-2375 63 79 , , PUNCT iajs-2375 63 80 respectively respectively ADV iajs-2375 63 81 in in ADP iajs-2375 63 82 equation equation NOUN iajs-2375 63 83 ( ( PUNCT iajs-2375 63 84 11 11 NUM iajs-2375 63 85 ) ) PUNCT iajs-2375 63 86 𝛹 𝛹 PROPN iajs-2375 63 87 ( ( PUNCT iajs-2375 63 88 Μ‚ Μ‚ X iajs-2375 63 89 ) ) PUNCT iajs-2375 63 90 = = SYM iajs-2375 64 1 = = PUNCT iajs-2375 64 2 , , PUNCT iajs-2375 64 3 and and CCONJ iajs-2375 64 4 𝛹 𝛹 PROPN iajs-2375 64 5 ( ( PUNCT iajs-2375 64 6 Μ‚ Μ‚ X iajs-2375 64 7 ) ) PUNCT iajs-2375 64 8 = = SYM iajs-2375 64 9 = = PUNCT iajs-2375 64 10 . . PUNCT iajs-2375 65 1 Μ‚ Μ‚ X iajs-2375 65 2 = = PUNCT iajs-2375 66 1 Μ‚ Μ‚ PUNCT iajs-2375 66 2 + + CCONJ iajs-2375 66 3 ( ( PUNCT iajs-2375 66 4 for for ADP iajs-2375 66 5 i= i= PROPN iajs-2375 66 6 1 1 NUM iajs-2375 66 7 , , PUNCT iajs-2375 66 8 2 2 NUM iajs-2375 66 9 . . PUNCT iajs-2375 67 1 ( ( PUNCT iajs-2375 67 2 17 17 NUM iajs-2375 67 3 ) ) PUNCT iajs-2375 67 4 the the DET iajs-2375 67 5 corresponding correspond VERB iajs-2375 67 6 s s NOUN iajs-2375 67 7 - - PUNCT iajs-2375 67 8 s s NOUN iajs-2375 67 9 reliability reliability NOUN iajs-2375 67 10 estimation estimation NOUN iajs-2375 67 11 was be AUX iajs-2375 67 12 used use VERB iajs-2375 67 13 using use VERB iajs-2375 67 14 equation equation NOUN iajs-2375 67 15 ( ( PUNCT iajs-2375 67 16 17 17 NUM iajs-2375 67 17 ) ) PUNCT iajs-2375 67 18 as as SCONJ iajs-2375 67 19 follows follow VERB iajs-2375 67 20 ; ; PUNCT iajs-2375 67 21 οΏ½ οΏ½ PROPN iajs-2375 67 22 Μ‚ Μ‚ NUM iajs-2375 67 23 οΏ½ οΏ½ PROPN iajs-2375 67 24 Μ‚ Μ‚ PUNCT iajs-2375 67 25 Μ‚ Μ‚ PUNCT iajs-2375 67 26 Μ‚ Μ‚ PUNCT iajs-2375 67 27 ( ( PUNCT iajs-2375 67 28 18 18 NUM iajs-2375 67 29 ) ) PUNCT iajs-2375 67 30 2 2 NUM iajs-2375 67 31 . . NOUN iajs-2375 68 1 3 3 NUM iajs-2375 68 2 . . NOUN iajs-2375 68 3 3 3 NUM iajs-2375 68 4 . . NUM iajs-2375 68 5 modified modify VERB iajs-2375 68 6 thompson thompson PROPN iajs-2375 68 7 type type NOUN iajs-2375 68 8 shrinkage shrinkage NOUN iajs-2375 68 9 weight weight NOUN iajs-2375 68 10 factor factor NOUN iajs-2375 68 11 ( ( PUNCT iajs-2375 68 12 shth shth PROPN iajs-2375 68 13 ) ) PUNCT iajs-2375 68 14 the the DET iajs-2375 68 15 shrinkage shrinkage NOUN iajs-2375 68 16 weight weight NOUN iajs-2375 68 17 factor factor NOUN iajs-2375 68 18 which which PRON iajs-2375 68 19 was be AUX iajs-2375 68 20 considered consider VERB iajs-2375 68 21 by by ADP iajs-2375 68 22 thompson thompson PROPN iajs-2375 68 23 in in ADP iajs-2375 68 24 1968 1968 NUM iajs-2375 68 25 will will AUX iajs-2375 68 26 be be AUX iajs-2375 68 27 modified modify VERB iajs-2375 68 28 in in ADP iajs-2375 68 29 this this DET iajs-2375 68 30 subsection subsection NOUN iajs-2375 68 31 as as SCONJ iajs-2375 68 32 follows follow VERB iajs-2375 68 33 : : PUNCT iajs-2375 68 34 881 881 NUM iajs-2375 68 35 ibn ibn PROPN iajs-2375 68 36 al al PROPN iajs-2375 68 37 - - PUNCT iajs-2375 68 38 haitham haitham PROPN iajs-2375 68 39 jour jour X iajs-2375 68 40 . . 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