id sid tid token lemma pos iajs-3377 1 1 ihjpas ihjpas PROPN iajs-3377 1 2 . . PUNCT iajs-3377 2 1 36 36 NUM iajs-3377 2 2 ( ( PUNCT iajs-3377 2 3 3 3 NUM iajs-3377 2 4 ) ) PUNCT iajs-3377 2 5 2023 2023 NUM iajs-3377 2 6 437 437 NUM iajs-3377 2 7 this this DET iajs-3377 2 8 work work NOUN iajs-3377 2 9 is be AUX iajs-3377 2 10 licensed license VERB iajs-3377 2 11 under under ADP iajs-3377 2 12 a a DET iajs-3377 2 13 creative creative ADJ iajs-3377 2 14 commons common NOUN iajs-3377 2 15 attribution attribution NOUN iajs-3377 2 16 4.0 4.0 NUM iajs-3377 2 17 international international ADJ iajs-3377 2 18 license license NOUN iajs-3377 2 19 * * PUNCT iajs-3377 2 20 corresponding correspond VERB iajs-3377 2 21 author author NOUN iajs-3377 2 22 : : PUNCT iajs-3377 2 23 kehindebashiru@uniosun.edu.ng kehindebashiru@uniosun.edu.ng PROPN iajs-3377 2 24 abstract abstract VERB iajs-3377 2 25 a a DET iajs-3377 2 26 new new ADJ iajs-3377 2 27 family family NOUN iajs-3377 2 28 of of ADP iajs-3377 2 29 distribution distribution NOUN iajs-3377 2 30 named name VERB iajs-3377 2 31 double double ADJ iajs-3377 2 32 - - PUNCT iajs-3377 2 33 exponential exponential ADJ iajs-3377 2 34 - - PUNCT iajs-3377 2 35 x x SYM iajs-3377 2 36 family family NOUN iajs-3377 2 37 is be AUX iajs-3377 2 38 proposed propose VERB iajs-3377 2 39 . . PUNCT iajs-3377 3 1 the the DET iajs-3377 3 2 proposed propose VERB iajs-3377 3 3 family family NOUN iajs-3377 3 4 is be AUX iajs-3377 3 5 generated generate VERB iajs-3377 3 6 from from ADP iajs-3377 3 7 the the DET iajs-3377 3 8 double double ADJ iajs-3377 3 9 exponential exponential ADJ iajs-3377 3 10 distribution distribution NOUN iajs-3377 3 11 . . PUNCT iajs-3377 4 1 the the DET iajs-3377 4 2 forms form NOUN iajs-3377 4 3 of of ADP iajs-3377 4 4 the the DET iajs-3377 4 5 probability probability NOUN iajs-3377 4 6 densities density NOUN iajs-3377 4 7 and and CCONJ iajs-3377 4 8 hazard hazard NOUN iajs-3377 4 9 functions function NOUN iajs-3377 4 10 of of ADP iajs-3377 4 11 two two NUM iajs-3377 4 12 distinct distinct ADJ iajs-3377 4 13 subfamilies subfamily NOUN iajs-3377 4 14 of of ADP iajs-3377 4 15 the the DET iajs-3377 4 16 proposed propose VERB iajs-3377 4 17 family family NOUN iajs-3377 4 18 are be AUX iajs-3377 4 19 examined examine VERB iajs-3377 4 20 and and CCONJ iajs-3377 4 21 reported report VERB iajs-3377 4 22 . . PUNCT iajs-3377 5 1 general general ADJ iajs-3377 5 2 properties property NOUN iajs-3377 5 3 such such ADJ iajs-3377 5 4 as as ADP iajs-3377 5 5 moment moment NOUN iajs-3377 5 6 , , PUNCT iajs-3377 5 7 survival survival NOUN iajs-3377 5 8 , , PUNCT iajs-3377 5 9 order order NOUN iajs-3377 5 10 statistics statistic NOUN iajs-3377 5 11 , , PUNCT iajs-3377 5 12 probability probability NOUN iajs-3377 5 13 weighted weight VERB iajs-3377 5 14 moments moment NOUN iajs-3377 5 15 and and CCONJ iajs-3377 5 16 quartile quartile ADJ iajs-3377 5 17 functions function NOUN iajs-3377 5 18 of of ADP iajs-3377 5 19 the the DET iajs-3377 5 20 models model NOUN iajs-3377 5 21 are be AUX iajs-3377 5 22 investigated investigate VERB iajs-3377 5 23 . . PUNCT iajs-3377 6 1 a a DET iajs-3377 6 2 sub sub NOUN iajs-3377 6 3 family family NOUN iajs-3377 6 4 of of ADP iajs-3377 6 5 the the DET iajs-3377 6 6 developed developed ADJ iajs-3377 6 7 family family NOUN iajs-3377 6 8 of of ADP iajs-3377 6 9 double double ADJ iajs-3377 6 10 – – PUNCT iajs-3377 6 11 exponential exponential ADJ iajs-3377 6 12 - - PUNCT iajs-3377 6 13 x x SYM iajs-3377 6 14 family family NOUN iajs-3377 6 15 of of ADP iajs-3377 6 16 the the DET iajs-3377 6 17 distribution distribution NOUN iajs-3377 6 18 known know VERB iajs-3377 6 19 as as ADP iajs-3377 6 20 double double ADJ iajs-3377 6 21 - - PUNCT iajs-3377 6 22 exponential exponential ADJ iajs-3377 6 23 - - PUNCT iajs-3377 6 24 pareto pareto VERB iajs-3377 6 25 distribution distribution NOUN iajs-3377 6 26 was be AUX iajs-3377 6 27 used use VERB iajs-3377 6 28 to to PART iajs-3377 6 29 fit fit VERB iajs-3377 6 30 a a DET iajs-3377 6 31 real real ADJ iajs-3377 6 32 life life NOUN iajs-3377 6 33 data datum NOUN iajs-3377 6 34 on on ADP iajs-3377 6 35 the the DET iajs-3377 6 36 use use NOUN iajs-3377 6 37 of of ADP iajs-3377 6 38 antiretroviral antiretroviral ADJ iajs-3377 6 39 drugs drug NOUN iajs-3377 6 40 . . PUNCT iajs-3377 7 1 montecarlo montecarlo PROPN iajs-3377 7 2 simulation simulation PROPN iajs-3377 7 3 of of ADP iajs-3377 7 4 efficacy efficacy NOUN iajs-3377 7 5 of of ADP iajs-3377 7 6 antiretroviral antiretroviral ADJ iajs-3377 7 7 drugs drug NOUN iajs-3377 7 8 is be AUX iajs-3377 7 9 conducted conduct VERB iajs-3377 7 10 to to PART iajs-3377 7 11 evaluate evaluate VERB iajs-3377 7 12 the the DET iajs-3377 7 13 performance performance NOUN iajs-3377 7 14 of of ADP iajs-3377 7 15 the the DET iajs-3377 7 16 model model NOUN iajs-3377 7 17 . . PUNCT iajs-3377 8 1 the the DET iajs-3377 8 2 models model NOUN iajs-3377 8 3 were be AUX iajs-3377 8 4 tested test VERB iajs-3377 8 5 using use VERB iajs-3377 8 6 some some DET iajs-3377 8 7 models model NOUN iajs-3377 8 8 diagnostic diagnostic ADJ iajs-3377 8 9 tests test NOUN iajs-3377 8 10 and and CCONJ iajs-3377 8 11 it it PRON iajs-3377 8 12 was be AUX iajs-3377 8 13 revealed reveal VERB iajs-3377 8 14 that that SCONJ iajs-3377 8 15 the the DET iajs-3377 8 16 proposed propose VERB iajs-3377 8 17 model model NOUN iajs-3377 8 18 was be AUX iajs-3377 8 19 better well ADJ iajs-3377 8 20 than than ADP iajs-3377 8 21 the the DET iajs-3377 8 22 ones one NOUN iajs-3377 8 23 proposed propose VERB iajs-3377 8 24 before before ADP iajs-3377 8 25 it it PRON iajs-3377 8 26 from from ADP iajs-3377 8 27 the the DET iajs-3377 8 28 same same ADJ iajs-3377 8 29 family family NOUN iajs-3377 8 30 and and CCONJ iajs-3377 8 31 also also ADV iajs-3377 8 32 , , PUNCT iajs-3377 8 33 the the DET iajs-3377 8 34 stochastic stochastic ADJ iajs-3377 8 35 dominance dominance NOUN iajs-3377 8 36 method method NOUN iajs-3377 8 37 was be AUX iajs-3377 8 38 used use VERB iajs-3377 8 39 to to PART iajs-3377 8 40 affirm affirm VERB iajs-3377 8 41 the the DET iajs-3377 8 42 best good ADJ iajs-3377 8 43 antiretroviral antiretroviral ADJ iajs-3377 8 44 drugs drug NOUN iajs-3377 8 45 used use VERB iajs-3377 8 46 in in ADP iajs-3377 8 47 the the DET iajs-3377 8 48 study study NOUN iajs-3377 8 49 . . PUNCT iajs-3377 9 1 keywords keyword NOUN iajs-3377 9 2 : : PUNCT iajs-3377 9 3 double double ADJ iajs-3377 9 4 exponential exponential ADJ iajs-3377 9 5 distribution distribution NOUN iajs-3377 9 6 , , PUNCT iajs-3377 9 7 hazard hazard NOUN iajs-3377 9 8 function function NOUN iajs-3377 9 9 , , PUNCT iajs-3377 9 10 molecular molecular ADJ iajs-3377 9 11 simulation simulation NOUN iajs-3377 9 12 , , PUNCT iajs-3377 9 13 stochastic stochastic ADJ iajs-3377 9 14 dominance dominance NOUN iajs-3377 9 15 . . PUNCT iajs-3377 10 1 doi.org/10.30526/36.3.3377 doi.org/10.30526/36.3.3377 NOUN iajs-3377 10 2 article article NOUN iajs-3377 10 3 history history NOUN iajs-3377 10 4 : : PUNCT iajs-3377 10 5 received receive VERB iajs-3377 10 6 25 25 NUM iajs-3377 10 7 january january PROPN iajs-3377 10 8 2023 2023 NUM iajs-3377 10 9 , , PUNCT iajs-3377 10 10 accepted accept VERB iajs-3377 10 11 14 14 NUM iajs-3377 10 12 march march NOUN iajs-3377 10 13 2023 2023 NUM iajs-3377 10 14 , , PUNCT iajs-3377 10 15 published publish VERB iajs-3377 10 16 in in ADP iajs-3377 10 17 july july PROPN iajs-3377 10 18 2023 2023 NUM iajs-3377 10 19 . . PUNCT iajs-3377 11 1 ibn ibn PROPN iajs-3377 11 2 al al PROPN iajs-3377 11 3 - - PUNCT iajs-3377 11 4 haitham haitham PROPN iajs-3377 11 5 journal journal PROPN iajs-3377 11 6 for for ADP iajs-3377 11 7 pure pure ADJ iajs-3377 11 8 and and CCONJ iajs-3377 11 9 applied applied ADJ iajs-3377 11 10 sciences sciences PROPN iajs-3377 11 11 journal journal PROPN iajs-3377 11 12 homepage homepage NOUN iajs-3377 11 13 : : PUNCT iajs-3377 11 14 jih.uobaghdad.edu.iq jih.uobaghdad.edu.iq VERB iajs-3377 11 15 double double ADJ iajs-3377 11 16 - - PUNCT iajs-3377 11 17 exponential exponential ADJ iajs-3377 11 18 - - PUNCT iajs-3377 11 19 x x SYM iajs-3377 11 20 family family NOUN iajs-3377 11 21 of of ADP iajs-3377 11 22 distributions distribution NOUN iajs-3377 11 23 : : PUNCT iajs-3377 11 24 properties property NOUN iajs-3377 11 25 and and CCONJ iajs-3377 11 26 applications application NOUN iajs-3377 11 27 kehinde kehinde VERB iajs-3377 11 28 adekunle adekunle NOUN iajs-3377 11 29 bashiru bashiru NOUN iajs-3377 11 30 * * PUNCT iajs-3377 11 31 department department PROPN iajs-3377 11 32 of of ADP iajs-3377 11 33 statistics statistic NOUN iajs-3377 11 34 , , PUNCT iajs-3377 11 35 osun osun PROPN iajs-3377 11 36 state state PROPN iajs-3377 11 37 university university PROPN iajs-3377 11 38 , , PUNCT iajs-3377 11 39 osogbo osogbo PROPN iajs-3377 11 40 , , PUNCT iajs-3377 11 41 nigeria nigeria PROPN iajs-3377 11 42 taiwo taiwo PROPN iajs-3377 11 43 adetola adetola PROPN iajs-3377 12 1 ojurongbe ojurongbe PROPN iajs-3377 12 2 department department PROPN iajs-3377 12 3 of of ADP iajs-3377 12 4 statistics statistic NOUN iajs-3377 12 5 , , PUNCT iajs-3377 12 6 osun osun PROPN iajs-3377 12 7 state state PROPN iajs-3377 12 8 university university PROPN iajs-3377 12 9 , , PUNCT iajs-3377 12 10 osogbo osogbo PROPN iajs-3377 12 11 , , PUNCT iajs-3377 12 12 nigeria nigeria PROPN iajs-3377 12 13 lawal lawal PROPN iajs-3377 12 14 sola sola PROPN iajs-3377 12 15 department department PROPN iajs-3377 12 16 of of ADP iajs-3377 12 17 statistics statistic NOUN iajs-3377 12 18 , , PUNCT iajs-3377 12 19 osun osun PROPN iajs-3377 12 20 state state PROPN iajs-3377 12 21 college college PROPN iajs-3377 12 22 of of ADP iajs-3377 12 23 technology technology PROPN iajs-3377 12 24 , , PUNCT iajs-3377 12 25 esa esa PROPN iajs-3377 12 26 oke oke PROPN iajs-3377 12 27 , , PUNCT iajs-3377 12 28 nigeria nigeria PROPN iajs-3377 12 29 nureni nureni ADJ iajs-3377 12 30 .olawale .olawale PUNCT iajs-3377 13 1 adeboye adeboye PROPN iajs-3377 13 2 department department NOUN iajs-3377 13 3 of of ADP iajs-3377 13 4 statistics statistic NOUN iajs-3377 13 5 , , PUNCT iajs-3377 13 6 osun osun PROPN iajs-3377 13 7 state state PROPN iajs-3377 13 8 university university PROPN iajs-3377 13 9 , , PUNCT iajs-3377 13 10 osogbo osogbo PROPN iajs-3377 13 11 , , PUNCT iajs-3377 13 12 nigeria nigeria PROPN iajs-3377 13 13 habeeb habeeb PROPN iajs-3377 13 14 abiodun abiodun PROPN iajs-3377 13 15 afolabi afolabi PROPN iajs-3377 13 16 department department PROPN iajs-3377 13 17 of of ADP iajs-3377 13 18 statistics statistic NOUN iajs-3377 13 19 , , PUNCT iajs-3377 13 20 osun osun PROPN iajs-3377 13 21 state state PROPN iajs-3377 13 22 university university PROPN iajs-3377 13 23 , , PUNCT iajs-3377 13 24 osogbo osogbo PROPN iajs-3377 13 25 , , PUNCT iajs-3377 13 26 nigeria nigeria PROPN iajs-3377 13 27 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ PROPN iajs-3377 13 28 mailto:%20kehindebashiru@uniosun.edu.ng mailto:%20kehindebashiru@uniosun.edu.ng NOUN iajs-3377 13 29 mailto:kehindebashiru@uniosun.edu.ng mailto:kehindebashiru@uniosun.edu.ng NOUN iajs-3377 13 30 mailto:taiwo.ojurongbe@uniosun.edu.ng mailto:taiwo.ojurongbe@uniosun.edu.ng ADV iajs-3377 13 31 mailto:slawal@gmail.com mailto:slawal@gmail.com NOUN iajs-3377 13 32 mailto:nureni.adeboye@uniosun.edu.ng mailto:nureni.adeboye@uniosun.edu.ng PROPN iajs-3377 13 33 mailto:habeeb.afolabi@uniosun.edu.ng mailto:habeeb.afolabi@uniosun.edu.ng PROPN iajs-3377 13 34 ihjpas ihjpas NOUN iajs-3377 13 35 . . PUNCT iajs-3377 14 1 36 36 NUM iajs-3377 14 2 ( ( PUNCT iajs-3377 14 3 3 3 NUM iajs-3377 14 4 ) ) PUNCT iajs-3377 14 5 2023 2023 NUM iajs-3377 14 6 438 438 NUM iajs-3377 14 7 1 1 NUM iajs-3377 14 8 . . PUNCT iajs-3377 14 9 introduction introduction NOUN iajs-3377 14 10 in in ADP iajs-3377 14 11 the the DET iajs-3377 14 12 past past ADJ iajs-3377 14 13 few few ADJ iajs-3377 14 14 decades decade NOUN iajs-3377 14 15 , , PUNCT iajs-3377 14 16 a a DET iajs-3377 14 17 variety variety NOUN iajs-3377 14 18 of of ADP iajs-3377 14 19 classical classical ADJ iajs-3377 14 20 or or CCONJ iajs-3377 14 21 general general ADJ iajs-3377 14 22 distributions distribution NOUN iajs-3377 14 23 have have AUX iajs-3377 14 24 been be AUX iajs-3377 14 25 widely widely ADV iajs-3377 14 26 used use VERB iajs-3377 14 27 to to PART iajs-3377 14 28 structure structure VERB iajs-3377 14 29 data datum NOUN iajs-3377 14 30 in in ADP iajs-3377 14 31 the the DET iajs-3377 14 32 fields field NOUN iajs-3377 14 33 of of ADP iajs-3377 14 34 engineering engineering NOUN iajs-3377 14 35 , , PUNCT iajs-3377 14 36 actuarial actuarial ADJ iajs-3377 14 37 , , PUNCT iajs-3377 14 38 environmental environmental ADJ iajs-3377 14 39 science science NOUN iajs-3377 14 40 , , PUNCT iajs-3377 14 41 biology biology NOUN iajs-3377 14 42 , , PUNCT iajs-3377 14 43 demography demography NOUN iajs-3377 14 44 , , PUNCT iajs-3377 14 45 economy economy NOUN iajs-3377 14 46 , , PUNCT iajs-3377 14 47 insurance insurance NOUN iajs-3377 14 48 , , PUNCT iajs-3377 14 49 and and CCONJ iajs-3377 14 50 finance finance NOUN iajs-3377 14 51 . . PUNCT iajs-3377 15 1 despite despite SCONJ iajs-3377 15 2 this this PRON iajs-3377 15 3 , , PUNCT iajs-3377 15 4 there there PRON iajs-3377 15 5 continue continue VERB iajs-3377 15 6 to to PART iajs-3377 15 7 be be AUX iajs-3377 15 8 problems problem NOUN iajs-3377 15 9 in in ADP iajs-3377 15 10 each each PRON iajs-3377 15 11 of of ADP iajs-3377 15 12 the the DET iajs-3377 15 13 aforementioned aforementioned ADJ iajs-3377 15 14 fields field NOUN iajs-3377 15 15 . . PUNCT iajs-3377 16 1 naturally naturally ADV iajs-3377 16 2 , , PUNCT iajs-3377 16 3 this this PRON iajs-3377 16 4 may may AUX iajs-3377 16 5 be be AUX iajs-3377 16 6 attributed attribute VERB iajs-3377 16 7 to to ADP iajs-3377 16 8 the the DET iajs-3377 16 9 fact fact NOUN iajs-3377 16 10 that that SCONJ iajs-3377 16 11 , , PUNCT iajs-3377 16 12 as as ADP iajs-3377 16 13 a a DET iajs-3377 16 14 result result NOUN iajs-3377 16 15 of of ADP iajs-3377 16 16 the the DET iajs-3377 16 17 growth growth NOUN iajs-3377 16 18 of of ADP iajs-3377 16 19 science science NOUN iajs-3377 16 20 and and CCONJ iajs-3377 16 21 technology technology NOUN iajs-3377 16 22 , , PUNCT iajs-3377 16 23 the the DET iajs-3377 16 24 underlying underlie VERB iajs-3377 16 25 distributions distribution NOUN iajs-3377 16 26 are be AUX iajs-3377 16 27 no no ADV iajs-3377 16 28 longer long ADV iajs-3377 16 29 able able ADJ iajs-3377 16 30 to to PART iajs-3377 16 31 suit suit VERB iajs-3377 16 32 the the DET iajs-3377 16 33 data datum NOUN iajs-3377 16 34 set set VERB iajs-3377 16 35 . . PUNCT iajs-3377 17 1 because because SCONJ iajs-3377 17 2 of of ADP iajs-3377 17 3 this this PRON iajs-3377 17 4 , , PUNCT iajs-3377 17 5 it it PRON iajs-3377 17 6 is be AUX iajs-3377 17 7 necessary necessary ADJ iajs-3377 17 8 to to PART iajs-3377 17 9 create create VERB iajs-3377 17 10 new new ADJ iajs-3377 17 11 kinds kind NOUN iajs-3377 17 12 of of ADP iajs-3377 17 13 extended extended ADJ iajs-3377 17 14 distributions distribution NOUN iajs-3377 17 15 that that PRON iajs-3377 17 16 can can AUX iajs-3377 17 17 handle handle VERB iajs-3377 17 18 these these DET iajs-3377 17 19 fresh fresh ADJ iajs-3377 17 20 difficulties difficulty NOUN iajs-3377 17 21 . . PUNCT iajs-3377 18 1 as as ADP iajs-3377 18 2 a a DET iajs-3377 18 3 result result NOUN iajs-3377 18 4 , , PUNCT iajs-3377 18 5 numerous numerous ADJ iajs-3377 18 6 methods method NOUN iajs-3377 18 7 have have AUX iajs-3377 18 8 been be AUX iajs-3377 18 9 proposed propose VERB iajs-3377 18 10 and and CCONJ iajs-3377 18 11 researched research VERB iajs-3377 18 12 to to PART iajs-3377 18 13 develop develop VERB iajs-3377 18 14 or or CCONJ iajs-3377 18 15 introduce introduce VERB iajs-3377 18 16 new new ADJ iajs-3377 18 17 families family NOUN iajs-3377 18 18 of of ADP iajs-3377 18 19 distribution distribution NOUN iajs-3377 18 20 by by ADP iajs-3377 18 21 including include VERB iajs-3377 18 22 a a DET iajs-3377 18 23 parameter parameter NOUN iajs-3377 18 24 or or CCONJ iajs-3377 18 25 several several ADJ iajs-3377 18 26 parameters parameter NOUN iajs-3377 18 27 in in ADP iajs-3377 18 28 the the DET iajs-3377 18 29 baseline baseline ADJ iajs-3377 18 30 random random ADJ iajs-3377 18 31 variable variable ADJ iajs-3377 18 32 model model NOUN iajs-3377 18 33 while while SCONJ iajs-3377 18 34 providing provide VERB iajs-3377 18 35 a a DET iajs-3377 18 36 great great ADJ iajs-3377 18 37 degree degree NOUN iajs-3377 18 38 of of ADP iajs-3377 18 39 flexibility flexibility NOUN iajs-3377 18 40 in in ADP iajs-3377 18 41 actual actual ADJ iajs-3377 18 42 data datum NOUN iajs-3377 18 43 modeling modeling NOUN iajs-3377 18 44 , , PUNCT iajs-3377 18 45 including include VERB iajs-3377 18 46 beta beta NOUN iajs-3377 18 47 - - PUNCT iajs-3377 18 48 g g NOUN iajs-3377 18 49 [ [ X iajs-3377 18 50 1,2 1,2 NUM iajs-3377 18 51 ] ] PUNCT iajs-3377 18 52 , , PUNCT iajs-3377 18 53 gamma gamma PROPN iajs-3377 18 54 - - PUNCT iajs-3377 18 55 g g NOUN iajs-3377 18 56 type-1 type-1 PROPN iajs-3377 19 1 [ [ X iajs-3377 19 2 3 3 NUM iajs-3377 19 3 ] ] PUNCT iajs-3377 19 4 , , PUNCT iajs-3377 19 5 mc mc PROPN iajs-3377 19 6 - - PUNCT iajs-3377 19 7 g g PROPN iajs-3377 20 1 [ [ X iajs-3377 20 2 4 4 NUM iajs-3377 20 3 ] ] PUNCT iajs-3377 20 4 , , PUNCT iajs-3377 20 5 log log NOUN iajs-3377 20 6 - - PUNCT iajs-3377 20 7 gamma gamma NOUN iajs-3377 20 8 - - PUNCT iajs-3377 20 9 g g NOUN iajs-3377 20 10 type-2 type-2 NUM iajs-3377 21 1 [ [ X iajs-3377 21 2 5 5 NUM iajs-3377 21 3 ] ] PUNCT iajs-3377 21 4 , , PUNCT iajs-3377 21 5 gamma gamma NOUN iajs-3377 21 6 - - PUNCT iajs-3377 21 7 g g NOUN iajs-3377 21 8 type-3 type-3 NOUN iajs-3377 21 9 [ [ X iajs-3377 21 10 6 6 NUM iajs-3377 21 11 ] ] PUNCT iajs-3377 21 12 , , PUNCT iajs-3377 21 13 weibull weibull PROPN iajs-3377 21 14 - - PUNCT iajs-3377 21 15 x x SYM iajs-3377 21 16 family family NOUN iajs-3377 21 17 of of ADP iajs-3377 21 18 distributions distribution NOUN iajs-3377 21 19 [ [ X iajs-3377 21 20 7 7 NUM iajs-3377 21 21 ] ] PUNCT iajs-3377 21 22 , , PUNCT iajs-3377 21 23 odd odd ADJ iajs-3377 21 24 generalized generalized ADJ iajs-3377 21 25 exponential exponential NOUN iajs-3377 21 26 - - PUNCT iajs-3377 21 27 g g NOUN iajs-3377 21 28 [ [ X iajs-3377 21 29 8,9 8,9 NUM iajs-3377 21 30 ] ] PUNCT iajs-3377 21 31 , , PUNCT iajs-3377 21 32 type-1 type-1 NUM iajs-3377 21 33 half half ADJ iajs-3377 21 34 - - PUNCT iajs-3377 21 35 logistic logistic ADJ iajs-3377 21 36 family family NOUN iajs-3377 21 37 [ [ X iajs-3377 21 38 10 10 NUM iajs-3377 21 39 ] ] PUNCT iajs-3377 21 40 , , PUNCT iajs-3377 21 41 kumaraswamy kumaraswamy NOUN iajs-3377 21 42 - - PUNCT iajs-3377 21 43 weibull weibull NOUN iajs-3377 21 44 - - PUNCT iajs-3377 21 45 generated generate VERB iajs-3377 21 46 family family NOUN iajs-3377 22 1 [ [ X iajs-3377 22 2 11 11 NUM iajs-3377 22 3 ] ] PUNCT iajs-3377 22 4 , , PUNCT iajs-3377 22 5 new new ADJ iajs-3377 22 6 weibullg weibullg NOUN iajs-3377 22 7 family family NOUN iajs-3377 23 1 [ [ X iajs-3377 23 2 12 12 NUM iajs-3377 23 3 ] ] PUNCT iajs-3377 23 4 , , PUNCT iajs-3377 23 5 generalized generalize VERB iajs-3377 23 6 transmutedg transmutedg NOUN iajs-3377 23 7 [ [ X iajs-3377 23 8 13 13 NUM iajs-3377 23 9 ] ] PUNCT iajs-3377 23 10 taking take VERB iajs-3377 23 11 𝑣(𝑑 𝑣(𝑑 NOUN iajs-3377 23 12 ) ) PUNCT iajs-3377 23 13 to to PART iajs-3377 23 14 be be AUX iajs-3377 23 15 the the DET iajs-3377 23 16 probability probability NOUN iajs-3377 23 17 density density NOUN iajs-3377 23 18 function function NOUN iajs-3377 23 19 ( ( PUNCT iajs-3377 23 20 pdf pdf NOUN iajs-3377 23 21 ) ) PUNCT iajs-3377 23 22 of of ADP iajs-3377 23 23 a a DET iajs-3377 23 24 random random ADJ iajs-3377 23 25 variable variable NOUN iajs-3377 23 26 , , PUNCT iajs-3377 23 27 say say INTJ iajs-3377 23 28 , , PUNCT iajs-3377 23 29 which which PRON iajs-3377 23 30 belongs belong VERB iajs-3377 23 31 to to ADP iajs-3377 23 32 m m PROPN iajs-3377 23 33 and and CCONJ iajs-3377 23 34 n n CCONJ iajs-3377 23 35 , , PUNCT iajs-3377 23 36 that that PRON iajs-3377 23 37 is be AUX iajs-3377 23 38 t∈ t∈ ADJ iajs-3377 23 39 [ [ X iajs-3377 23 40 π‘š π‘š NOUN iajs-3377 23 41 , , PUNCT iajs-3377 23 42 𝑛 𝑛 NOUN iajs-3377 23 43 ] ] PUNCT iajs-3377 23 44 for for ADP iajs-3377 23 45 -∞ -∞ SYM iajs-3377 23 46 ≀ ≀ NUM iajs-3377 23 47 m m VERB iajs-3377 23 48 < < X iajs-3377 23 49 n n X iajs-3377 23 50 < < X iajs-3377 23 51 ∞ ∞ NOUN iajs-3377 23 52 and and CCONJ iajs-3377 23 53 also also ADV iajs-3377 23 54 , , PUNCT iajs-3377 23 55 let let VERB iajs-3377 23 56 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ NOUN iajs-3377 23 57 , , PUNCT iajs-3377 23 58 πœ‰ πœ‰ X iajs-3377 23 59 ) ) PUNCT iajs-3377 23 60 ] ] PUNCT iajs-3377 23 61 be be AUX iajs-3377 23 62 a a DET iajs-3377 23 63 function function NOUN iajs-3377 23 64 of of ADP iajs-3377 23 65 cumulative cumulative ADJ iajs-3377 23 66 distribution distribution NOUN iajs-3377 23 67 function function NOUN iajs-3377 23 68 ( ( PUNCT iajs-3377 23 69 cdf cdf PROPN iajs-3377 23 70 ) ) PUNCT iajs-3377 23 71 of of ADP iajs-3377 23 72 a a DET iajs-3377 23 73 random random ADJ iajs-3377 23 74 variable variable NOUN iajs-3377 23 75 , , PUNCT iajs-3377 23 76 say say VERB iajs-3377 23 77 x x PUNCT iajs-3377 23 78 which which PRON iajs-3377 23 79 depends depend VERB iajs-3377 23 80 on on ADP iajs-3377 23 81 the the DET iajs-3377 23 82 parameter parameter NOUN iajs-3377 23 83 πœ‰ πœ‰ PROPN iajs-3377 23 84 which which PRON iajs-3377 23 85 satisfies satisfy VERB iajs-3377 23 86 the the DET iajs-3377 23 87 conditions condition NOUN iajs-3377 23 88 : : PUNCT iajs-3377 23 89 i i PRON iajs-3377 23 90 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 23 91 , , PUNCT iajs-3377 23 92 πœ‰ πœ‰ X iajs-3377 23 93 ) ) PUNCT iajs-3377 23 94 ] ] PUNCT iajs-3377 23 95 is be AUX iajs-3377 23 96 bounded bound VERB iajs-3377 23 97 between between ADP iajs-3377 23 98 m m PROPN iajs-3377 23 99 and and CCONJ iajs-3377 23 100 n n PRON iajs-3377 23 101 ii ii PROPN iajs-3377 23 102 . . PUNCT iajs-3377 24 1 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 24 2 , , PUNCT iajs-3377 24 3 πœ‰ πœ‰ X iajs-3377 24 4 ) ) PUNCT iajs-3377 24 5 ] ] PUNCT iajs-3377 24 6 is be AUX iajs-3377 24 7 differentiable differentiable ADJ iajs-3377 24 8 and and CCONJ iajs-3377 24 9 monotonically monotonically ADV iajs-3377 24 10 increasing increase VERB iajs-3377 24 11 iii iii NOUN iajs-3377 24 12 . . PUNCT iajs-3377 25 1 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 25 2 , , PUNCT iajs-3377 25 3 πœ‰ πœ‰ X iajs-3377 25 4 ) ) PUNCT iajs-3377 25 5 ] ] PUNCT iajs-3377 26 1 β†’m β†’m PUNCT iajs-3377 26 2 as as ADP iajs-3377 26 3 xβ†’-∞ xβ†’-∞ NOUN iajs-3377 26 4 and and CCONJ iajs-3377 26 5 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 26 6 , , PUNCT iajs-3377 26 7 πœ‰)]β†’n πœ‰)]β†’n ADP iajs-3377 26 8 as as ADP iajs-3377 26 9 xβ†’βˆž xβ†’βˆž NUM iajs-3377 26 10 the the DET iajs-3377 26 11 cdf cdf PROPN iajs-3377 26 12 of of ADP iajs-3377 26 13 the the DET iajs-3377 26 14 t t PROPN iajs-3377 26 15 - - PUNCT iajs-3377 26 16 x x NOUN iajs-3377 26 17 family family NOUN iajs-3377 26 18 of of ADP iajs-3377 26 19 distribution distribution NOUN iajs-3377 26 20 as as SCONJ iajs-3377 26 21 recently recently ADV iajs-3377 26 22 used use VERB iajs-3377 26 23 by by ADP iajs-3377 26 24 [ [ X iajs-3377 26 25 14 14 NUM iajs-3377 26 26 ] ] PUNCT iajs-3377 26 27 as as ADP iajs-3377 26 28 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-3377 26 29 ) ) PUNCT iajs-3377 26 30 = = SYM iajs-3377 26 31 ∫ ∫ PROPN iajs-3377 26 32 𝑣(𝑑)𝑑𝑑 𝑣(𝑑)𝑑𝑑 NUM iajs-3377 26 33 𝑀(𝐹(π‘₯;πœ‰ 𝑀(𝐹(π‘₯;πœ‰ NUM iajs-3377 26 34 ) ) PUNCT iajs-3377 26 35 ) ) PUNCT iajs-3377 26 36 π‘š π‘š NOUN iajs-3377 26 37 , , PUNCT iajs-3377 26 38 π‘₯ π‘₯ PRON iajs-3377 26 39 ∈ ∈ PROPN iajs-3377 26 40 𝑅 𝑅 PROPN iajs-3377 26 41 ( ( PUNCT iajs-3377 26 42 1 1 NUM iajs-3377 26 43 ) ) PUNCT iajs-3377 26 44 and and CCONJ iajs-3377 26 45 the the DET iajs-3377 26 46 pdf pdf NOUN iajs-3377 26 47 corresponding correspond VERB iajs-3377 26 48 to to ADP iajs-3377 26 49 ( ( PUNCT iajs-3377 26 50 1 1 X iajs-3377 26 51 ) ) PUNCT iajs-3377 26 52 is be AUX iajs-3377 26 53 given give VERB iajs-3377 26 54 as as ADP iajs-3377 26 55 : : PUNCT iajs-3377 26 56 𝑔(π‘₯ 𝑔(π‘₯ NUM iajs-3377 26 57 ) ) PUNCT iajs-3377 26 58 = = PRON iajs-3377 27 1 { { PUNCT iajs-3377 27 2 𝑑 𝑑 NOUN iajs-3377 27 3 𝑑π‘₯ 𝑑π‘₯ NOUN iajs-3377 27 4 𝑀[𝐹(π‘₯ 𝑀[𝐹(π‘₯ NOUN iajs-3377 27 5 ; ; PUNCT iajs-3377 27 6 πœ‰ πœ‰ X iajs-3377 27 7 ) ) PUNCT iajs-3377 27 8 ] ] PUNCT iajs-3377 27 9 } } PUNCT iajs-3377 27 10 𝑉{𝑀[𝐹(π‘₯ 𝑉{𝑀[𝐹(π‘₯ NOUN iajs-3377 27 11 : : PUNCT iajs-3377 27 12 πœ‰ πœ‰ X iajs-3377 27 13 ) ) PUNCT iajs-3377 27 14 ] ] PUNCT iajs-3377 27 15 } } PUNCT iajs-3377 27 16 π‘₯ π‘₯ PRON iajs-3377 27 17 ∈ ∈ PROPN iajs-3377 27 18 𝑅 𝑅 PROPN iajs-3377 27 19 several several ADJ iajs-3377 27 20 new new ADJ iajs-3377 27 21 families family NOUN iajs-3377 27 22 of of ADP iajs-3377 27 23 distributions distribution NOUN iajs-3377 27 24 have have AUX iajs-3377 27 25 been be AUX iajs-3377 27 26 postulated postulate VERB iajs-3377 27 27 using use VERB iajs-3377 27 28 the the DET iajs-3377 27 29 concept concept NOUN iajs-3377 27 30 of of ADP iajs-3377 27 31 t t PROPN iajs-3377 27 32 - - PUNCT iajs-3377 27 33 x x NOUN iajs-3377 27 34 family family NOUN iajs-3377 27 35 as as SCONJ iajs-3377 27 36 proposed propose VERB iajs-3377 27 37 [ [ X iajs-3377 27 38 14 14 NUM iajs-3377 27 39 ] ] PUNCT iajs-3377 27 40 . . PUNCT iajs-3377 28 1 different different ADJ iajs-3377 28 2 functions function NOUN iajs-3377 28 3 of of ADP iajs-3377 28 4 π‘Š[𝐹(𝑋 π‘Š[𝐹(𝑋 NOUN iajs-3377 28 5 ; ; PUNCT iajs-3377 28 6 ∈ ∈ PROPN iajs-3377 28 7 ) ) PUNCT iajs-3377 28 8 ] ] PUNCT iajs-3377 28 9 have have AUX iajs-3377 28 10 been be AUX iajs-3377 28 11 employed employ VERB iajs-3377 28 12 in in ADP iajs-3377 28 13 the the DET iajs-3377 28 14 literature literature NOUN iajs-3377 28 15 for for ADP iajs-3377 28 16 the the DET iajs-3377 28 17 tx tx PROPN iajs-3377 28 18 family family NOUN iajs-3377 28 19 which which PRON iajs-3377 28 20 are be AUX iajs-3377 28 21 revealed reveal VERB iajs-3377 28 22 in in ADP iajs-3377 28 23 table1 table1 PROPN iajs-3377 28 24 . . PUNCT iajs-3377 29 1 this this DET iajs-3377 29 2 research research NOUN iajs-3377 29 3 aims aim VERB iajs-3377 29 4 to to PART iajs-3377 29 5 introduce introduce VERB iajs-3377 29 6 a a DET iajs-3377 29 7 new new ADJ iajs-3377 29 8 family family NOUN iajs-3377 29 9 of of ADP iajs-3377 29 10 continuous continuous ADJ iajs-3377 29 11 distributions distribution NOUN iajs-3377 29 12 , , PUNCT iajs-3377 29 13 which which PRON iajs-3377 29 14 is be AUX iajs-3377 29 15 named name VERB iajs-3377 29 16 as as ADP iajs-3377 29 17 double double ADJ iajs-3377 29 18 exponential exponential NOUN iajs-3377 29 19 - - PUNCT iajs-3377 29 20 x x X iajs-3377 29 21 ( ( PUNCT iajs-3377 29 22 β€œ " PUNCT iajs-3377 29 23 de de X iajs-3377 29 24 - - NOUN iajs-3377 29 25 x x NOUN iajs-3377 29 26 ” " PUNCT iajs-3377 29 27 for for ADP iajs-3377 29 28 short short ADJ iajs-3377 29 29 ) ) PUNCT iajs-3377 29 30 family family NOUN iajs-3377 29 31 . . PUNCT iajs-3377 30 1 this this DET iajs-3377 30 2 family family NOUN iajs-3377 30 3 's 's PART iajs-3377 30 4 two two NUM iajs-3377 30 5 distinct distinct ADJ iajs-3377 30 6 sub sub NOUN iajs-3377 30 7 - - NOUN iajs-3377 30 8 models model NOUN iajs-3377 30 9 are be AUX iajs-3377 30 10 looked look VERB iajs-3377 30 11 into into ADP iajs-3377 30 12 and and CCONJ iajs-3377 30 13 discussed discuss VERB iajs-3377 30 14 . . PUNCT iajs-3377 31 1 both both PRON iajs-3377 31 2 real real ADJ iajs-3377 31 3 life life NOUN iajs-3377 31 4 and and CCONJ iajs-3377 31 5 simulated simulated ADJ iajs-3377 31 6 data datum NOUN iajs-3377 31 7 are be AUX iajs-3377 31 8 used use VERB iajs-3377 31 9 to to PART iajs-3377 31 10 illustrate illustrate VERB iajs-3377 31 11 the the DET iajs-3377 31 12 essence essence NOUN iajs-3377 31 13 of of ADP iajs-3377 31 14 the the DET iajs-3377 31 15 new new ADJ iajs-3377 31 16 model model NOUN iajs-3377 31 17 in in ADP iajs-3377 31 18 the the DET iajs-3377 31 19 area area NOUN iajs-3377 31 20 of of ADP iajs-3377 31 21 applied apply VERB iajs-3377 31 22 science science NOUN iajs-3377 31 23 . . PUNCT iajs-3377 32 1 this this DET iajs-3377 32 2 paper paper NOUN iajs-3377 32 3 's 's PART iajs-3377 32 4 remaining remain VERB iajs-3377 32 5 sections section NOUN iajs-3377 32 6 are be AUX iajs-3377 32 7 divided divide VERB iajs-3377 32 8 as as SCONJ iajs-3377 32 9 follows follow VERB iajs-3377 32 10 : : PUNCT iajs-3377 32 11 in in ADP iajs-3377 32 12 the the DET iajs-3377 32 13 section section NOUN iajs-3377 32 14 titled title VERB iajs-3377 32 15 " " PUNCT iajs-3377 32 16 double double ADJ iajs-3377 32 17 - - PUNCT iajs-3377 32 18 exponential exponential NOUN iajs-3377 32 19 x x PROPN iajs-3377 32 20 family family NOUN iajs-3377 32 21 , , PUNCT iajs-3377 32 22 " " PUNCT iajs-3377 32 23 we we PRON iajs-3377 32 24 define define VERB iajs-3377 32 25 the the DET iajs-3377 32 26 de de PROPN iajs-3377 32 27 - - ADJ iajs-3377 32 28 x x ADJ iajs-3377 32 29 family family NOUN iajs-3377 32 30 of of ADP iajs-3377 32 31 distributions distribution NOUN iajs-3377 32 32 , , PUNCT iajs-3377 32 33 provide provide VERB iajs-3377 32 34 a a DET iajs-3377 32 35 mathematical mathematical ADJ iajs-3377 32 36 derivation derivation NOUN iajs-3377 32 37 of of ADP iajs-3377 32 38 some some PRON iajs-3377 32 39 of of ADP iajs-3377 32 40 the the DET iajs-3377 32 41 family family NOUN iajs-3377 32 42 's 's PART iajs-3377 32 43 fundamental fundamental ADJ iajs-3377 32 44 statistical statistical ADJ iajs-3377 32 45 properties property NOUN iajs-3377 32 46 , , PUNCT iajs-3377 32 47 including include VERB iajs-3377 32 48 the the DET iajs-3377 32 49 moment moment NOUN iajs-3377 32 50 , , PUNCT iajs-3377 32 51 survival survival NOUN iajs-3377 32 52 function function NOUN iajs-3377 32 53 , , PUNCT iajs-3377 32 54 order order NOUN iajs-3377 32 55 statistics statistic NOUN iajs-3377 32 56 , , PUNCT iajs-3377 32 57 probability probability NOUN iajs-3377 32 58 weighted weight VERB iajs-3377 32 59 moment moment NOUN iajs-3377 32 60 ( ( PUNCT iajs-3377 32 61 pwm pwm NOUN iajs-3377 32 62 ) ) PUNCT iajs-3377 32 63 , , PUNCT iajs-3377 32 64 and and CCONJ iajs-3377 32 65 quartile quartile ADJ iajs-3377 32 66 function function NOUN iajs-3377 32 67 , , PUNCT iajs-3377 32 68 and and CCONJ iajs-3377 32 69 provide provide VERB iajs-3377 32 70 a a DET iajs-3377 32 71 maximum maximum ADJ iajs-3377 32 72 likelihood likelihood NOUN iajs-3377 32 73 estimation estimation NOUN iajs-3377 32 74 method method NOUN iajs-3377 32 75 for for ADP iajs-3377 32 76 determining determine VERB iajs-3377 32 77 the the DET iajs-3377 32 78 model model NOUN iajs-3377 32 79 parameters parameter NOUN iajs-3377 32 80 . . PUNCT iajs-3377 33 1 the the DET iajs-3377 33 2 de de ADJ iajs-3377 33 3 - - ADJ iajs-3377 33 4 pareto pareto ADJ iajs-3377 33 5 distribution distribution NOUN iajs-3377 33 6 sub sub NOUN iajs-3377 33 7 - - NOUN iajs-3377 33 8 model model NOUN iajs-3377 33 9 constructed construct VERB iajs-3377 33 10 from from ADP iajs-3377 33 11 this this DET iajs-3377 33 12 family family NOUN iajs-3377 33 13 was be AUX iajs-3377 33 14 fitted fit VERB iajs-3377 33 15 to to PART iajs-3377 33 16 reallife reallife VERB iajs-3377 33 17 data datum NOUN iajs-3377 33 18 of of ADP iajs-3377 33 19 viral viral ADJ iajs-3377 33 20 load load NOUN iajs-3377 33 21 ( ( PUNCT iajs-3377 33 22 copies copy NOUN iajs-3377 33 23 / / SYM iajs-3377 33 24 ml ml NOUN iajs-3377 33 25 ) ) PUNCT iajs-3377 33 26 of of ADP iajs-3377 33 27 some some DET iajs-3377 33 28 patients patient NOUN iajs-3377 33 29 receiving receive VERB iajs-3377 33 30 antiretroviral antiretroviral ADJ iajs-3377 33 31 medication medication NOUN iajs-3377 33 32 . . PUNCT iajs-3377 34 1 in in ADP iajs-3377 34 2 order order NOUN iajs-3377 34 3 to to PART iajs-3377 34 4 calculate calculate VERB iajs-3377 34 5 the the DET iajs-3377 34 6 average average ADJ iajs-3377 34 7 binding bind VERB iajs-3377 34 8 affinity affinity NOUN iajs-3377 34 9 ihjpas ihjpa NOUN iajs-3377 34 10 . . PUNCT iajs-3377 35 1 36 36 NUM iajs-3377 35 2 ( ( PUNCT iajs-3377 35 3 3 3 NUM iajs-3377 35 4 ) ) PUNCT iajs-3377 35 5 2023 2023 NUM iajs-3377 35 6 439 439 NUM iajs-3377 35 7 of of ADP iajs-3377 35 8 abacavir abacavir NOUN iajs-3377 35 9 and and CCONJ iajs-3377 35 10 neviranpine neviranpine ADV iajs-3377 35 11 as as SCONJ iajs-3377 35 12 they they PRON iajs-3377 35 13 docked dock VERB iajs-3377 35 14 ( ( PUNCT iajs-3377 35 15 using use VERB iajs-3377 35 16 molecular molecular ADJ iajs-3377 35 17 docking docking NOUN iajs-3377 35 18 ) ) PUNCT iajs-3377 35 19 , , PUNCT iajs-3377 35 20 simulated simulate VERB iajs-3377 35 21 data datum NOUN iajs-3377 35 22 ( ( PUNCT iajs-3377 35 23 from from ADP iajs-3377 35 24 simulation simulation NOUN iajs-3377 35 25 of of ADP iajs-3377 35 26 molecular molecular ADJ iajs-3377 35 27 dynamics dynamic NOUN iajs-3377 35 28 ) ) PUNCT iajs-3377 35 29 was be AUX iajs-3377 35 30 also also ADV iajs-3377 35 31 used use VERB iajs-3377 35 32 . . PUNCT iajs-3377 36 1 table table NOUN iajs-3377 36 2 1 1 NUM iajs-3377 36 3 : : PUNCT iajs-3377 36 4 a a DET iajs-3377 36 5 few few ADJ iajs-3377 36 6 t t PROPN iajs-3377 36 7 - - PUNCT iajs-3377 36 8 x x NOUN iajs-3377 36 9 family family NOUN iajs-3377 36 10 members member NOUN iajs-3377 36 11 currently currently ADV iajs-3377 36 12 in in ADP iajs-3377 36 13 existence existence NOUN iajs-3377 36 14 𝑾[𝑭(𝒙 𝑾[𝑭(𝒙 VERB iajs-3377 36 15 ; ; PUNCT iajs-3377 36 16 𝝃 𝝃 NOUN iajs-3377 36 17 ) ) PUNCT iajs-3377 36 18 ] ] PUNCT iajs-3377 37 1 range range NOUN iajs-3377 37 2 of of ADP iajs-3377 37 3 𝑿 𝑿 ADJ iajs-3377 37 4 members member NOUN iajs-3377 37 5 of of ADP iajs-3377 37 6 t t PROPN iajs-3377 37 7 – – PUNCT iajs-3377 37 8 x x SYM iajs-3377 37 9 family family NOUN iajs-3377 37 10 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 37 11 , , PUNCT iajs-3377 37 12 πœ‰ πœ‰ NOUN iajs-3377 37 13 ) ) PUNCT iajs-3377 37 14 ( ( PUNCT iajs-3377 37 15 0,1 0,1 NOUN iajs-3377 37 16 ) ) PUNCT iajs-3377 37 17 beta beta NOUN iajs-3377 37 18 – – PUNCT iajs-3377 37 19 g g X iajs-3377 37 20 [ [ X iajs-3377 37 21 1 1 NUM iajs-3377 37 22 ] ] PUNCT iajs-3377 37 23 βˆ’ βˆ’ PUNCT iajs-3377 37 24 log[𝐹(π‘₯ log[𝐹(π‘₯ ADJ iajs-3377 37 25 ; ; PUNCT iajs-3377 37 26 πœ‰ πœ‰ X iajs-3377 37 27 ) ) PUNCT iajs-3377 37 28 ] ] PUNCT iajs-3377 37 29 ( ( PUNCT iajs-3377 37 30 0 0 NUM iajs-3377 37 31 , , PUNCT iajs-3377 37 32 ∞ ∞ NOUN iajs-3377 37 33 ) ) PUNCT iajs-3377 37 34 gamma gamma NOUN iajs-3377 37 35 - - PUNCT iajs-3377 37 36 gtype-22 gtype-22 PROPN iajs-3377 37 37 ) ) PUNCT iajs-3377 38 1 [ [ X iajs-3377 38 2 15 15 NUM iajs-3377 38 3 ] ] SYM iajs-3377 38 4 βˆ’ βˆ’ PROPN iajs-3377 38 5 log[1 log[1 NUM iajs-3377 38 6 βˆ’ βˆ’ PROPN iajs-3377 38 7 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 38 8 ; ; PUNCT iajs-3377 38 9 πœ‰ πœ‰ X iajs-3377 38 10 ) ) PUNCT iajs-3377 38 11 ] ] PUNCT iajs-3377 38 12 ( ( PUNCT iajs-3377 38 13 0 0 NUM iajs-3377 38 14 , , PUNCT iajs-3377 38 15 ∞ ∞ NOUN iajs-3377 38 16 ) ) PUNCT iajs-3377 38 17 gamma gamma NOUN iajs-3377 38 18 - - PUNCT iajs-3377 38 19 gtype-1[3 gtype-1[3 PROPN iajs-3377 38 20 ] ] X iajs-3377 38 21 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 38 22 , , PUNCT iajs-3377 38 23 πœ‰ πœ‰ NOUN iajs-3377 38 24 ) ) PUNCT iajs-3377 38 25 1 1 NUM iajs-3377 38 26 βˆ’ βˆ’ PROPN iajs-3377 38 27 𝐹(π‘₯ 𝐹(π‘₯ NOUN iajs-3377 38 28 , , PUNCT iajs-3377 38 29 πœ‰ πœ‰ NOUN iajs-3377 38 30 ) ) PUNCT iajs-3377 38 31 ( ( PUNCT iajs-3377 38 32 0 0 NUM iajs-3377 38 33 , , PUNCT iajs-3377 38 34 ∞ ∞ NOUN iajs-3377 38 35 ) ) PUNCT iajs-3377 38 36 gamma gamma NOUN iajs-3377 38 37 - - PUNCT iajs-3377 38 38 gtype-3 gtype-3 PROPN iajs-3377 38 39 [ [ NOUN iajs-3377 38 40 6 6 NUM iajs-3377 38 41 ] ] PUNCT iajs-3377 38 42 βˆ’ βˆ’ PROPN iajs-3377 38 43 log[1 log[1 NUM iajs-3377 38 44 βˆ’ βˆ’ PROPN iajs-3377 38 45 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 38 46 , , PUNCT iajs-3377 38 47 πœ‰ πœ‰ NOUN iajs-3377 38 48 ) ) PUNCT iajs-3377 38 49 ] ] PUNCT iajs-3377 38 50 ( ( PUNCT iajs-3377 38 51 0 0 NUM iajs-3377 38 52 , , PUNCT iajs-3377 38 53 ∞ ∞ NUM iajs-3377 38 54 ) ) PUNCT iajs-3377 38 55 exponentiated exponentiate VERB iajs-3377 38 56 t t PROPN iajs-3377 38 57 – – PUNCT iajs-3377 38 58 x x PUNCT iajs-3377 39 1 [ [ X iajs-3377 39 2 14 14 NUM iajs-3377 39 3 ] ] X iajs-3377 39 4 log log NOUN iajs-3377 39 5 { { PUNCT iajs-3377 39 6 𝐹(π‘₯ 𝐹(π‘₯ NOUN iajs-3377 39 7 , , PUNCT iajs-3377 39 8 πœ‰ πœ‰ NOUN iajs-3377 39 9 ) ) PUNCT iajs-3377 39 10 1 1 NUM iajs-3377 39 11 βˆ’ βˆ’ PROPN iajs-3377 39 12 𝐹(π‘₯ 𝐹(π‘₯ NOUN iajs-3377 39 13 , , PUNCT iajs-3377 39 14 πœ‰ πœ‰ NOUN iajs-3377 39 15 ) ) PUNCT iajs-3377 39 16 } } PUNCT iajs-3377 39 17 ( ( PUNCT iajs-3377 39 18 βˆ’βˆž βˆ’βˆž NOUN iajs-3377 39 19 , , PUNCT iajs-3377 39 20 ∞ ∞ NOUN iajs-3377 39 21 ) ) PUNCT iajs-3377 39 22 logistics logistic NOUN iajs-3377 39 23 – – PUNCT iajs-3377 39 24 g g X iajs-3377 39 25 [ [ X iajs-3377 39 26 16 16 NUM iajs-3377 39 27 ] ] PUNCT iajs-3377 39 28 log[βˆ’ log[βˆ’ NOUN iajs-3377 39 29 log{1 log{1 PROPN iajs-3377 39 30 βˆ’ βˆ’ PROPN iajs-3377 39 31 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 39 32 , , PUNCT iajs-3377 39 33 πœ‰ πœ‰ NOUN iajs-3377 39 34 ) ) PUNCT iajs-3377 39 35 } } PUNCT iajs-3377 39 36 ] ] PUNCT iajs-3377 39 37 ( ( PUNCT iajs-3377 39 38 0 0 NUM iajs-3377 39 39 , , PUNCT iajs-3377 39 40 ∞ ∞ NUM iajs-3377 39 41 ) ) PUNCT iajs-3377 39 42 the the DET iajs-3377 39 43 logistic logistic ADJ iajs-3377 39 44 – – PUNCT iajs-3377 39 45 x x SYM iajs-3377 39 46 family family NOUN iajs-3377 40 1 [ [ X iajs-3377 40 2 8,9 8,9 NUM iajs-3377 40 3 ] ] SYM iajs-3377 40 4 2 2 NUM iajs-3377 40 5 . . PUNCT iajs-3377 40 6 materials material NOUN iajs-3377 40 7 and and CCONJ iajs-3377 40 8 methods method NOUN iajs-3377 40 9 2.0 2.0 NUM iajs-3377 40 10 the the DET iajs-3377 40 11 double double ADJ iajs-3377 40 12 exponential exponential NOUN iajs-3377 40 13 - - PUNCT iajs-3377 40 14 x x VERB iajs-3377 40 15 family family NOUN iajs-3377 40 16 given give VERB iajs-3377 40 17 the the DET iajs-3377 40 18 pdf pdf NOUN iajs-3377 40 19 of of ADP iajs-3377 40 20 the the DET iajs-3377 40 21 double double ADJ iajs-3377 40 22 exponential exponential ADJ iajs-3377 40 23 distribution distribution NOUN iajs-3377 40 24 𝑉(π‘₯ 𝑉(π‘₯ ADP iajs-3377 40 25 ; ; PUNCT iajs-3377 40 26 𝑏 𝑏 NUM iajs-3377 40 27 ; ; PUNCT iajs-3377 40 28 Β΅ Β΅ X iajs-3377 40 29 ) ) PUNCT iajs-3377 40 30 = = SYM iajs-3377 41 1 1 1 NUM iajs-3377 41 2 2𝑏 2𝑏 NUM iajs-3377 41 3 𝑒 𝑒 X iajs-3377 41 4 |π‘₯βˆ’Β΅| |π‘₯βˆ’Β΅| PUNCT iajs-3377 41 5 𝑏 𝑏 PROPN iajs-3377 41 6 ( ( PUNCT iajs-3377 41 7 21 21 NUM iajs-3377 41 8 ) ) PUNCT iajs-3377 41 9 ( ( PUNCT iajs-3377 41 10 2 2 NUM iajs-3377 41 11 ) ) PUNCT iajs-3377 41 12 and and CCONJ iajs-3377 41 13 the the DET iajs-3377 41 14 corresponding correspond VERB iajs-3377 41 15 cdf cdf PROPN iajs-3377 41 16 with with ADP iajs-3377 41 17 high high ADJ iajs-3377 41 18 reliability reliability NOUN iajs-3377 41 19 on on ADP iajs-3377 41 20 the the DET iajs-3377 41 21 support support NOUN iajs-3377 41 22 is be AUX iajs-3377 41 23 given give VERB iajs-3377 41 24 by by ADP iajs-3377 41 25 : : PUNCT iajs-3377 41 26 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 41 27 ; ; PUNCT iajs-3377 41 28 Β΅ Β΅ NUM iajs-3377 41 29 ; ; PUNCT iajs-3377 41 30 𝑏 𝑏 NUM iajs-3377 41 31 ) ) PUNCT iajs-3377 41 32 = = SYM iajs-3377 41 33 1 1 NUM iajs-3377 41 34 2 2 NUM iajs-3377 41 35 𝑒 𝑒 X iajs-3377 41 36 βˆ’(Β΅βˆ’π‘₯ βˆ’(Β΅βˆ’π‘₯ NOUN iajs-3377 41 37 ) ) PUNCT iajs-3377 41 38 𝑏 𝑏 PROPN iajs-3377 41 39 ifπ‘₯ ifπ‘₯ PROPN iajs-3377 41 40 ≀ ≀ PROPN iajs-3377 41 41 Β΅ Β΅ X iajs-3377 41 42 ( ( PUNCT iajs-3377 41 43 3 3 NUM iajs-3377 41 44 ) ) PUNCT iajs-3377 41 45 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 41 46 ; ; PUNCT iajs-3377 41 47 Β΅ Β΅ NUM iajs-3377 41 48 ; ; PUNCT iajs-3377 41 49 𝑏 𝑏 NUM iajs-3377 41 50 ) ) PUNCT iajs-3377 41 51 = = SYM iajs-3377 42 1 1 1 NUM iajs-3377 42 2 βˆ’ βˆ’ NUM iajs-3377 42 3 1 1 NUM iajs-3377 42 4 2 2 NUM iajs-3377 42 5 𝑒 𝑒 ADP iajs-3377 42 6 βˆ’(π‘₯βˆ’Β΅ βˆ’(π‘₯βˆ’Β΅ PROPN iajs-3377 42 7 ) ) PUNCT iajs-3377 42 8 𝑏 𝑏 PROPN iajs-3377 42 9 ifπ‘₯ ifπ‘₯ PROPN iajs-3377 42 10 β‰₯ β‰₯ PROPN iajs-3377 42 11 Β΅ Β΅ X iajs-3377 42 12 ( ( PUNCT iajs-3377 42 13 4 4 NUM iajs-3377 42 14 ) ) PUNCT iajs-3377 42 15 then then ADV iajs-3377 42 16 , , PUNCT iajs-3377 42 17 if if SCONJ iajs-3377 42 18 π‘₯ π‘₯ PRON iajs-3377 42 19 β‰₯ β‰₯ NOUN iajs-3377 42 20 0 0 NUM iajs-3377 42 21 , , PUNCT iajs-3377 42 22 then then ADV iajs-3377 42 23 the the DET iajs-3377 42 24 cdf cdf PROPN iajs-3377 42 25 changes change NOUN iajs-3377 42 26 to to ADP iajs-3377 42 27 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 42 28 ; ; PUNCT iajs-3377 42 29 𝑏 𝑏 X iajs-3377 42 30 ) ) PUNCT iajs-3377 42 31 = = SYM iajs-3377 43 1 1 1 NUM iajs-3377 43 2 βˆ’ βˆ’ NUM iajs-3377 43 3 1 1 NUM iajs-3377 43 4 2 2 NUM iajs-3377 43 5 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 43 6 π‘₯ π‘₯ NOUN iajs-3377 43 7 𝑏 𝑏 NOUN iajs-3377 43 8 ( ( PUNCT iajs-3377 43 9 5 5 NUM iajs-3377 43 10 ) ) PUNCT iajs-3377 43 11 and and CCONJ iajs-3377 43 12 its its PRON iajs-3377 43 13 corresponding correspond VERB iajs-3377 43 14 pdf pdf NOUN iajs-3377 43 15 is be AUX iajs-3377 43 16 given give VERB iajs-3377 43 17 as as ADP iajs-3377 43 18 : : PUNCT iajs-3377 43 19 𝑉(π‘₯ 𝑉(π‘₯ PROPN iajs-3377 43 20 ; ; PUNCT iajs-3377 43 21 𝑏 𝑏 X iajs-3377 43 22 ) ) PUNCT iajs-3377 43 23 = = SYM iajs-3377 43 24 1 1 NUM iajs-3377 43 25 2𝑏 2𝑏 NUM iajs-3377 43 26 𝑒 𝑒 ADP iajs-3377 43 27 βˆ’π‘₯ βˆ’π‘₯ PUNCT iajs-3377 43 28 𝑏 𝑏 NOUN iajs-3377 43 29 ( ( PUNCT iajs-3377 43 30 6 6 NUM iajs-3377 43 31 ) ) PUNCT iajs-3377 43 32 if if SCONJ iajs-3377 43 33 π‘₯ π‘₯ PROPN iajs-3377 43 34 follows follow VERB iajs-3377 43 35 ( ( PUNCT iajs-3377 43 36 6 6 NUM iajs-3377 43 37 ) ) PUNCT iajs-3377 43 38 and and CCONJ iajs-3377 43 39 setting set VERB iajs-3377 43 40 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ NOUN iajs-3377 43 41 , , PUNCT iajs-3377 43 42 πœ‰)]= πœ‰)]= NOUN iajs-3377 43 43 1 1 NUM iajs-3377 43 44 1βˆ’πΉ(π‘₯,πœ‰ 1βˆ’πΉ(π‘₯,πœ‰ NUM iajs-3377 43 45 ) ) PUNCT iajs-3377 43 46 in in ADP iajs-3377 43 47 ( ( PUNCT iajs-3377 43 48 1 1 NUM iajs-3377 43 49 ) ) PUNCT iajs-3377 43 50 , , PUNCT iajs-3377 43 51 we we PRON iajs-3377 43 52 define define VERB iajs-3377 43 53 the the DET iajs-3377 43 54 cdf cdf NOUN iajs-3377 43 55 of of ADP iajs-3377 43 56 the the DET iajs-3377 43 57 double double ADJ iajs-3377 43 58 exponential exponential NOUN iajs-3377 43 59 - - PUNCT iajs-3377 43 60 x x VERB iajs-3377 43 61 family family NOUN iajs-3377 43 62 by by ADP iajs-3377 43 63 g(π‘₯ g(π‘₯ PROPN iajs-3377 43 64 , , PUNCT iajs-3377 43 65 𝑏 𝑏 PROPN iajs-3377 43 66 , , PUNCT iajs-3377 43 67 πœ‰ πœ‰ NOUN iajs-3377 43 68 ) ) PUNCT iajs-3377 43 69 = = SYM iajs-3377 43 70 1 1 NUM iajs-3377 43 71 2 2 NUM iajs-3377 43 72 [ [ PUNCT iajs-3377 43 73 1 1 NUM iajs-3377 43 74 βˆ’ βˆ’ NUM iajs-3377 43 75 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 43 76 1 1 NUM iajs-3377 43 77 𝑏 𝑏 NOUN iajs-3377 43 78 ( ( PUNCT iajs-3377 43 79 π‘Š[𝐹(π‘₯,πœ‰ π‘Š[𝐹(π‘₯,πœ‰ NOUN iajs-3377 43 80 ) ) PUNCT iajs-3377 43 81 ] ] PUNCT iajs-3377 43 82 ) ) PUNCT iajs-3377 43 83 ] ] PUNCT iajs-3377 44 1 = = SYM iajs-3377 44 2 1 1 NUM iajs-3377 44 3 2 2 NUM iajs-3377 44 4 βˆ’ βˆ’ NOUN iajs-3377 44 5 1 1 NUM iajs-3377 44 6 2 2 NUM iajs-3377 44 7 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 44 8 1 1 NUM iajs-3377 44 9 𝑏 𝑏 NOUN iajs-3377 44 10 ( ( PUNCT iajs-3377 44 11 π‘Š[𝐹(π‘₯,πœ‰ π‘Š[𝐹(π‘₯,πœ‰ NOUN iajs-3377 44 12 ) ) PUNCT iajs-3377 44 13 ] ] PUNCT iajs-3377 44 14 ) ) PUNCT iajs-3377 44 15 , , PUNCT iajs-3377 44 16 b b X iajs-3377 44 17 , , PUNCT iajs-3377 44 18 πœ‰ πœ‰ X iajs-3377 44 19 > > X iajs-3377 44 20 0 0 NUM iajs-3377 44 21 , , PUNCT iajs-3377 44 22 π‘₯ π‘₯ PRON iajs-3377 44 23 ∈ ∈ PROPN iajs-3377 44 24 𝑅 𝑅 PROPN iajs-3377 44 25 ( ( PUNCT iajs-3377 44 26 7 7 NUM iajs-3377 44 27 ) ) PUNCT iajs-3377 44 28 where where SCONJ iajs-3377 44 29 the the DET iajs-3377 44 30 baseline baseline ADJ iajs-3377 44 31 distribution distribution NOUN iajs-3377 44 32 's 's PART iajs-3377 44 33 cdf cdf NOUN iajs-3377 44 34 , , PUNCT iajs-3377 44 35 which which PRON iajs-3377 44 36 is be AUX iajs-3377 44 37 dependent dependent ADJ iajs-3377 44 38 on on ADP iajs-3377 44 39 the the DET iajs-3377 44 40 vector vector NOUN iajs-3377 44 41 parameter parameter NOUN iajs-3377 44 42 , , PUNCT iajs-3377 44 43 is be AUX iajs-3377 44 44 denoted denote VERB iajs-3377 44 45 by by ADP iajs-3377 44 46 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 44 47 , , PUNCT iajs-3377 44 48 πœ‰ πœ‰ NOUN iajs-3377 44 49 ) ) PUNCT iajs-3377 44 50 , , PUNCT iajs-3377 44 51 πœ‰ πœ‰ PROPN iajs-3377 44 52 and and CCONJ iajs-3377 44 53 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 44 54 , , PUNCT iajs-3377 44 55 πœ‰)]= πœ‰)]= NOUN iajs-3377 44 56 1 1 NUM iajs-3377 44 57 1βˆ’πΉ(π‘₯,πœ‰ 1βˆ’πΉ(π‘₯,πœ‰ NUM iajs-3377 44 58 ) ) PUNCT iajs-3377 44 59 is be AUX iajs-3377 44 60 a a DET iajs-3377 44 61 special special ADJ iajs-3377 44 62 transformation transformation NOUN iajs-3377 44 63 . . PUNCT iajs-3377 45 1 the the DET iajs-3377 45 2 corresponding correspond VERB iajs-3377 45 3 pdf pdf NOUN iajs-3377 45 4 is be AUX iajs-3377 45 5 obtained obtain VERB iajs-3377 45 6 via via ADP iajs-3377 45 7 the the DET iajs-3377 45 8 first first ADJ iajs-3377 45 9 derivative derivative NOUN iajs-3377 45 10 of of ADP iajs-3377 45 11 the the DET iajs-3377 45 12 cdf cdf NOUN iajs-3377 45 13 , , PUNCT iajs-3377 45 14 g(π‘₯ g(π‘₯ PROPN iajs-3377 45 15 , , PUNCT iajs-3377 45 16 𝑏 𝑏 PROPN iajs-3377 45 17 , , PUNCT iajs-3377 45 18 πœ‰ πœ‰ NOUN iajs-3377 45 19 ) ) PUNCT iajs-3377 45 20 and and CCONJ iajs-3377 45 21 it it PRON iajs-3377 45 22 is be AUX iajs-3377 45 23 shown show VERB iajs-3377 45 24 by by ADP iajs-3377 45 25 : : PUNCT iajs-3377 45 26 𝑔(π‘₯ 𝑔(π‘₯ PROPN iajs-3377 45 27 , , PUNCT iajs-3377 45 28 𝑏 𝑏 NOUN iajs-3377 45 29 , , PUNCT iajs-3377 45 30 πœ‰ πœ‰ NOUN iajs-3377 45 31 ) ) PUNCT iajs-3377 45 32 = = SYM iajs-3377 45 33 1 1 NUM iajs-3377 45 34 2𝑏 2𝑏 NUM iajs-3377 45 35 [ [ PUNCT iajs-3377 45 36 𝑑 𝑑 NOUN iajs-3377 45 37 𝑑π‘₯ 𝑑π‘₯ X iajs-3377 45 38 ( ( PUNCT iajs-3377 45 39 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 45 40 , , PUNCT iajs-3377 45 41 πœ‰ πœ‰ NOUN iajs-3377 45 42 ) ) PUNCT iajs-3377 45 43 ] ] PUNCT iajs-3377 45 44 ) ) PUNCT iajs-3377 45 45 ] ] PUNCT iajs-3377 46 1 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 46 2 { { PUNCT iajs-3377 46 3 1 1 NUM iajs-3377 46 4 𝑏 𝑏 NOUN iajs-3377 46 5 ( ( PUNCT iajs-3377 46 6 π‘Š[𝐹(π‘₯,πœ‰ π‘Š[𝐹(π‘₯,πœ‰ NOUN iajs-3377 46 7 ) ) PUNCT iajs-3377 46 8 ] ] PUNCT iajs-3377 46 9 ) ) PUNCT iajs-3377 46 10 } } PUNCT iajs-3377 46 11 , , PUNCT iajs-3377 46 12 𝑏 𝑏 NOUN iajs-3377 46 13 , , PUNCT iajs-3377 46 14 πœ‰ πœ‰ X iajs-3377 46 15 > > X iajs-3377 46 16 0 0 PUNCT iajs-3377 47 1 ( ( PUNCT iajs-3377 47 2 8) 8) NUM iajs-3377 47 3 𝑔(π‘₯ 𝑔(π‘₯ PROPN iajs-3377 47 4 , , PUNCT iajs-3377 47 5 𝑏 𝑏 NOUN iajs-3377 47 6 , , PUNCT iajs-3377 47 7 πœ‰)= πœ‰)= NOUN iajs-3377 47 8 𝑔(π‘₯ 𝑔(π‘₯ NOUN iajs-3377 47 9 , , PUNCT iajs-3377 47 10 𝑏 𝑏 NOUN iajs-3377 47 11 , , PUNCT iajs-3377 47 12 πœ‰ πœ‰ NOUN iajs-3377 47 13 ) ) PUNCT iajs-3377 47 14 = = SYM iajs-3377 47 15 1 1 NUM iajs-3377 47 16 2𝑏 2𝑏 NUM iajs-3377 47 17 [ [ X iajs-3377 47 18 ( ( PUNCT iajs-3377 47 19 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 47 20 , , PUNCT iajs-3377 47 21 πœ‰)])β€²]π‘’βˆ’ πœ‰)])β€²]π‘’βˆ’ NOUN iajs-3377 47 22 { { PUNCT iajs-3377 47 23 1 1 NUM iajs-3377 47 24 𝑏 𝑏 NOUN iajs-3377 47 25 ( ( PUNCT iajs-3377 47 26 π‘Š[𝐹(π‘₯,πœ‰ π‘Š[𝐹(π‘₯,πœ‰ NOUN iajs-3377 47 27 ) ) PUNCT iajs-3377 47 28 ] ] PUNCT iajs-3377 47 29 ) ) PUNCT iajs-3377 47 30 } } PUNCT iajs-3377 47 31 , , PUNCT iajs-3377 47 32 where where SCONJ iajs-3377 47 33 ( ( PUNCT iajs-3377 47 34 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 47 35 , , PUNCT iajs-3377 47 36 πœ‰)])β€² πœ‰)])β€² NOUN iajs-3377 48 1 = = PUNCT iajs-3377 48 2 𝑑 𝑑 NOUN iajs-3377 48 3 𝑑π‘₯ 𝑑π‘₯ X iajs-3377 48 4 ( ( PUNCT iajs-3377 48 5 π‘Š[𝐹(π‘₯ π‘Š[𝐹(π‘₯ PROPN iajs-3377 48 6 , , PUNCT iajs-3377 48 7 πœ‰ πœ‰ NOUN iajs-3377 48 8 ) ) PUNCT iajs-3377 48 9 ] ] PUNCT iajs-3377 48 10 ) ) PUNCT iajs-3377 48 11 and and CCONJ iajs-3377 48 12 𝑏 𝑏 NOUN iajs-3377 48 13 , , PUNCT iajs-3377 48 14 πœ‰ πœ‰ X iajs-3377 48 15 > > X iajs-3377 48 16 0 0 NUM iajs-3377 48 17 ihjpas ihjpas PROPN iajs-3377 48 18 . . PUNCT iajs-3377 49 1 36 36 NUM iajs-3377 49 2 ( ( PUNCT iajs-3377 49 3 3 3 NUM iajs-3377 49 4 ) ) PUNCT iajs-3377 49 5 2023 2023 NUM iajs-3377 49 6 440 440 NUM iajs-3377 49 7 the the DET iajs-3377 49 8 motivations motivation NOUN iajs-3377 49 9 behind behind ADP iajs-3377 49 10 using use VERB iajs-3377 49 11 de de PROPN iajs-3377 49 12 - - ADJ iajs-3377 49 13 x x ADJ iajs-3377 49 14 family family NOUN iajs-3377 49 15 in in ADP iajs-3377 49 16 the the DET iajs-3377 49 17 real real ADJ iajs-3377 49 18 life life NOUN iajs-3377 49 19 situations situation NOUN iajs-3377 49 20 include include VERB iajs-3377 49 21 : : PUNCT iajs-3377 49 22 ο‚· ο‚· PRON iajs-3377 49 23 it it PRON iajs-3377 49 24 is be AUX iajs-3377 49 25 a a DET iajs-3377 49 26 popular popular ADJ iajs-3377 49 27 technique technique NOUN iajs-3377 49 28 for for ADP iajs-3377 49 29 inserting insert VERB iajs-3377 49 30 extra extra ADJ iajs-3377 49 31 parameter(s parameter(s NOUN iajs-3377 49 32 ) ) PUNCT iajs-3377 49 33 to to PART iajs-3377 49 34 produce produce VERB iajs-3377 49 35 an an DET iajs-3377 49 36 expanded expand VERB iajs-3377 49 37 baseline baseline NOUN iajs-3377 49 38 distribution distribution NOUN iajs-3377 49 39 , , PUNCT iajs-3377 49 40 ο‚· ο‚· PRON iajs-3377 49 41 to to PART iajs-3377 49 42 enhance enhance VERB iajs-3377 49 43 the the DET iajs-3377 49 44 properties property NOUN iajs-3377 49 45 of of ADP iajs-3377 49 46 the the DET iajs-3377 49 47 traditional traditional ADJ iajs-3377 49 48 distributions distribution NOUN iajs-3377 49 49 , , PUNCT iajs-3377 49 50 ο‚· ο‚· PRON iajs-3377 49 51 to to PART iajs-3377 49 52 continuously continuously ADV iajs-3377 49 53 offer offer VERB iajs-3377 49 54 better well ADJ iajs-3377 49 55 fits fit NOUN iajs-3377 49 56 compared compare VERB iajs-3377 49 57 to to ADP iajs-3377 49 58 other other ADJ iajs-3377 49 59 produced produce VERB iajs-3377 49 60 distributions distribution NOUN iajs-3377 49 61 with with ADP iajs-3377 49 62 the the DET iajs-3377 49 63 same same ADJ iajs-3377 49 64 or or CCONJ iajs-3377 49 65 more more ADJ iajs-3377 49 66 parameters parameter NOUN iajs-3377 49 67 , , PUNCT iajs-3377 49 68 2.1 2.1 NUM iajs-3377 49 69 special special ADJ iajs-3377 49 70 sub sub NOUN iajs-3377 49 71 - - NOUN iajs-3377 49 72 models model NOUN iajs-3377 49 73 most most ADV iajs-3377 49 74 often often ADV iajs-3377 49 75 for for ADP iajs-3377 49 76 one one NUM iajs-3377 49 77 reason reason NOUN iajs-3377 49 78 or or CCONJ iajs-3377 49 79 another another PRON iajs-3377 49 80 , , PUNCT iajs-3377 49 81 extended extend VERB iajs-3377 49 82 versions version NOUN iajs-3377 49 83 of of ADP iajs-3377 49 84 distributions distribution NOUN iajs-3377 49 85 are be AUX iajs-3377 49 86 introduced introduce VERB iajs-3377 49 87 for for ADP iajs-3377 49 88 the the DET iajs-3377 49 89 following follow VERB iajs-3377 49 90 reasons reason NOUN iajs-3377 49 91 ; ; PUNCT iajs-3377 50 1 1 1 X iajs-3377 50 2 . . X iajs-3377 50 3 an an DET iajs-3377 50 4 alternate alternate ADJ iajs-3377 50 5 model model NOUN iajs-3377 50 6 to to ADP iajs-3377 50 7 the the DET iajs-3377 50 8 existing exist VERB iajs-3377 50 9 distribution distribution NOUN iajs-3377 50 10 that that PRON iajs-3377 50 11 has have AUX iajs-3377 50 12 been be AUX iajs-3377 50 13 successfully successfully ADV iajs-3377 50 14 applied apply VERB iajs-3377 50 15 in in ADP iajs-3377 50 16 the the DET iajs-3377 50 17 past past ADJ iajs-3377 50 18 2 2 NUM iajs-3377 50 19 . . PUNCT iajs-3377 51 1 a a DET iajs-3377 51 2 flexible flexible ADJ iajs-3377 51 3 statistical statistical ADJ iajs-3377 51 4 model model NOUN iajs-3377 51 5 that that PRON iajs-3377 51 6 provides provide VERB iajs-3377 51 7 a a DET iajs-3377 51 8 good good ADJ iajs-3377 51 9 match match NOUN iajs-3377 51 10 to to ADP iajs-3377 51 11 the the DET iajs-3377 51 12 data datum NOUN iajs-3377 51 13 3 3 NUM iajs-3377 51 14 . . PUNCT iajs-3377 51 15 a a DET iajs-3377 51 16 model model NOUN iajs-3377 51 17 with with ADP iajs-3377 51 18 closed closed ADJ iajs-3377 51 19 cdf cdf PROPN iajs-3377 51 20 , , PUNCT iajs-3377 51 21 survival survival NOUN iajs-3377 51 22 function function NOUN iajs-3377 51 23 ( ( PUNCT iajs-3377 51 24 sf sf PROPN iajs-3377 51 25 ) ) PUNCT iajs-3377 51 26 , , PUNCT iajs-3377 51 27 hazard hazard NOUN iajs-3377 51 28 rate rate NOUN iajs-3377 51 29 function function NOUN iajs-3377 51 30 ( ( PUNCT iajs-3377 51 31 hrf hrf NOUN iajs-3377 51 32 ) ) PUNCT iajs-3377 51 33 forms form NOUN iajs-3377 51 34 and and CCONJ iajs-3377 51 35 a a DET iajs-3377 51 36 strong strong ADJ iajs-3377 51 37 propensity propensity NOUN iajs-3377 51 38 to to PART iajs-3377 51 39 lessen lessen VERB iajs-3377 51 40 estimation estimation NOUN iajs-3377 51 41 challenges challenge NOUN iajs-3377 51 42 . . PUNCT iajs-3377 52 1 thus thus ADV iajs-3377 52 2 , , PUNCT iajs-3377 52 3 we we PRON iajs-3377 52 4 introduce introduce VERB iajs-3377 52 5 two two NUM iajs-3377 52 6 unique unique ADJ iajs-3377 52 7 sub sub NOUN iajs-3377 52 8 - - NOUN iajs-3377 52 9 models model NOUN iajs-3377 52 10 of of ADP iajs-3377 52 11 the the DET iajs-3377 52 12 de de PROPN iajs-3377 52 13 - - PROPN iajs-3377 52 14 x x ADJ iajs-3377 52 15 family family NOUN iajs-3377 52 16 that that PRON iajs-3377 52 17 have have VERB iajs-3377 52 18 at at ADV iajs-3377 52 19 least least ADJ iajs-3377 52 20 one one NUM iajs-3377 52 21 of of ADP iajs-3377 52 22 the the DET iajs-3377 52 23 aforementioned aforementioned ADJ iajs-3377 52 24 characteristics characteristic NOUN iajs-3377 52 25 . . PUNCT iajs-3377 53 1 2.1.1 2.1.1 NUM iajs-3377 53 2 the the DET iajs-3377 53 3 de de ADJ iajs-3377 53 4 - - NOUN iajs-3377 53 5 pareto pareto ADJ iajs-3377 53 6 ( ( PUNCT iajs-3377 53 7 de de NOUN iajs-3377 53 8 - - ADJ iajs-3377 53 9 p p ADJ iajs-3377 53 10 ) ) PUNCT iajs-3377 53 11 distribution distribution NOUN iajs-3377 53 12 the the DET iajs-3377 53 13 pdf pdf NOUN iajs-3377 53 14 and and CCONJ iajs-3377 53 15 the the DET iajs-3377 53 16 cdf cdf PROPN iajs-3377 53 17 of of ADP iajs-3377 53 18 the the DET iajs-3377 53 19 pareto pareto ADJ iajs-3377 53 20 random random ADJ iajs-3377 53 21 variable variable NOUN iajs-3377 53 22 are be AUX iajs-3377 53 23 f(π‘₯ f(π‘₯ NOUN iajs-3377 53 24 , , PUNCT iajs-3377 53 25 ⍬ ⍬ VERB iajs-3377 53 26 , , PUNCT iajs-3377 53 27 𝛼 𝛼 NOUN iajs-3377 53 28 ) ) PUNCT iajs-3377 53 29 = = PUNCT iajs-3377 54 1 𝛼(𝛼 𝛼(𝛼 PROPN iajs-3377 54 2 ⍬ ⍬ PROPN iajs-3377 54 3 ) ) PUNCT iajs-3377 55 1 π‘₯ π‘₯ NOUN iajs-3377 55 2 ⍬ ⍬ VERB iajs-3377 55 3 +1 +1 ADJ iajs-3377 55 4 and and CCONJ iajs-3377 55 5 f(π‘₯ f(π‘₯ NOUN iajs-3377 55 6 , , PUNCT iajs-3377 55 7 𝛼 𝛼 X iajs-3377 55 8 , , PUNCT iajs-3377 55 9 πœƒ πœƒ NOUN iajs-3377 55 10 ) ) PUNCT iajs-3377 55 11 = = SYM iajs-3377 55 12 1 1 NUM iajs-3377 55 13 βˆ’ βˆ’ PROPN iajs-3377 55 14 ( ( PUNCT iajs-3377 55 15 𝛼 𝛼 NOUN iajs-3377 55 16 π‘₯ π‘₯ NOUN iajs-3377 55 17 ) ) PUNCT iajs-3377 55 18 ⍬ ⍬ INTJ iajs-3377 55 19 , , PUNCT iajs-3377 55 20 π‘₯>0 π‘₯>0 PROPN iajs-3377 55 21 , , PUNCT iajs-3377 55 22 𝛼 𝛼 NOUN iajs-3377 55 23 , , PUNCT iajs-3377 55 24 πœƒ>0 πœƒ>0 NOUN iajs-3377 55 25 , , PUNCT iajs-3377 55 26 . . PUNCT iajs-3377 56 1 then then ADV iajs-3377 56 2 the the DET iajs-3377 56 3 cdf cdf PROPN iajs-3377 56 4 and and CCONJ iajs-3377 56 5 the the DET iajs-3377 56 6 pdf pdf NOUN iajs-3377 56 7 of of ADP iajs-3377 56 8 the the DET iajs-3377 56 9 de de PROPN iajs-3377 56 10 - - ADJ iajs-3377 56 11 p p ADJ iajs-3377 56 12 model model NOUN iajs-3377 56 13 are be AUX iajs-3377 56 14 given give VERB iajs-3377 56 15 by by ADP iajs-3377 56 16 ( ( PUNCT iajs-3377 56 17 9 9 NUM iajs-3377 56 18 ) ) PUNCT iajs-3377 56 19 and and CCONJ iajs-3377 56 20 ( ( PUNCT iajs-3377 56 21 11 11 NUM iajs-3377 56 22 ) ) PUNCT iajs-3377 56 23 respectively respectively ADV iajs-3377 56 24 . . PUNCT iajs-3377 57 1 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-3377 57 2 , , PUNCT iajs-3377 57 3 𝑏 𝑏 NOUN iajs-3377 57 4 , , PUNCT iajs-3377 57 5 𝛼 𝛼 PROPN iajs-3377 57 6 , , PUNCT iajs-3377 57 7 πœƒ πœƒ NOUN iajs-3377 57 8 ) ) PUNCT iajs-3377 57 9 = = SYM iajs-3377 57 10 1 1 NUM iajs-3377 57 11 2 2 NUM iajs-3377 57 12 βˆ’ βˆ’ NOUN iajs-3377 57 13 1 1 NUM iajs-3377 57 14 2 2 NUM iajs-3377 57 15 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 57 16 1 1 NUM iajs-3377 57 17 𝑏 𝑏 NOUN iajs-3377 57 18 ( ( PUNCT iajs-3377 57 19 π‘₯ π‘₯ X iajs-3377 57 20 𝛼 𝛼 X iajs-3377 57 21 ) ) PUNCT iajs-3377 57 22 πœƒ πœƒ NOUN iajs-3377 57 23 , , PUNCT iajs-3377 57 24 b b X iajs-3377 57 25 , , PUNCT iajs-3377 57 26 πœƒ πœƒ PROPN iajs-3377 57 27 , , PUNCT iajs-3377 57 28 𝛼>0 𝛼>0 NOUN iajs-3377 57 29 ( ( PUNCT iajs-3377 57 30 9 9 NUM iajs-3377 57 31 ) ) PUNCT iajs-3377 57 32 hence hence ADV iajs-3377 57 33 , , PUNCT iajs-3377 57 34 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-3377 57 35 , , PUNCT iajs-3377 57 36 𝑏 𝑏 NOUN iajs-3377 57 37 , , PUNCT iajs-3377 57 38 𝛼 𝛼 PROPN iajs-3377 57 39 , , PUNCT iajs-3377 57 40 πœƒ πœƒ NOUN iajs-3377 57 41 ) ) PUNCT iajs-3377 57 42 = = SYM iajs-3377 57 43 1 1 NUM iajs-3377 57 44 2 2 NUM iajs-3377 57 45 ( ( PUNCT iajs-3377 57 46 1 1 NUM iajs-3377 57 47 βˆ’ βˆ’ NOUN iajs-3377 57 48 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 57 49 1 1 NUM iajs-3377 57 50 𝑏 𝑏 NOUN iajs-3377 57 51 ( ( PUNCT iajs-3377 57 52 π‘₯ π‘₯ X iajs-3377 57 53 𝛼 𝛼 X iajs-3377 57 54 ) ) PUNCT iajs-3377 57 55 πœƒ πœƒ NOUN iajs-3377 57 56 ) ) PUNCT iajs-3377 57 57 b b NOUN iajs-3377 57 58 , , PUNCT iajs-3377 57 59 πœƒ πœƒ PROPN iajs-3377 57 60 , , PUNCT iajs-3377 57 61 𝛼 𝛼 ADJ iajs-3377 57 62 > > X iajs-3377 57 63 0(10 0(10 NUM iajs-3377 57 64 ) ) PUNCT iajs-3377 57 65 ( ( PUNCT iajs-3377 57 66 10 10 NUM iajs-3377 57 67 ) ) PUNCT iajs-3377 57 68 hence,𝑔(π‘₯ hence,𝑔(π‘₯ PROPN iajs-3377 57 69 , , PUNCT iajs-3377 57 70 𝑏 𝑏 NOUN iajs-3377 57 71 , , PUNCT iajs-3377 57 72 𝛼 𝛼 PROPN iajs-3377 57 73 , , PUNCT iajs-3377 57 74 πœƒ)= πœƒ)= VERB iajs-3377 57 75 ⍬ ⍬ PROPN iajs-3377 57 76 2𝛼𝑏 2𝛼𝑏 NOUN iajs-3377 57 77 ( ( PUNCT iajs-3377 57 78 π‘₯ π‘₯ X iajs-3377 57 79 𝛼 𝛼 X iajs-3377 57 80 ) ) PUNCT iajs-3377 57 81 ⍬ ⍬ VERB iajs-3377 57 82 βˆ’1 βˆ’1 NOUN iajs-3377 57 83 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 57 84 1 1 NUM iajs-3377 57 85 𝑏 𝑏 NOUN iajs-3377 57 86 ( ( PUNCT iajs-3377 57 87 π‘₯ π‘₯ X iajs-3377 57 88 𝛼 𝛼 X iajs-3377 57 89 ) ) PUNCT iajs-3377 57 90 ⍬ ⍬ INTJ iajs-3377 57 91 , , PUNCT iajs-3377 57 92 π‘₯ π‘₯ PRON iajs-3377 57 93 , , PUNCT iajs-3377 57 94 b,πœƒ b,πœƒ NOUN iajs-3377 57 95 , , PUNCT iajs-3377 57 96 Ξ± Ξ± NOUN iajs-3377 57 97 > > X iajs-3377 57 98 0 0 PUNCT iajs-3377 58 1 ( ( PUNCT iajs-3377 58 2 11 11 NUM iajs-3377 58 3 ) ) PUNCT iajs-3377 58 4 plots plot NOUN iajs-3377 58 5 of of ADP iajs-3377 58 6 the the DET iajs-3377 58 7 de de PROPN iajs-3377 58 8 - - ADJ iajs-3377 58 9 p p ADJ iajs-3377 58 10 density density NOUN iajs-3377 58 11 and and CCONJ iajs-3377 58 12 hazard hazard NOUN iajs-3377 58 13 rate rate NOUN iajs-3377 58 14 function function NOUN iajs-3377 58 15 for for ADP iajs-3377 58 16 selected select VERB iajs-3377 58 17 parameter parameter NOUN iajs-3377 58 18 values value NOUN iajs-3377 58 19 are be AUX iajs-3377 58 20 presented present VERB iajs-3377 58 21 in in ADP iajs-3377 58 22 fig.1 fig.1 PROPN iajs-3377 58 23 and and CCONJ iajs-3377 58 24 fig.2 fig.2 PROPN iajs-3377 58 25 respectively respectively ADV iajs-3377 58 26 below below ADV iajs-3377 58 27 : : PUNCT iajs-3377 58 28 figure.1 figure.1 PROPN iajs-3377 58 29 : : PUNCT iajs-3377 58 30 pdf pdf NOUN iajs-3377 58 31 plot plot NOUN iajs-3377 58 32 at at ADP iajs-3377 58 33 fixed fix VERB iajs-3377 58 34 b b NOUN iajs-3377 58 35 = = NOUN iajs-3377 58 36 1 1 NUM iajs-3377 58 37 and and CCONJ iajs-3377 58 38 increasing increase VERB iajs-3377 58 39 𝛼 𝛼 NOUN iajs-3377 58 40 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ NOUN iajs-3377 58 41 πœƒ πœƒ NOUN iajs-3377 58 42 ihjpas ihjpa VERB iajs-3377 58 43 . . PUNCT iajs-3377 59 1 36 36 NUM iajs-3377 59 2 ( ( PUNCT iajs-3377 59 3 3 3 NUM iajs-3377 59 4 ) ) PUNCT iajs-3377 59 5 2023 2023 NUM iajs-3377 59 6 441 441 NUM iajs-3377 59 7 figure.2 figure.2 ADJ iajs-3377 59 8 : : PUNCT iajs-3377 59 9 hazard hazard NOUN iajs-3377 59 10 plot plot NOUN iajs-3377 59 11 at at ADP iajs-3377 59 12 fixed fix VERB iajs-3377 59 13 b b NOUN iajs-3377 59 14 = = NOUN iajs-3377 59 15 1 1 NUM iajs-3377 59 16 and and CCONJ iajs-3377 59 17 increasing increase VERB iajs-3377 59 18 𝛼 𝛼 PRON iajs-3377 59 19 π‘Žπ‘›π‘‘ π‘Žπ‘›π‘‘ NOUN iajs-3377 59 20 πœƒ πœƒ NUM iajs-3377 59 21 2.1.2 2.1.2 NUM iajs-3377 59 22 the the DET iajs-3377 59 23 de de ADJ iajs-3377 59 24 - - NOUN iajs-3377 59 25 paretoii paretoii ADJ iajs-3377 59 26 ( ( PUNCT iajs-3377 59 27 de de NOUN iajs-3377 59 28 - - NOUN iajs-3377 59 29 p2 p2 NOUN iajs-3377 59 30 ) ) PUNCT iajs-3377 59 31 given give VERB iajs-3377 59 32 the the DET iajs-3377 59 33 pdf pdf NOUN iajs-3377 59 34 and and CCONJ iajs-3377 59 35 cdf cdf PROPN iajs-3377 59 36 of of ADP iajs-3377 59 37 the the DET iajs-3377 59 38 pareto pareto NOUN iajs-3377 59 39 type-2 type-2 NUM iajs-3377 59 40 distribution𝑓(π‘₯ distribution𝑓(π‘₯ PROPN iajs-3377 59 41 , , PUNCT iajs-3377 59 42 π‘Ž π‘Ž NOUN iajs-3377 59 43 , , PUNCT iajs-3377 59 44 𝑏 𝑏 NOUN iajs-3377 59 45 ) ) PUNCT iajs-3377 60 1 = = SYM iajs-3377 61 1 𝑏 𝑏 SYM iajs-3377 61 2 π‘Ž π‘Ž X iajs-3377 61 3 ( ( PUNCT iajs-3377 61 4 π‘Ž π‘Ž PROPN iajs-3377 61 5 π‘₯βˆ’π‘Ž π‘₯βˆ’π‘Ž PROPN iajs-3377 61 6 ) ) PUNCT iajs-3377 61 7 𝑏+1 𝑏+1 PROPN iajs-3377 61 8 , , PUNCT iajs-3377 61 9 b b PROPN iajs-3377 61 10 , , PUNCT iajs-3377 61 11 a a PRON iajs-3377 61 12 , , PUNCT iajs-3377 61 13 π‘₯ π‘₯ PROPN iajs-3377 61 14 > > X iajs-3377 61 15 0 0 PUNCT iajs-3377 61 16 and and CCONJ iajs-3377 61 17 𝐹(π‘₯ 𝐹(π‘₯ NUM iajs-3377 61 18 ; ; PUNCT iajs-3377 61 19 π‘Ž π‘Ž X iajs-3377 61 20 , , PUNCT iajs-3377 61 21 𝑏 𝑏 NOUN iajs-3377 61 22 ) ) PUNCT iajs-3377 61 23 = = SYM iajs-3377 61 24 1 1 NUM iajs-3377 61 25 βˆ’ βˆ’ NOUN iajs-3377 61 26 ( ( PUNCT iajs-3377 61 27 π‘Ž π‘Ž PROPN iajs-3377 61 28 π‘₯βˆ’π‘Ž π‘₯βˆ’π‘Ž PROPN iajs-3377 61 29 ) ) PUNCT iajs-3377 61 30 𝑏 𝑏 NOUN iajs-3377 61 31 , , PUNCT iajs-3377 61 32 x x X iajs-3377 61 33 , , PUNCT iajs-3377 61 34 b b PROPN iajs-3377 61 35 , , PUNCT iajs-3377 61 36 a a PRON iajs-3377 61 37 , , PUNCT iajs-3377 61 38 > > X iajs-3377 61 39 0 0 X iajs-3377 61 40 . . PUNCT iajs-3377 62 1 then then ADV iajs-3377 62 2 the the DET iajs-3377 62 3 cdf cdf PROPN iajs-3377 62 4 and and CCONJ iajs-3377 62 5 pdf pdf NOUN iajs-3377 62 6 of of ADP iajs-3377 62 7 de de PROPN iajs-3377 62 8 - - NOUN iajs-3377 62 9 pii pii PROPN iajs-3377 62 10 model model NOUN iajs-3377 62 11 are be AUX iajs-3377 62 12 given give VERB iajs-3377 62 13 as as ADP iajs-3377 62 14 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-3377 62 15 , , PUNCT iajs-3377 62 16 𝑏 𝑏 NOUN iajs-3377 62 17 , , PUNCT iajs-3377 62 18 π‘Ž π‘Ž NOUN iajs-3377 62 19 , , PUNCT iajs-3377 62 20 πœ‰ πœ‰ NOUN iajs-3377 62 21 ) ) PUNCT iajs-3377 62 22 = = SYM iajs-3377 62 23 1 1 NUM iajs-3377 62 24 2 2 NUM iajs-3377 63 1 [ [ PUNCT iajs-3377 63 2 1 1 NUM iajs-3377 63 3 βˆ’ βˆ’ NUM iajs-3377 63 4 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 63 5 1 1 NUM iajs-3377 63 6 𝑏 𝑏 NOUN iajs-3377 63 7 ( ( PUNCT iajs-3377 63 8 π‘₯βˆ’π‘Ž π‘₯βˆ’π‘Ž PROPN iajs-3377 63 9 π‘Ž π‘Ž X iajs-3377 63 10 ) ) PUNCT iajs-3377 63 11 πœƒ πœƒ NOUN iajs-3377 63 12 ] ] X iajs-3377 63 13 , , PUNCT iajs-3377 63 14 a a PRON iajs-3377 63 15 , , PUNCT iajs-3377 63 16 b,πœƒ b,πœƒ NOUN iajs-3377 63 17 > > X iajs-3377 63 18 0 0 NUM iajs-3377 63 19 ; ; PUNCT iajs-3377 63 20 π‘₯ π‘₯ X iajs-3377 63 21 > > X iajs-3377 63 22 0 0 NUM iajs-3377 63 23 0 0 NUM iajs-3377 63 24 ( ( PUNCT iajs-3377 63 25 12 12 NUM iajs-3377 63 26 ) ) PUNCT iajs-3377 63 27 for for ADP iajs-3377 63 28 the the DET iajs-3377 63 29 pdf pdf NOUN iajs-3377 63 30 , , PUNCT iajs-3377 63 31 𝑔(π‘₯ 𝑔(π‘₯ PROPN iajs-3377 63 32 , , PUNCT iajs-3377 63 33 a a DET iajs-3377 63 34 , , PUNCT iajs-3377 63 35 b b NOUN iajs-3377 63 36 , , PUNCT iajs-3377 63 37 πœ‰ πœ‰ NOUN iajs-3377 63 38 ) ) PUNCT iajs-3377 63 39 = = PUNCT iajs-3377 64 1 πœƒ πœƒ NUM iajs-3377 64 2 2π‘π‘Ž 2π‘π‘Ž NOUN iajs-3377 64 3 ( ( PUNCT iajs-3377 64 4 π‘₯βˆ’π‘Ž π‘₯βˆ’π‘Ž PROPN iajs-3377 64 5 π‘Ž π‘Ž X iajs-3377 64 6 ) ) PUNCT iajs-3377 64 7 πœƒβˆ’1 πœƒβˆ’1 PROPN iajs-3377 64 8 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 64 9 1 1 NUM iajs-3377 64 10 𝑏 𝑏 NOUN iajs-3377 64 11 ( ( PUNCT iajs-3377 64 12 π‘₯βˆ’π‘Ž π‘₯βˆ’π‘Ž PROPN iajs-3377 64 13 π‘Ž π‘Ž X iajs-3377 64 14 ) ) PUNCT iajs-3377 64 15 πœƒ πœƒ NOUN iajs-3377 64 16 , , PUNCT iajs-3377 64 17 a a DET iajs-3377 64 18 , , PUNCT iajs-3377 64 19 b b NOUN iajs-3377 64 20 , , PUNCT iajs-3377 64 21 πœƒ πœƒ X iajs-3377 64 22 > > X iajs-3377 64 23 0 0 NUM iajs-3377 64 24 ; ; PUNCT iajs-3377 64 25 π‘₯ π‘₯ PROPN iajs-3377 64 26 > > X iajs-3377 64 27 0 0 PUNCT iajs-3377 65 1 ( ( PUNCT iajs-3377 65 2 13 13 NUM iajs-3377 65 3 ) ) PUNCT iajs-3377 65 4 fig.3 fig.3 PROPN iajs-3377 65 5 and and CCONJ iajs-3377 65 6 fig.4 fig.4 PROPN iajs-3377 65 7 give give VERB iajs-3377 65 8 the the DET iajs-3377 65 9 plots plot NOUN iajs-3377 65 10 of of ADP iajs-3377 65 11 the the DET iajs-3377 65 12 pdf pdf NOUN iajs-3377 65 13 and and CCONJ iajs-3377 65 14 hrf hrf PROPN iajs-3377 65 15 of of ADP iajs-3377 65 16 de de PROPN iajs-3377 65 17 - - NOUN iajs-3377 65 18 pii pii NOUN iajs-3377 65 19 distribution distribution NOUN iajs-3377 65 20 for for ADP iajs-3377 65 21 selected select VERB iajs-3377 65 22 parameter parameter NOUN iajs-3377 65 23 values value NOUN iajs-3377 65 24 . . PUNCT iajs-3377 66 1 figure.3 figure.3 PROPN iajs-3377 66 2 the the DET iajs-3377 66 3 pdf pdf NOUN iajs-3377 66 4 of of ADP iajs-3377 66 5 double double ADJ iajs-3377 66 6 exponential exponential ADJ iajs-3377 66 7 - - PUNCT iajs-3377 66 8 paretoii paretoii NOUN iajs-3377 66 9 distribution distribution NOUN iajs-3377 66 10 at at ADP iajs-3377 66 11 different different ADJ iajs-3377 66 12 values value NOUN iajs-3377 66 13 of of ADP iajs-3377 66 14 parameters parameter NOUN iajs-3377 66 15 ihjpas ihjpa VERB iajs-3377 66 16 . . PUNCT iajs-3377 67 1 36 36 NUM iajs-3377 67 2 ( ( PUNCT iajs-3377 67 3 3 3 NUM iajs-3377 67 4 ) ) PUNCT iajs-3377 67 5 2023 2023 NUM iajs-3377 67 6 442 442 NUM iajs-3377 67 7 figure.4 figure.4 NOUN iajs-3377 67 8 showing show VERB iajs-3377 67 9 the the DET iajs-3377 67 10 hazard hazard NOUN iajs-3377 67 11 of of ADP iajs-3377 67 12 double double ADJ iajs-3377 67 13 exponential exponential ADJ iajs-3377 67 14 - - PUNCT iajs-3377 67 15 paretoii paretoii NOUN iajs-3377 67 16 distribution distribution NOUN iajs-3377 67 17 at at ADP iajs-3377 67 18 different different ADJ iajs-3377 67 19 values value NOUN iajs-3377 67 20 of of ADP iajs-3377 67 21 parameters parameter NOUN iajs-3377 67 22 2.2 2.2 NUM iajs-3377 67 23 basic basic ADJ iajs-3377 67 24 mathematical mathematical ADJ iajs-3377 67 25 properties property NOUN iajs-3377 67 26 of of ADP iajs-3377 67 27 de de NOUN iajs-3377 67 28 - - NOUN iajs-3377 67 29 pareto pareto NOUN iajs-3377 67 30 here here ADV iajs-3377 67 31 , , PUNCT iajs-3377 67 32 we we PRON iajs-3377 67 33 provide provide VERB iajs-3377 67 34 the the DET iajs-3377 67 35 basic basic ADJ iajs-3377 67 36 properties property NOUN iajs-3377 67 37 of of ADP iajs-3377 67 38 de de NOUN iajs-3377 67 39 - - ADJ iajs-3377 67 40 x x ADJ iajs-3377 67 41 family family NOUN iajs-3377 67 42 of of ADP iajs-3377 67 43 distributions distribution NOUN iajs-3377 67 44 . . PUNCT iajs-3377 68 1 2.2.1 2.2.1 NUM iajs-3377 68 2 moments moment NOUN iajs-3377 68 3 of of ADP iajs-3377 68 4 de de ADJ iajs-3377 68 5 - - NOUN iajs-3377 68 6 pareto pareto ADJ iajs-3377 68 7 assuming assume VERB iajs-3377 68 8 x x PRON iajs-3377 68 9 follows follow VERB iajs-3377 68 10 de de PROPN iajs-3377 68 11 - - ADJ iajs-3377 68 12 x x ADJ iajs-3377 68 13 family family NOUN iajs-3377 68 14 with with ADP iajs-3377 68 15 density density NOUN iajs-3377 68 16 𝑔(π‘₯ 𝑔(π‘₯ PROPN iajs-3377 68 17 , , PUNCT iajs-3377 68 18 a a DET iajs-3377 68 19 , , PUNCT iajs-3377 68 20 b b NOUN iajs-3377 68 21 , , PUNCT iajs-3377 68 22 πœ‰ πœ‰ NOUN iajs-3377 68 23 ) ) PUNCT iajs-3377 68 24 , , PUNCT iajs-3377 68 25 then then ADV iajs-3377 68 26 its its PRON iajs-3377 68 27 π‘Ÿπ‘‘β„Ž π‘Ÿπ‘‘β„Ž NOUN iajs-3377 68 28 moment moment NOUN iajs-3377 68 29 is be AUX iajs-3377 68 30 Β΅r Β΅r ADP iajs-3377 68 31 1=∫ 1=∫ NUM iajs-3377 68 32 xr∞ xr∞ PROPN iajs-3377 68 33 βˆ’βˆž βˆ’βˆž ADP iajs-3377 68 34 g(x g(x PROPN iajs-3377 68 35 , , PUNCT iajs-3377 68 36 a a PRON iajs-3377 68 37 , , PUNCT iajs-3377 68 38 b b NOUN iajs-3377 68 39 , , PUNCT iajs-3377 68 40 ΞΎ)dx ΞΎ)dx PROPN iajs-3377 68 41 e(xr e(xr X iajs-3377 68 42 ) ) PUNCT iajs-3377 68 43 = = SYM iajs-3377 69 1 ∫ ∫ PROPN iajs-3377 69 2 xr∞ xr∞ PROPN iajs-3377 69 3 0 0 NUM iajs-3377 69 4 ⍬ ⍬ PROPN iajs-3377 69 5 2Ξ±b 2Ξ±b ADJ iajs-3377 69 6 ( ( PUNCT iajs-3377 69 7 x x SYM iajs-3377 69 8 Ξ± Ξ± NOUN iajs-3377 69 9 ) ) PUNCT iajs-3377 69 10 ⍬ ⍬ VERB iajs-3377 69 11 βˆ’1 βˆ’1 NOUN iajs-3377 69 12 eβˆ’ eβˆ’ PROPN iajs-3377 69 13 1 1 NUM iajs-3377 69 14 b b X iajs-3377 69 15 ( ( PUNCT iajs-3377 69 16 x x NOUN iajs-3377 69 17 Ξ± Ξ± NOUN iajs-3377 69 18 ) ) PUNCT iajs-3377 70 1 ⍬ ⍬ PROPN iajs-3377 70 2 dx dx PROPN iajs-3377 70 3 ( ( PUNCT iajs-3377 70 4 14 14 NUM iajs-3377 70 5 ) ) PUNCT iajs-3377 70 6 e(xr e(xr PROPN iajs-3377 70 7 ) ) PUNCT iajs-3377 70 8 = = SYM iajs-3377 70 9 1 1 NUM iajs-3377 70 10 2 2 NUM iajs-3377 70 11 ( ( PUNCT iajs-3377 70 12 Ξ± Ξ± NOUN iajs-3377 70 13 √b √b ADJ iajs-3377 70 14 ΞΈ ΞΈ NOUN iajs-3377 70 15 ) ) PUNCT iajs-3377 70 16 r r NOUN iajs-3377 70 17 β”Œ β”Œ PROPN iajs-3377 70 18 ( ( PUNCT iajs-3377 70 19 r r NOUN iajs-3377 70 20 ΞΈ ΞΈ PROPN iajs-3377 70 21 + + NOUN iajs-3377 70 22 1 1 NUM iajs-3377 70 23 ) ) PUNCT iajs-3377 70 24 e(x)= e(x)= VERB iajs-3377 71 1 Ξ± Ξ± PRON iajs-3377 71 2 √b √b ADJ iajs-3377 71 3 ΞΈ ΞΈ PROPN iajs-3377 71 4 2 2 NUM iajs-3377 71 5 β”Œ β”Œ PROPN iajs-3377 71 6 ( ( PUNCT iajs-3377 71 7 1 1 NUM iajs-3377 71 8 ΞΈ ΞΈ NOUN iajs-3377 71 9 + + NOUN iajs-3377 71 10 1 1 NUM iajs-3377 71 11 ) ) PUNCT iajs-3377 71 12 ; ; PUNCT iajs-3377 71 13 r r NOUN iajs-3377 71 14 = = SYM iajs-3377 71 15 1 1 NUM iajs-3377 71 16 ( ( PUNCT iajs-3377 71 17 15 15 NUM iajs-3377 71 18 ) ) PUNCT iajs-3377 71 19 variance variance NOUN iajs-3377 71 20 : : PUNCT iajs-3377 71 21 var(x)= var(x)= DET iajs-3377 71 22 ( ( PUNCT iajs-3377 71 23 Ξ± Ξ± PROPN iajs-3377 71 24 √b √b ADJ iajs-3377 71 25 ΞΈ ΞΈ NOUN iajs-3377 71 26 ) ) PUNCT iajs-3377 71 27 2 2 NUM iajs-3377 71 28 [ [ PUNCT iajs-3377 71 29 1 1 NUM iajs-3377 71 30 2 2 NUM iajs-3377 71 31 β”Œ β”Œ PROPN iajs-3377 71 32 ( ( PUNCT iajs-3377 71 33 2 2 NUM iajs-3377 71 34 ΞΈ ΞΈ NOUN iajs-3377 71 35 + + NOUN iajs-3377 71 36 1 1 X iajs-3377 71 37 ) ) PUNCT iajs-3377 71 38 βˆ’ βˆ’ PROPN iajs-3377 71 39 ( ( PUNCT iajs-3377 71 40 1 1 NUM iajs-3377 71 41 2 2 NUM iajs-3377 71 42 β”Œ β”Œ PROPN iajs-3377 71 43 ( ( PUNCT iajs-3377 71 44 1 1 NUM iajs-3377 71 45 ΞΈ ΞΈ NOUN iajs-3377 71 46 + + NOUN iajs-3377 71 47 1 1 NUM iajs-3377 71 48 ) ) PUNCT iajs-3377 71 49 ) ) PUNCT iajs-3377 71 50 2 2 NUM iajs-3377 71 51 ] ] PUNCT iajs-3377 71 52 ( ( PUNCT iajs-3377 71 53 16 16 NUM iajs-3377 71 54 ) ) PUNCT iajs-3377 71 55 2.2.2 2.2.2 NUM iajs-3377 71 56 survival survival NOUN iajs-3377 71 57 function function NOUN iajs-3377 71 58 of of ADP iajs-3377 71 59 de de ADJ iajs-3377 71 60 - - ADJ iajs-3377 71 61 pareto pareto ADJ iajs-3377 71 62 the the DET iajs-3377 71 63 survival survival NOUN iajs-3377 71 64 function function NOUN iajs-3377 71 65 of of ADP iajs-3377 71 66 de de PROPN iajs-3377 71 67 - - ADJ iajs-3377 71 68 x x ADJ iajs-3377 71 69 family family NOUN iajs-3377 71 70 is be AUX iajs-3377 71 71 given give VERB iajs-3377 71 72 as as ADP iajs-3377 71 73 𝑆(π‘₯ 𝑆(π‘₯ NOUN iajs-3377 71 74 ) ) PUNCT iajs-3377 71 75 = = SYM iajs-3377 71 76 1 1 NUM iajs-3377 71 77 βˆ’ βˆ’ NOUN iajs-3377 71 78 𝐺(π‘₯ 𝐺(π‘₯ NOUN iajs-3377 71 79 , , PUNCT iajs-3377 71 80 𝑏 𝑏 NOUN iajs-3377 71 81 , , PUNCT iajs-3377 71 82 𝛼 𝛼 PROPN iajs-3377 71 83 , , PUNCT iajs-3377 71 84 πœƒ πœƒ NOUN iajs-3377 71 85 ) ) PUNCT iajs-3377 71 86 ( ( PUNCT iajs-3377 71 87 17 17 NUM iajs-3377 71 88 ) ) PUNCT iajs-3377 71 89 𝑆(π‘₯ 𝑆(π‘₯ NUM iajs-3377 71 90 ) ) PUNCT iajs-3377 71 91 = = SYM iajs-3377 71 92 1 1 NUM iajs-3377 71 93 2 2 NUM iajs-3377 71 94 ( ( PUNCT iajs-3377 71 95 1 1 NUM iajs-3377 71 96 + + NUM iajs-3377 71 97 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 71 98 1 1 NUM iajs-3377 71 99 𝑏 𝑏 NOUN iajs-3377 71 100 ( ( PUNCT iajs-3377 71 101 π‘₯ π‘₯ X iajs-3377 71 102 𝛼 𝛼 X iajs-3377 71 103 ) ) PUNCT iajs-3377 71 104 πœƒ πœƒ NOUN iajs-3377 71 105 ) ) PUNCT iajs-3377 71 106 ( ( PUNCT iajs-3377 71 107 18 18 NUM iajs-3377 71 108 ) ) PUNCT iajs-3377 71 109 2.2.3 2.2.3 NUM iajs-3377 71 110 probability probability NOUN iajs-3377 71 111 weighted weight VERB iajs-3377 71 112 moments moment NOUN iajs-3377 71 113 of of ADP iajs-3377 71 114 de de ADJ iajs-3377 71 115 - - NOUN iajs-3377 71 116 pareto pareto ADJ iajs-3377 71 117 the the DET iajs-3377 71 118 probability probability NOUN iajs-3377 71 119 weighted weight VERB iajs-3377 71 120 moment moment NOUN iajs-3377 71 121 ( ( PUNCT iajs-3377 71 122 pwm pwm NOUN iajs-3377 71 123 ) ) PUNCT iajs-3377 71 124 of of ADP iajs-3377 71 125 de de NOUN iajs-3377 71 126 - - ADJ iajs-3377 71 127 x x ADJ iajs-3377 71 128 random random ADJ iajs-3377 71 129 variable variable NOUN iajs-3377 71 130 is be AUX iajs-3377 71 131 π‘€π‘Ÿπ‘ (π‘₯ π‘€π‘Ÿπ‘ (π‘₯ ADJ iajs-3377 71 132 ) ) PUNCT iajs-3377 72 1 = = SYM iajs-3377 72 2 ∫ ∫ PROPN iajs-3377 72 3 π‘₯π‘ βˆž π‘₯π‘ βˆž PROPN iajs-3377 72 4 βˆ’βˆž βˆ’βˆž ADP iajs-3377 72 5 𝑔(π‘₯ 𝑔(π‘₯ PROPN iajs-3377 72 6 , , PUNCT iajs-3377 72 7 𝑏 𝑏 NOUN iajs-3377 72 8 , , PUNCT iajs-3377 72 9 π‘Ž π‘Ž NOUN iajs-3377 72 10 , , PUNCT iajs-3377 72 11 πœ‰)𝐺(π‘₯ πœ‰)𝐺(π‘₯ PROPN iajs-3377 72 12 , , PUNCT iajs-3377 72 13 𝑏 𝑏 PROPN iajs-3377 72 14 , , PUNCT iajs-3377 72 15 π‘Ž π‘Ž NOUN iajs-3377 72 16 , , PUNCT iajs-3377 72 17 πœ‰))𝑠𝑑π‘₯ πœ‰))𝑠𝑑π‘₯ ADJ iajs-3377 72 18 ( ( PUNCT iajs-3377 72 19 19 19 NUM iajs-3377 72 20 ) ) PUNCT iajs-3377 72 21 2.2.4 2.2.4 NUM iajs-3377 72 22 hazard hazard NOUN iajs-3377 72 23 function function NOUN iajs-3377 72 24 of of ADP iajs-3377 72 25 de de ADJ iajs-3377 72 26 - - ADJ iajs-3377 72 27 pareto pareto ADJ iajs-3377 72 28 𝐻(π‘₯ 𝐻(π‘₯ NOUN iajs-3377 72 29 ; ; PUNCT iajs-3377 72 30 𝛼 𝛼 X iajs-3377 72 31 , , PUNCT iajs-3377 72 32 𝑏 𝑏 NOUN iajs-3377 72 33 , , PUNCT iajs-3377 72 34 πœƒ πœƒ NOUN iajs-3377 72 35 ) ) PUNCT iajs-3377 72 36 = = SYM iajs-3377 72 37 𝑔(π‘₯ 𝑔(π‘₯ NOUN iajs-3377 72 38 ) ) PUNCT iajs-3377 72 39 𝑆(π‘₯ 𝑆(π‘₯ X iajs-3377 72 40 ) ) PUNCT iajs-3377 72 41 = = PUNCT iajs-3377 72 42 ⍬ ⍬ PROPN iajs-3377 72 43 2𝛼𝑏 2𝛼𝑏 NOUN iajs-3377 72 44 ( ( PUNCT iajs-3377 72 45 π‘₯ π‘₯ X iajs-3377 72 46 𝛼 𝛼 X iajs-3377 72 47 ) ) PUNCT iajs-3377 72 48 ⍬ ⍬ PROPN iajs-3377 72 49 βˆ’1 βˆ’1 NOUN iajs-3377 72 50 𝑒 𝑒 NOUN iajs-3377 72 51 βˆ’ βˆ’ PROPN iajs-3377 72 52 1 1 NUM iajs-3377 72 53 𝑏 𝑏 PROPN iajs-3377 72 54 ( ( PUNCT iajs-3377 72 55 π‘₯ π‘₯ X iajs-3377 72 56 𝛼 𝛼 X iajs-3377 72 57 ) ) PUNCT iajs-3377 72 58 ⍬ ⍬ PROPN iajs-3377 72 59 1 1 NUM iajs-3377 72 60 2 2 NUM iajs-3377 72 61 ( ( PUNCT iajs-3377 72 62 1+𝑒 1+𝑒 NUM iajs-3377 72 63 βˆ’ βˆ’ NOUN iajs-3377 72 64 1 1 NUM iajs-3377 72 65 𝑏 𝑏 PROPN iajs-3377 72 66 ( ( PUNCT iajs-3377 72 67 π‘₯ π‘₯ X iajs-3377 72 68 𝛼 𝛼 NOUN iajs-3377 72 69 ) ) PUNCT iajs-3377 72 70 πœƒ πœƒ NOUN iajs-3377 72 71 ) ) PUNCT iajs-3377 72 72 = = PUNCT iajs-3377 73 1 ⍬ ⍬ INTJ iajs-3377 73 2 𝛼𝑏 𝛼𝑏 INTJ iajs-3377 73 3 ( ( PUNCT iajs-3377 73 4 π‘₯ π‘₯ X iajs-3377 73 5 𝛼 𝛼 X iajs-3377 73 6 ) ) PUNCT iajs-3377 73 7 ⍬ ⍬ PROPN iajs-3377 73 8 βˆ’1 βˆ’1 NOUN iajs-3377 73 9 𝑒 𝑒 NOUN iajs-3377 73 10 βˆ’ βˆ’ PROPN iajs-3377 73 11 1 1 NUM iajs-3377 73 12 𝑏 𝑏 PROPN iajs-3377 73 13 ( ( PUNCT iajs-3377 73 14 π‘₯ π‘₯ X iajs-3377 73 15 𝛼 𝛼 X iajs-3377 73 16 ) ) PUNCT iajs-3377 73 17 ⍬ ⍬ PROPN iajs-3377 74 1 1+𝑒 1+𝑒 NUM iajs-3377 74 2 βˆ’ βˆ’ NOUN iajs-3377 74 3 1 1 NUM iajs-3377 74 4 𝑏 𝑏 PROPN iajs-3377 74 5 ( ( PUNCT iajs-3377 74 6 π‘₯ π‘₯ X iajs-3377 74 7 𝛼 𝛼 NOUN iajs-3377 74 8 ) ) PUNCT iajs-3377 74 9 πœƒ πœƒ NOUN iajs-3377 74 10 ( ( PUNCT iajs-3377 74 11 20 20 NUM iajs-3377 74 12 ) ) PUNCT iajs-3377 74 13 2.2.5 2.2.5 NUM iajs-3377 74 14 renyi renyi PROPN iajs-3377 74 15 entropy entropy NOUN iajs-3377 74 16 of of ADP iajs-3377 74 17 de de ADJ iajs-3377 74 18 - - ADJ iajs-3377 74 19 pareto pareto ADJ iajs-3377 74 20 π›Ώπ‘Ÿ π›Ώπ‘Ÿ NOUN iajs-3377 74 21 = = SYM iajs-3377 74 22 1 1 NUM iajs-3377 74 23 1βˆ’π‘Ÿ 1βˆ’π‘Ÿ NUM iajs-3377 74 24 π‘™π‘œπ‘” π‘™π‘œπ‘” PROPN iajs-3377 74 25 ∫ ∫ PROPN iajs-3377 74 26 π‘“π‘Ÿ(π‘₯)𝑑π‘₯ π‘“π‘Ÿ(π‘₯)𝑑π‘₯ NOUN iajs-3377 74 27 ∞ ∞ PROPN iajs-3377 74 28 0 0 NUM iajs-3377 75 1 = = SYM iajs-3377 75 2 1 1 NUM iajs-3377 75 3 1βˆ’π‘Ÿ 1βˆ’π‘Ÿ NUM iajs-3377 75 4 π‘™π‘œπ‘” π‘™π‘œπ‘” NOUN iajs-3377 75 5 ∫ ∫ PROPN iajs-3377 75 6 ( ( PUNCT iajs-3377 75 7 ⍬ ⍬ PROPN iajs-3377 75 8 2𝛼𝑏 2𝛼𝑏 NOUN iajs-3377 75 9 ( ( PUNCT iajs-3377 75 10 π‘₯ π‘₯ X iajs-3377 75 11 𝛼 𝛼 X iajs-3377 75 12 ) ) PUNCT iajs-3377 75 13 ⍬ ⍬ VERB iajs-3377 75 14 βˆ’1 βˆ’1 NOUN iajs-3377 75 15 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 75 16 1 1 NUM iajs-3377 75 17 𝑏 𝑏 NOUN iajs-3377 75 18 ( ( PUNCT iajs-3377 75 19 π‘₯ π‘₯ X iajs-3377 75 20 𝛼 𝛼 X iajs-3377 75 21 ) ) PUNCT iajs-3377 75 22 ⍬ ⍬ PROPN iajs-3377 75 23 ) ) PUNCT iajs-3377 76 1 𝒓 𝒓 PROPN iajs-3377 76 2 𝑑π‘₯ 𝑑π‘₯ VERB iajs-3377 76 3 ∞ ∞ PROPN iajs-3377 76 4 𝟎 𝟎 NUM iajs-3377 76 5 ( ( PUNCT iajs-3377 76 6 21 21 NUM iajs-3377 76 7 ) ) PUNCT iajs-3377 76 8 ihjpas ihjpa NOUN iajs-3377 76 9 . . PUNCT iajs-3377 77 1 36 36 NUM iajs-3377 77 2 ( ( PUNCT iajs-3377 77 3 3 3 NUM iajs-3377 77 4 ) ) PUNCT iajs-3377 77 5 2023 2023 NUM iajs-3377 77 6 443 443 NUM iajs-3377 77 7 π›Ώπ‘Ÿ π›Ώπ‘Ÿ NOUN iajs-3377 77 8 = = SYM iajs-3377 77 9 1 1 NUM iajs-3377 77 10 1βˆ’π‘Ÿ 1βˆ’π‘Ÿ NUM iajs-3377 77 11 π‘™π‘œπ‘” π‘™π‘œπ‘” NOUN iajs-3377 77 12 ( ( PUNCT iajs-3377 77 13 π‘πœƒ π‘πœƒ PROPN iajs-3377 77 14 2π‘Ÿπ›Όπ‘ 2π‘Ÿπ›Όπ‘ NUM iajs-3377 77 15 √ √ ADP iajs-3377 77 16 π‘Ÿ π‘Ÿ PRON iajs-3377 77 17 𝑏 𝑏 PROPN iajs-3377 77 18 πœƒ πœƒ PROPN iajs-3377 77 19 ) ) PUNCT iajs-3377 77 20 π‘Ÿ π‘Ÿ NOUN iajs-3377 77 21 ( ( PUNCT iajs-3377 77 22 𝛼 𝛼 NOUN iajs-3377 77 23 πœƒ πœƒ NOUN iajs-3377 77 24 √ √ NOUN iajs-3377 77 25 𝑏 𝑏 PRON iajs-3377 77 26 π‘Ÿ π‘Ÿ PRON iajs-3377 77 27 πœƒ πœƒ X iajs-3377 77 28 ) ) PUNCT iajs-3377 77 29 β”Œ β”Œ PROPN iajs-3377 77 30 ( ( PUNCT iajs-3377 77 31 π‘Ÿ π‘Ÿ NOUN iajs-3377 77 32 βˆ’ βˆ’ ADP iajs-3377 77 33 π‘Ÿ π‘Ÿ X iajs-3377 77 34 πœƒ πœƒ X iajs-3377 78 1 + + NUM iajs-3377 78 2 1 1 NUM iajs-3377 78 3 πœƒ πœƒ NOUN iajs-3377 78 4 ) ) PUNCT iajs-3377 78 5 ( ( PUNCT iajs-3377 78 6 22 22 NUM iajs-3377 78 7 ) ) PUNCT iajs-3377 78 8 2.3 2.3 NUM iajs-3377 78 9 . . PUNCT iajs-3377 79 1 estimation estimation NOUN iajs-3377 79 2 we we PRON iajs-3377 79 3 describe describe VERB iajs-3377 79 4 the the DET iajs-3377 79 5 maximum maximum ADJ iajs-3377 79 6 likelihood likelihood NOUN iajs-3377 79 7 method method NOUN iajs-3377 79 8 of of ADP iajs-3377 79 9 estimation estimation NOUN iajs-3377 79 10 in in ADP iajs-3377 79 11 this this DET iajs-3377 79 12 section section NOUN iajs-3377 79 13 for for ADP iajs-3377 79 14 the the DET iajs-3377 79 15 unknown unknown ADJ iajs-3377 79 16 parameters parameter NOUN iajs-3377 79 17 of of ADP iajs-3377 79 18 the the DET iajs-3377 79 19 de de PROPN iajs-3377 79 20 - - ADJ iajs-3377 79 21 x x ADJ iajs-3377 79 22 family family NOUN iajs-3377 79 23 . . PUNCT iajs-3377 80 1 the the DET iajs-3377 80 2 method method NOUN iajs-3377 80 3 of of ADP iajs-3377 80 4 maximum maximum ADJ iajs-3377 80 5 likelihood likelihood NOUN iajs-3377 80 6 estimation estimation NOUN iajs-3377 80 7 is be AUX iajs-3377 80 8 adjudged adjudge VERB iajs-3377 80 9 to to PART iajs-3377 80 10 be be AUX iajs-3377 80 11 the the DET iajs-3377 80 12 best good ADJ iajs-3377 80 13 method method NOUN iajs-3377 80 14 of of ADP iajs-3377 80 15 estimating estimate VERB iajs-3377 80 16 parameters parameter NOUN iajs-3377 80 17 of of ADP iajs-3377 80 18 distributions distribution NOUN iajs-3377 80 19 . . PUNCT iajs-3377 81 1 2.3.1 2.3.1 NUM iajs-3377 81 2 maximum maximum ADJ iajs-3377 81 3 likelihood likelihood NOUN iajs-3377 81 4 estimation estimation NOUN iajs-3377 81 5 de de X iajs-3377 81 6 - - NOUN iajs-3377 81 7 pareto pareto ADJ iajs-3377 81 8 in in ADP iajs-3377 81 9 this this PRON iajs-3377 81 10 , , PUNCT iajs-3377 81 11 let let VERB iajs-3377 81 12 𝑋1 𝑋1 PROPN iajs-3377 81 13 , , PUNCT iajs-3377 81 14 𝑋2 𝑋2 VERB iajs-3377 81 15 , , PUNCT iajs-3377 81 16 … … PUNCT iajs-3377 81 17 , , PUNCT iajs-3377 81 18 π‘‹π‘˜ π‘‹π‘˜ INTJ iajs-3377 81 19 be be AUX iajs-3377 81 20 the the DET iajs-3377 81 21 observed observe VERB iajs-3377 81 22 values value NOUN iajs-3377 81 23 for for ADP iajs-3377 81 24 de de NOUN iajs-3377 81 25 - - ADJ iajs-3377 81 26 x x ADJ iajs-3377 81 27 distribution distribution NOUN iajs-3377 81 28 with with ADP iajs-3377 81 29 parameters𝑏 parameters𝑏 NOUN iajs-3377 81 30 , , PUNCT iajs-3377 81 31 π‘Ž π‘Ž PROPN iajs-3377 81 32 , , PUNCT iajs-3377 81 33 πœ‰. πœ‰. PROPN iajs-3377 81 34 the the DET iajs-3377 81 35 total total ADJ iajs-3377 81 36 log log NOUN iajs-3377 81 37 - - PUNCT iajs-3377 81 38 likelihood likelihood NOUN iajs-3377 81 39 function function NOUN iajs-3377 81 40 corresponding correspond VERB iajs-3377 81 41 to to ADP iajs-3377 81 42 ( ( PUNCT iajs-3377 81 43 11 11 NUM iajs-3377 81 44 ) ) PUNCT iajs-3377 81 45 is be AUX iajs-3377 81 46 presented present VERB iajs-3377 81 47 as as ADP iajs-3377 81 48 log log NOUN iajs-3377 81 49 l(π‘₯ l(π‘₯ PROPN iajs-3377 81 50 , , PUNCT iajs-3377 81 51 𝑏 𝑏 NOUN iajs-3377 81 52 , , PUNCT iajs-3377 81 53 π‘Ž π‘Ž NOUN iajs-3377 81 54 , , PUNCT iajs-3377 81 55 πœ‰ πœ‰ NOUN iajs-3377 81 56 ) ) PUNCT iajs-3377 81 57 = = SYM iajs-3377 81 58 ∏ ∏ PROPN iajs-3377 81 59 ⍬ ⍬ PROPN iajs-3377 81 60 2𝛼𝑏 2𝛼𝑏 NOUN iajs-3377 81 61 ( ( PUNCT iajs-3377 81 62 π‘₯ π‘₯ X iajs-3377 81 63 𝛼 𝛼 X iajs-3377 81 64 ) ) PUNCT iajs-3377 81 65 ⍬ ⍬ VERB iajs-3377 81 66 βˆ’1 βˆ’1 NOUN iajs-3377 81 67 π‘’βˆ’ π‘’βˆ’ NOUN iajs-3377 81 68 1 1 NUM iajs-3377 81 69 𝑏 𝑏 NOUN iajs-3377 81 70 ( ( PUNCT iajs-3377 81 71 π‘₯ π‘₯ X iajs-3377 81 72 𝛼 𝛼 X iajs-3377 81 73 ) ) PUNCT iajs-3377 81 74 ⍬ ⍬ VERB iajs-3377 82 1 𝑛 𝑛 PRON iajs-3377 82 2 𝑖=1 𝑖=1 PROPN iajs-3377 82 3 ( ( PUNCT iajs-3377 82 4 23 23 NUM iajs-3377 82 5 ) ) PUNCT iajs-3377 82 6 3 3 NUM iajs-3377 82 7 . . NOUN iajs-3377 82 8 results result VERB iajs-3377 82 9 3.1 3.1 NUM iajs-3377 82 10 fitting fit VERB iajs-3377 82 11 the the DET iajs-3377 82 12 model model NOUN iajs-3377 82 13 to to ADP iajs-3377 82 14 molecular molecular ADJ iajs-3377 82 15 dynamics dynamic NOUN iajs-3377 82 16 simulated simulate VERB iajs-3377 82 17 data datum NOUN iajs-3377 82 18 the the DET iajs-3377 82 19 two two NUM iajs-3377 82 20 approved approve VERB iajs-3377 82 21 hiv hiv PROPN iajs-3377 82 22 drugs drug NOUN iajs-3377 82 23 were be AUX iajs-3377 82 24 obtained obtain VERB iajs-3377 82 25 from from ADP iajs-3377 82 26 the the DET iajs-3377 82 27 drug drug NOUN iajs-3377 82 28 bank bank PROPN iajs-3377 82 29 archive archive NOUN iajs-3377 82 30 online online ADV iajs-3377 82 31 , , PUNCT iajs-3377 82 32 modeled model VERB iajs-3377 82 33 using use VERB iajs-3377 82 34 ( ( PUNCT iajs-3377 82 35 spartan’14 spartan’14 VERB iajs-3377 82 36 version version NOUN iajs-3377 82 37 1.18 1.18 NUM iajs-3377 82 38 by by ADP iajs-3377 82 39 wave wave PROPN iajs-3377 82 40 function function PROPN iajs-3377 82 41 inc inc PROPN iajs-3377 82 42 ) ) PUNCT iajs-3377 82 43 i. i. PROPN iajs-3377 82 44 geometry geometry NOUN iajs-3377 82 45 optimization optimization NOUN iajs-3377 82 46 and and CCONJ iajs-3377 82 47 calculation calculation NOUN iajs-3377 82 48 of of ADP iajs-3377 82 49 the the DET iajs-3377 82 50 two two NUM iajs-3377 82 51 drugs drug NOUN iajs-3377 82 52 were be AUX iajs-3377 82 53 done do VERB iajs-3377 82 54 using use VERB iajs-3377 82 55 density density NOUN iajs-3377 82 56 functional functional ADJ iajs-3377 82 57 theory theory NOUN iajs-3377 82 58 ( ( PUNCT iajs-3377 82 59 dft dft PROPN iajs-3377 82 60 ) ) PUNCT iajs-3377 82 61 with with ADP iajs-3377 82 62 6 6 NUM iajs-3377 82 63 - - SYM iajs-3377 82 64 31 31 NUM iajs-3377 82 65 g g NOUN iajs-3377 82 66 * * NOUN iajs-3377 82 67 basis basis NOUN iajs-3377 82 68 set set VERB iajs-3377 82 69 to to PART iajs-3377 82 70 obtain obtain VERB iajs-3377 82 71 the the DET iajs-3377 82 72 molecular molecular ADJ iajs-3377 82 73 parameters parameter NOUN iajs-3377 82 74 responsible responsible ADJ iajs-3377 82 75 for for ADP iajs-3377 82 76 the the DET iajs-3377 82 77 cytotoxicity cytotoxicity NOUN iajs-3377 82 78 of of ADP iajs-3377 82 79 the the DET iajs-3377 82 80 compounds compound NOUN iajs-3377 82 81 under under ADP iajs-3377 82 82 investigation investigation NOUN iajs-3377 82 83 and and CCONJ iajs-3377 82 84 then then ADV iajs-3377 82 85 saved save VERB iajs-3377 82 86 as as ADP iajs-3377 82 87 pdb pdb NOUN iajs-3377 82 88 files file NOUN iajs-3377 82 89 for for ADP iajs-3377 82 90 simulation simulation PROPN iajs-3377 82 91 study study PROPN iajs-3377 82 92 ii ii PROPN iajs-3377 82 93 . . PUNCT iajs-3377 83 1 the the DET iajs-3377 83 2 protein protein NOUN iajs-3377 83 3 receptors receptor NOUN iajs-3377 83 4 responsible responsible ADJ iajs-3377 83 5 for for ADP iajs-3377 83 6 hiv(that hiv(that PRON iajs-3377 83 7 is be AUX iajs-3377 83 8 , , PUNCT iajs-3377 83 9 the the DET iajs-3377 83 10 hiv hiv NOUN iajs-3377 83 11 - - PUNCT iajs-3377 83 12 causing cause VERB iajs-3377 83 13 organisms organism NOUN iajs-3377 83 14 ) ) PUNCT iajs-3377 83 15 used use VERB iajs-3377 83 16 were be AUX iajs-3377 83 17 gotten get VERB iajs-3377 83 18 from from ADP iajs-3377 83 19 protein protein NOUN iajs-3377 83 20 data datum NOUN iajs-3377 83 21 bank bank PROPN iajs-3377 83 22 ( ( PUNCT iajs-3377 83 23 pdb pdb PROPN iajs-3377 83 24 ) ) PUNCT iajs-3377 84 1 [ [ X iajs-3377 84 2 18 18 NUM iajs-3377 84 3 ] ] SYM iajs-3377 84 4 iii iii X iajs-3377 84 5 . . PUNCT iajs-3377 84 6 with with ADP iajs-3377 84 7 no no DET iajs-3377 84 8 missing miss VERB iajs-3377 84 9 residues residue NOUN iajs-3377 84 10 and and CCONJ iajs-3377 84 11 a a DET iajs-3377 84 12 single single ADJ iajs-3377 84 13 strand strand NOUN iajs-3377 84 14 were be AUX iajs-3377 84 15 obtained obtain VERB iajs-3377 84 16 by by ADP iajs-3377 84 17 deleting delete VERB iajs-3377 84 18 multiple multiple ADJ iajs-3377 84 19 ligands ligand NOUN iajs-3377 84 20 , , PUNCT iajs-3377 84 21 nonprotein nonprotein NOUN iajs-3377 84 22 and and CCONJ iajs-3377 84 23 other other ADJ iajs-3377 84 24 protein protein NOUN iajs-3377 84 25 parts part NOUN iajs-3377 84 26 from from ADP iajs-3377 84 27 the the DET iajs-3377 84 28 pdb pdb PROPN iajs-3377 84 29 files file NOUN iajs-3377 84 30 . . PUNCT iajs-3377 85 1 autoduck autoduck ADJ iajs-3377 85 2 tools tool NOUN iajs-3377 85 3 version version NOUN iajs-3377 85 4 1.5.6 1.5.6 NUM iajs-3377 85 5 was be AUX iajs-3377 85 6 used use VERB iajs-3377 85 7 to to PART iajs-3377 85 8 locate locate VERB iajs-3377 85 9 the the DET iajs-3377 85 10 binding bind VERB iajs-3377 85 11 site site NOUN iajs-3377 85 12 and and CCONJ iajs-3377 85 13 to to PART iajs-3377 85 14 add add VERB iajs-3377 85 15 hydrogen hydrogen NOUN iajs-3377 85 16 to to ADP iajs-3377 85 17 the the DET iajs-3377 85 18 prepared prepared ADJ iajs-3377 85 19 protein protein NOUN iajs-3377 85 20 receptor receptor NOUN iajs-3377 85 21 and and CCONJ iajs-3377 85 22 finally finally ADV iajs-3377 85 23 converted convert VERB iajs-3377 85 24 to to ADP iajs-3377 85 25 a a DET iajs-3377 85 26 protein protein NOUN iajs-3377 85 27 data datum NOUN iajs-3377 85 28 bank bank NOUN iajs-3377 85 29 format format NOUN iajs-3377 85 30 ( ( PUNCT iajs-3377 85 31 pdbqt pdbqt NOUN iajs-3377 85 32 ) ) PUNCT iajs-3377 85 33 for for ADP iajs-3377 85 34 the the DET iajs-3377 85 35 molecular molecular ADJ iajs-3377 85 36 simulation simulation NOUN iajs-3377 85 37 . . PUNCT iajs-3377 86 1 autodockvina autodockvina PROPN iajs-3377 86 2 were be AUX iajs-3377 86 3 used use VERB iajs-3377 86 4 for for ADP iajs-3377 86 5 the the DET iajs-3377 86 6 simulation simulation NOUN iajs-3377 86 7 process process NOUN iajs-3377 86 8 and and CCONJ iajs-3377 86 9 the the DET iajs-3377 86 10 simulation simulation NOUN iajs-3377 86 11 was be AUX iajs-3377 86 12 repeated repeat VERB iajs-3377 86 13 for for ADP iajs-3377 86 14 seven seven NUM iajs-3377 86 15 different different ADJ iajs-3377 86 16 in in ADP iajs-3377 86 17 order order NOUN iajs-3377 86 18 to to PART iajs-3377 86 19 obtain obtain VERB iajs-3377 86 20 the the DET iajs-3377 86 21 most most ADV iajs-3377 86 22 stable stable ADJ iajs-3377 86 23 conformation conformation NOUN iajs-3377 86 24 of of ADP iajs-3377 86 25 the the DET iajs-3377 86 26 drug drug NOUN iajs-3377 86 27 - - PUNCT iajs-3377 86 28 receptor receptor NOUN iajs-3377 86 29 complex complex NOUN iajs-3377 86 30 and and CCONJ iajs-3377 86 31 post post VERB iajs-3377 86 32 docking docking NOUN iajs-3377 86 33 analysis analysis NOUN iajs-3377 86 34 was be AUX iajs-3377 86 35 done do VERB iajs-3377 86 36 using use VERB iajs-3377 86 37 edupymolversion edupymolversion NOUN iajs-3377 86 38 1.7.4.4 1.7.4.4 NUM iajs-3377 86 39 and and CCONJ iajs-3377 86 40 discovery discovery PROPN iajs-3377 86 41 studio studio NOUN iajs-3377 86 42 4.1 4.1 NUM iajs-3377 86 43 visualizer visualizer NOUN iajs-3377 86 44 . . PUNCT iajs-3377 87 1 figure figure NOUN iajs-3377 87 2 5a 5a NUM iajs-3377 87 3 : : PUNCT iajs-3377 87 4 fitting fit VERB iajs-3377 87 5 the the DET iajs-3377 87 6 models model NOUN iajs-3377 87 7 to to ADP iajs-3377 87 8 neviranpine neviranpine NOUN iajs-3377 87 9 data datum NOUN iajs-3377 87 10 ( ( PUNCT iajs-3377 87 11 obtained obtain VERB iajs-3377 87 12 via via ADP iajs-3377 87 13 molecular molecular ADJ iajs-3377 87 14 simulation simulation NOUN iajs-3377 87 15 ) ) PUNCT iajs-3377 87 16 ihjpas ihjpas PROPN iajs-3377 87 17 . . PUNCT iajs-3377 88 1 36 36 NUM iajs-3377 88 2 ( ( PUNCT iajs-3377 88 3 3 3 NUM iajs-3377 88 4 ) ) PUNCT iajs-3377 88 5 2023 2023 NUM iajs-3377 88 6 444 444 NUM iajs-3377 88 7 from from ADP iajs-3377 88 8 the the DET iajs-3377 88 9 figure figure NOUN iajs-3377 88 10 5a 5a NUM iajs-3377 88 11 above above ADV iajs-3377 88 12 , , PUNCT iajs-3377 88 13 we we PRON iajs-3377 88 14 can can AUX iajs-3377 88 15 say say VERB iajs-3377 88 16 that that SCONJ iajs-3377 88 17 the the DET iajs-3377 88 18 selected select VERB iajs-3377 88 19 distributions distribution NOUN iajs-3377 88 20 approximately approximately ADV iajs-3377 88 21 follow follow VERB iajs-3377 88 22 the the DET iajs-3377 88 23 distribution distribution NOUN iajs-3377 88 24 of of ADP iajs-3377 88 25 the the DET iajs-3377 88 26 data datum NOUN iajs-3377 88 27 , , PUNCT iajs-3377 88 28 thus thus ADV iajs-3377 88 29 , , PUNCT iajs-3377 88 30 making make VERB iajs-3377 88 31 the the DET iajs-3377 88 32 distributions distribution NOUN iajs-3377 88 33 suitable suitable ADJ iajs-3377 88 34 for for ADP iajs-3377 88 35 data datum NOUN iajs-3377 88 36 collected collect VERB iajs-3377 88 37 when when SCONJ iajs-3377 88 38 using use VERB iajs-3377 88 39 neviranpine neviranpine ADV iajs-3377 88 40 to to PART iajs-3377 88 41 dock dock VERB iajs-3377 88 42 hiv hiv PROPN iajs-3377 88 43 protein protein NOUN iajs-3377 88 44 receptor receptor NOUN iajs-3377 88 45 figure figure NOUN iajs-3377 88 46 5b 5b NOUN iajs-3377 88 47 : : PUNCT iajs-3377 88 48 fitting fit VERB iajs-3377 88 49 the the DET iajs-3377 88 50 models model NOUN iajs-3377 88 51 to to PART iajs-3377 88 52 abacavir abacavir PROPN iajs-3377 88 53 data data PROPN iajs-3377 88 54 ( ( PUNCT iajs-3377 88 55 obtained obtain VERB iajs-3377 88 56 via via ADP iajs-3377 88 57 molecular molecular ADJ iajs-3377 88 58 simulation simulation NOUN iajs-3377 88 59 ) ) PUNCT iajs-3377 88 60 from from ADP iajs-3377 88 61 the the DET iajs-3377 88 62 fig fig NOUN iajs-3377 88 63 . . PUNCT iajs-3377 89 1 5b 5b NOUN iajs-3377 89 2 above above ADV iajs-3377 89 3 , , PUNCT iajs-3377 89 4 we we PRON iajs-3377 89 5 can can AUX iajs-3377 89 6 say say VERB iajs-3377 89 7 that that SCONJ iajs-3377 89 8 the the DET iajs-3377 89 9 selected select VERB iajs-3377 89 10 distributions distribution NOUN iajs-3377 89 11 approximately approximately ADV iajs-3377 89 12 follow follow VERB iajs-3377 89 13 the the DET iajs-3377 89 14 distribution distribution NOUN iajs-3377 89 15 of of ADP iajs-3377 89 16 the the DET iajs-3377 89 17 data datum NOUN iajs-3377 89 18 , , PUNCT iajs-3377 89 19 thus thus ADV iajs-3377 89 20 , , PUNCT iajs-3377 89 21 making make VERB iajs-3377 89 22 the the DET iajs-3377 89 23 distributions distribution NOUN iajs-3377 89 24 suitable suitable ADJ iajs-3377 89 25 for for ADP iajs-3377 89 26 data datum NOUN iajs-3377 89 27 collected collect VERB iajs-3377 89 28 when when SCONJ iajs-3377 89 29 using use VERB iajs-3377 89 30 abacavir abacavir NOUN iajs-3377 89 31 to to PART iajs-3377 89 32 dock dock VERB iajs-3377 89 33 hiv hiv PROPN iajs-3377 89 34 protein protein NOUN iajs-3377 89 35 receptor receptor NOUN iajs-3377 89 36 table1 table1 PROPN iajs-3377 89 37 . . PUNCT iajs-3377 90 1 fitting fitting ADJ iajs-3377 90 2 cells cell NOUN iajs-3377 90 3 table table NOUN iajs-3377 90 4 with with ADP iajs-3377 90 5 the the DET iajs-3377 90 6 including include VERB iajs-3377 90 7 numbers number NOUN iajs-3377 90 8 model model NOUN iajs-3377 90 9 parameter parameter NOUN iajs-3377 90 10 criteria criterion NOUN iajs-3377 90 11 mean mean VERB iajs-3377 90 12 affinity affinity NOUN iajs-3377 90 13 epd epd PROPN iajs-3377 90 14 οΏ½ οΏ½ PROPN iajs-3377 90 15 Μ‚ Μ‚ PROPN iajs-3377 90 16 οΏ½ οΏ½ NOUN iajs-3377 90 17 = = SYM iajs-3377 90 18 0.029978(0.034 0.029978(0.034 NUM iajs-3377 90 19 ) ) PUNCT iajs-3377 90 20 οΏ½ οΏ½ PROPN iajs-3377 90 21 Μ‚ Μ‚ VERB iajs-3377 90 22 οΏ½ οΏ½ NOUN iajs-3377 90 23 = = SYM iajs-3377 90 24 0.9980(0.367 0.9980(0.367 NUM iajs-3377 90 25 ) ) PUNCT iajs-3377 90 26 οΏ½ οΏ½ PROPN iajs-3377 90 27 Μ‚ Μ‚ VERB iajs-3377 90 28 οΏ½ οΏ½ PROPN iajs-3377 90 29 = = SYM iajs-3377 90 30 0.996486(0.648 0.996486(0.648 NUM iajs-3377 90 31 ) ) PUNCT iajs-3377 90 32 aic=303.405 aic=303.405 NOUN iajs-3377 90 33 bic=303.6433 bic=303.6433 PROPN iajs-3377 90 34 caic=309.405 caic=309.405 PROPN iajs-3377 90 35 1.663157(0.902308 1.663157(0.902308 NUM iajs-3377 90 36 ) ) PUNCT iajs-3377 90 37 depd depd NOUN iajs-3377 90 38 οΏ½ οΏ½ PROPN iajs-3377 90 39 Μ‚ Μ‚ NOUN iajs-3377 90 40 οΏ½ οΏ½ NOUN iajs-3377 90 41 =1.978e+06(1.639e02 =1.978e+06(1.639e02 ADJ iajs-3377 90 42 ) ) PUNCT iajs-3377 90 43 οΏ½ οΏ½ PROPN iajs-3377 90 44 Μ‚ Μ‚ VERB iajs-3377 90 45 οΏ½ οΏ½ PROPN iajs-3377 90 46 = = SYM iajs-3377 90 47 1.503e04(5.307e-05 1.503e04(5.307e-05 NUM iajs-3377 90 48 ) ) PUNCT iajs-3377 90 49 οΏ½ οΏ½ PROPN iajs-3377 90 50 Μ‚ Μ‚ VERB iajs-3377 90 51 οΏ½ οΏ½ NOUN iajs-3377 90 52 =9.024e-01(2.211e04 =9.024e-01(2.211e04 NOUN iajs-3377 90 53 ) ) PUNCT iajs-3377 91 1 aic aic PROPN iajs-3377 91 2 = = PROPN iajs-3377 91 3 -27203950 -27203950 PROPN iajs-3377 91 4 bic= bic= PROPN iajs-3377 91 5 -27203950 -27203950 X iajs-3377 92 1 caic=27203944 caic=27203944 X iajs-3377 92 2 0.4511979(0.225 0.4511979(0.225 NUM iajs-3377 92 3 ) ) PUNCT iajs-3377 92 4 pd pd PROPN iajs-3377 92 5 οΏ½ οΏ½ PROPN iajs-3377 92 6 Μ‚ Μ‚ NOUN iajs-3377 92 7 οΏ½ οΏ½ NOUN iajs-3377 92 8 = = NOUN iajs-3377 92 9 8.089e+03 8.089e+03 NOUN iajs-3377 92 10 ( ( PUNCT iajs-3377 92 11 7.567e-02 7.567e-02 NUM iajs-3377 92 12 ) ) PUNCT iajs-3377 92 13 οΏ½ οΏ½ PROPN iajs-3377 92 14 Μ‚ Μ‚ SYM iajs-3377 92 15 οΏ½ οΏ½ NOUN iajs-3377 92 16 =( =( NOUN iajs-3377 92 17 3.372e+03 3.372e+03 NUM iajs-3377 92 18 ) ) PUNCT iajs-3377 92 19 9.268e-02 9.268e-02 NUM iajs-3377 93 1 aic=-810083 aic=-810083 NOUN iajs-3377 93 2 bic=-810082.8 bic=-810082.8 NOUN iajs-3377 93 3 caic=-810080.6 caic=-810080.6 X iajs-3377 94 1 3.3724(0.41697 3.3724(0.41697 NUM iajs-3377 94 2 ) ) PUNCT iajs-3377 94 3 from from ADP iajs-3377 94 4 table table NOUN iajs-3377 94 5 2 2 NUM iajs-3377 94 6 above above ADV iajs-3377 94 7 , , PUNCT iajs-3377 94 8 we we PRON iajs-3377 94 9 can can AUX iajs-3377 94 10 say say VERB iajs-3377 94 11 that that SCONJ iajs-3377 94 12 the the DET iajs-3377 94 13 parameter parameter NOUN iajs-3377 94 14 of of ADP iajs-3377 94 15 the the DET iajs-3377 94 16 model model NOUN iajs-3377 94 17 is be AUX iajs-3377 94 18 stable stable ADJ iajs-3377 94 19 and and CCONJ iajs-3377 94 20 the the DET iajs-3377 94 21 double double ADJ iajs-3377 94 22 exponential exponential ADJ iajs-3377 94 23 pareto pareto ADJ iajs-3377 94 24 distribution distribution NOUN iajs-3377 94 25 ( ( PUNCT iajs-3377 94 26 depd depd NOUN iajs-3377 94 27 ) ) PUNCT iajs-3377 94 28 appears appear VERB iajs-3377 94 29 to to PART iajs-3377 94 30 be be AUX iajs-3377 94 31 the the DET iajs-3377 94 32 best good ADJ iajs-3377 94 33 of of ADP iajs-3377 94 34 all all DET iajs-3377 94 35 the the DET iajs-3377 94 36 competing compete VERB iajs-3377 94 37 model model NOUN iajs-3377 94 38 ( ( PUNCT iajs-3377 94 39 model model NOUN iajs-3377 94 40 with with ADP iajs-3377 94 41 the the DET iajs-3377 94 42 lowest low ADJ iajs-3377 94 43 information information NOUN iajs-3377 94 44 criteria criterion NOUN iajs-3377 94 45 is be AUX iajs-3377 94 46 the the DET iajs-3377 94 47 best good ADJ iajs-3377 94 48 of of ADP iajs-3377 94 49 all all DET iajs-3377 94 50 the the DET iajs-3377 94 51 models model NOUN iajs-3377 94 52 ) ) PUNCT iajs-3377 94 53 . . PUNCT iajs-3377 95 1 the the DET iajs-3377 95 2 45.1198 45.1198 NUM iajs-3377 95 3 % % NOUN iajs-3377 95 4 of of ADP iajs-3377 95 5 the the DET iajs-3377 95 6 binding bind VERB iajs-3377 95 7 affinity affinity NOUN iajs-3377 95 8 is be AUX iajs-3377 95 9 attributed attribute VERB iajs-3377 95 10 to to ADP iajs-3377 95 11 neviranpine neviranpine NOUN iajs-3377 95 12 . . PUNCT iajs-3377 96 1 ihjpas ihjpas PROPN iajs-3377 96 2 . . PUNCT iajs-3377 97 1 36 36 NUM iajs-3377 97 2 ( ( PUNCT iajs-3377 97 3 3 3 NUM iajs-3377 97 4 ) ) PUNCT iajs-3377 97 5 2023 2023 NUM iajs-3377 97 6 445 445 NUM iajs-3377 97 7 fig fig NOUN iajs-3377 97 8 4 4 NUM iajs-3377 97 9 : : PUNCT iajs-3377 97 10 investigating investigate VERB iajs-3377 97 11 stochastic stochastic ADJ iajs-3377 97 12 dominance dominance NOUN iajs-3377 97 13 from from ADP iajs-3377 97 14 fig fig NOUN iajs-3377 97 15 4 4 NUM iajs-3377 97 16 above above ADV iajs-3377 97 17 , , PUNCT iajs-3377 97 18 we we PRON iajs-3377 97 19 can can AUX iajs-3377 97 20 say say VERB iajs-3377 97 21 that that SCONJ iajs-3377 97 22 neviranpine neviranpine NOUN iajs-3377 97 23 is be AUX iajs-3377 97 24 first first ADJ iajs-3377 97 25 order order NOUN iajs-3377 97 26 ( ( PUNCT iajs-3377 97 27 stochastically stochastically ADV iajs-3377 97 28 ) ) PUNCT iajs-3377 97 29 dominated dominate VERB iajs-3377 97 30 abacavir abacavir NOUN iajs-3377 97 31 . . PUNCT iajs-3377 98 1 that that PRON iajs-3377 98 2 is be AUX iajs-3377 98 3 , , PUNCT iajs-3377 98 4 the the DET iajs-3377 98 5 mean mean ADJ iajs-3377 98 6 effect effect NOUN iajs-3377 98 7 of of ADP iajs-3377 98 8 nevirapine nevirapine PROPN iajs-3377 98 9 has have AUX iajs-3377 98 10 dominated dominate VERB iajs-3377 98 11 that that PRON iajs-3377 98 12 of of ADP iajs-3377 98 13 abacavir abacavir NOUN iajs-3377 98 14 when when SCONJ iajs-3377 98 15 it it PRON iajs-3377 98 16 comes come VERB iajs-3377 98 17 to to ADP iajs-3377 98 18 the the DET iajs-3377 98 19 viral viral ADJ iajs-3377 98 20 load load NOUN iajs-3377 98 21 measurement measurement NOUN iajs-3377 98 22 ( ( PUNCT iajs-3377 98 23 copies copy NOUN iajs-3377 98 24 / / SYM iajs-3377 98 25 ml ml NOUN iajs-3377 98 26 ) ) PUNCT iajs-3377 98 27 from from ADP iajs-3377 98 28 the the DET iajs-3377 98 29 patients patient NOUN iajs-3377 98 30 subjected subject VERB iajs-3377 98 31 to to ADP iajs-3377 98 32 anti anti ADJ iajs-3377 98 33 - - ADJ iajs-3377 98 34 retroviral retroviral ADJ iajs-3377 98 35 therapy therapy NOUN iajs-3377 98 36 . . PUNCT iajs-3377 99 1 3d 3d NUM iajs-3377 99 2 structures structure NOUN iajs-3377 99 3 of of ADP iajs-3377 99 4 nevirapine nevirapine ADJ iajs-3377 99 5 3d 3d NOUN iajs-3377 99 6 of of ADP iajs-3377 99 7 abacavir abacavir NOUN iajs-3377 99 8 figure figure VERB iajs-3377 99 9 5 5 NUM iajs-3377 99 10 : : PUNCT iajs-3377 99 11 the the DET iajs-3377 99 12 ligands ligand NOUN iajs-3377 99 13 ( ( PUNCT iajs-3377 99 14 nevirapine nevirapine ADJ iajs-3377 99 15 and and CCONJ iajs-3377 99 16 abacavir abacavir NOUN iajs-3377 99 17 ) ) PUNCT iajs-3377 99 18 used use VERB iajs-3377 99 19 as as ADP iajs-3377 99 20 the the DET iajs-3377 99 21 drug drug NOUN iajs-3377 99 22 in in ADP iajs-3377 99 23 anti anti ADJ iajs-3377 99 24 - - ADJ iajs-3377 99 25 retroveral retroveral ADJ iajs-3377 99 26 therapy therapy NOUN iajs-3377 99 27 ihjpas ihjpa VERB iajs-3377 99 28 . . PUNCT iajs-3377 100 1 36 36 NUM iajs-3377 100 2 ( ( PUNCT iajs-3377 100 3 3 3 NUM iajs-3377 100 4 ) ) PUNCT iajs-3377 100 5 2023 2023 NUM iajs-3377 100 6 446 446 NUM iajs-3377 100 7 3d 3d NUM iajs-3377 100 8 receptor receptor NOUN iajs-3377 100 9 responsible responsible ADJ iajs-3377 100 10 for for ADP iajs-3377 100 11 hiv hiv PROPN iajs-3377 100 12 ( ( PUNCT iajs-3377 100 13 protein protein NOUN iajs-3377 100 14 responsible responsible ADJ iajs-3377 100 15 for for ADP iajs-3377 100 16 hiv hiv PROPN iajs-3377 100 17 ) ) PUNCT iajs-3377 100 18 interaction interaction NOUN iajs-3377 100 19 of of ADP iajs-3377 100 20 abacavir abacavir NOUN iajs-3377 100 21 and and CCONJ iajs-3377 100 22 3plt 3plt NUM iajs-3377 100 23 interaction interaction NOUN iajs-3377 100 24 of of ADP iajs-3377 100 25 nevirapine nevirapine PROPN iajs-3377 100 26 and and CCONJ iajs-3377 100 27 3lpt 3lpt PROPN iajs-3377 100 28 figure figure NOUN iajs-3377 100 29 6 6 NUM iajs-3377 100 30 . . PUNCT iajs-3377 101 1 the the DET iajs-3377 101 2 docking docking NOUN iajs-3377 101 3 result result NOUN iajs-3377 101 4 of of ADP iajs-3377 101 5 abacavir abacavir NOUN iajs-3377 101 6 and and CCONJ iajs-3377 101 7 nevirapine nevirapine PROPN iajs-3377 101 8 the the DET iajs-3377 101 9 abacavir abacavir NOUN iajs-3377 101 10 and and CCONJ iajs-3377 101 11 nevirapine nevirapine PROPN iajs-3377 101 12 were be AUX iajs-3377 101 13 used use VERB iajs-3377 101 14 as as ADP iajs-3377 101 15 the the DET iajs-3377 101 16 ligands ligand NOUN iajs-3377 101 17 to to PART iajs-3377 101 18 dock dock VERB iajs-3377 101 19 hiv hiv PROPN iajs-3377 101 20 protein protein NOUN iajs-3377 101 21 receptor receptor NOUN iajs-3377 101 22 , , PUNCT iajs-3377 101 23 the the DET iajs-3377 101 24 fig fig NOUN iajs-3377 101 25 6 6 NUM iajs-3377 101 26 showed show VERB iajs-3377 101 27 interaction interaction NOUN iajs-3377 101 28 between between ADP iajs-3377 101 29 the the DET iajs-3377 101 30 ligands ligand NOUN iajs-3377 101 31 and and CCONJ iajs-3377 101 32 hiv hiv NOUN iajs-3377 101 33 protein protein NOUN iajs-3377 101 34 receptor receptor NOUN iajs-3377 101 35 . . PUNCT iajs-3377 102 1 ihjpas ihjpas PROPN iajs-3377 102 2 . . PUNCT iajs-3377 103 1 36 36 NUM iajs-3377 103 2 ( ( PUNCT iajs-3377 103 3 3 3 NUM iajs-3377 103 4 ) ) PUNCT iajs-3377 103 5 2023 2023 NUM iajs-3377 103 6 447 447 NUM iajs-3377 103 7 table table NOUN iajs-3377 103 8 5 5 NUM iajs-3377 103 9 : : PUNCT iajs-3377 103 10 the the DET iajs-3377 103 11 molecular molecular ADJ iajs-3377 103 12 properties property NOUN iajs-3377 103 13 of of ADP iajs-3377 103 14 the the DET iajs-3377 103 15 drug drug NOUN iajs-3377 103 16 used use VERB iajs-3377 103 17 in in ADP iajs-3377 103 18 this this DET iajs-3377 103 19 study study NOUN iajs-3377 103 20 ( ( PUNCT iajs-3377 103 21 molecular molecular ADJ iajs-3377 103 22 docking docking NOUN iajs-3377 103 23 ) ) PUNCT iajs-3377 103 24 descriptors descriptor VERB iajs-3377 103 25 nevirapine nevirapine ADJ iajs-3377 103 26 abacavir abacavir VERB iajs-3377 103 27 molecular molecular ADJ iajs-3377 103 28 formula formula NOUN iajs-3377 103 29 c15h14n4o c15h14n4o NOUN iajs-3377 103 30 c14h18n6o c14h18n6o VERB iajs-3377 104 1 molecular molecular ADJ iajs-3377 104 2 weight weight NOUN iajs-3377 104 3 266.30amu 266.30amu PROPN iajs-3377 104 4 286.34amu 286.34amu PROPN iajs-3377 104 5 area area NOUN iajs-3377 104 6 281.25a2 281.25a2 NUM iajs-3377 104 7 305.46a2 305.46a2 NUM iajs-3377 104 8 volume volume NOUN iajs-3377 104 9 269.04a3 269.04a3 NUM iajs-3377 104 10 285.66a3 285.66a3 NUM iajs-3377 104 11 polarizability polarizability NOUN iajs-3377 104 12 62.14 62.14 NUM iajs-3377 104 13 63.34 63.34 NUM iajs-3377 104 14 hydrogen hydrogen NOUN iajs-3377 104 15 bond bond NOUN iajs-3377 104 16 donor donor NOUN iajs-3377 104 17 ( ( PUNCT iajs-3377 104 18 hbd hbd NOUN iajs-3377 104 19 ) ) PUNCT iajs-3377 104 20 1 1 NUM iajs-3377 104 21 2 2 NUM iajs-3377 104 22 hydrogen hydrogen NOUN iajs-3377 104 23 bond bond NOUN iajs-3377 104 24 acceptor acceptor NOUN iajs-3377 104 25 ( ( PUNCT iajs-3377 104 26 hba hba NOUN iajs-3377 104 27 ) ) PUNCT iajs-3377 104 28 5 5 NUM iajs-3377 104 29 5 5 NUM iajs-3377 104 30 polar polar ADJ iajs-3377 104 31 surface surface NOUN iajs-3377 104 32 area area NOUN iajs-3377 104 33 ( ( PUNCT iajs-3377 104 34 psa psa NOUN iajs-3377 104 35 ) ) PUNCT iajs-3377 104 36 36.84 36.84 NUM iajs-3377 104 37 67.47 67.47 NUM iajs-3377 104 38 ovality ovality NOUN iajs-3377 104 39 1.40 1.40 NUM iajs-3377 104 40 1.46 1.46 NUM iajs-3377 104 41 log log NOUN iajs-3377 104 42 p p NOUN iajs-3377 104 43 0.13 0.13 NUM iajs-3377 104 44 0.16 0.16 NUM iajs-3377 104 45 dipole dipole NOUN iajs-3377 104 46 movement movement NOUN iajs-3377 104 47 2.33 2.33 NUM iajs-3377 104 48 1.93d 1.93d NUM iajs-3377 104 49 homo homo NOUN iajs-3377 104 50 -5.80ev -5.80ev PROPN iajs-3377 105 1 -5.28ev -5.28ev PROPN iajs-3377 105 2 lumo lumo NOUN iajs-3377 105 3 -1.32ev -1.32ev PROPN iajs-3377 105 4 -0.16ev -0.16ev PROPN iajs-3377 105 5 bg bg PROPN iajs-3377 105 6 4.58ev 4.58ev NUM iajs-3377 105 7 5.12ev 5.12ev NUM iajs-3377 105 8 4 4 NUM iajs-3377 105 9 . . PUNCT iajs-3377 105 10 discussion discussion NOUN iajs-3377 105 11 from from ADP iajs-3377 105 12 table5 table5 PROPN iajs-3377 105 13 , , PUNCT iajs-3377 105 14 the the DET iajs-3377 105 15 properties property NOUN iajs-3377 105 16 of of ADP iajs-3377 105 17 the the DET iajs-3377 105 18 drugs drug NOUN iajs-3377 105 19 used use VERB iajs-3377 105 20 in in ADP iajs-3377 105 21 determining determine VERB iajs-3377 105 22 the the DET iajs-3377 105 23 toxicity toxicity NOUN iajs-3377 105 24 are be AUX iajs-3377 105 25 clearly clearly ADV iajs-3377 105 26 displayed display VERB iajs-3377 105 27 , , PUNCT iajs-3377 105 28 as as ADP iajs-3377 105 29 behavior behavior NOUN iajs-3377 105 30 , , PUNCT iajs-3377 105 31 and and CCONJ iajs-3377 105 32 the the DET iajs-3377 105 33 general general ADJ iajs-3377 105 34 effect effect NOUN iajs-3377 105 35 of of ADP iajs-3377 105 36 each each DET iajs-3377 105 37 drug drug NOUN iajs-3377 105 38 on on ADP iajs-3377 105 39 the the DET iajs-3377 105 40 body body NOUN iajs-3377 105 41 system system NOUN iajs-3377 105 42 . . PUNCT iajs-3377 106 1 parameters parameter NOUN iajs-3377 106 2 such such ADJ iajs-3377 106 3 as as ADP iajs-3377 106 4 hba hba NOUN iajs-3377 106 5 , , PUNCT iajs-3377 106 6 hbd hbd NOUN iajs-3377 106 7 , , PUNCT iajs-3377 106 8 psa psa NOUN iajs-3377 106 9 , , PUNCT iajs-3377 106 10 logp logp NOUN iajs-3377 106 11 and and CCONJ iajs-3377 106 12 polarizability polarizability NOUN iajs-3377 106 13 are be AUX iajs-3377 106 14 used use VERB iajs-3377 106 15 to to PART iajs-3377 106 16 determine determine VERB iajs-3377 106 17 if if SCONJ iajs-3377 106 18 a a DET iajs-3377 106 19 particular particular ADJ iajs-3377 106 20 compound compound NOUN iajs-3377 106 21 is be AUX iajs-3377 106 22 a a DET iajs-3377 106 23 good good ADJ iajs-3377 106 24 drug drug NOUN iajs-3377 106 25 candidate candidate NOUN iajs-3377 106 26 . . PUNCT iajs-3377 107 1 this this PRON iajs-3377 107 2 reveals reveal VERB iajs-3377 107 3 the the DET iajs-3377 107 4 active active ADJ iajs-3377 107 5 properties property NOUN iajs-3377 107 6 of of ADP iajs-3377 107 7 the the DET iajs-3377 107 8 drugs drug NOUN iajs-3377 107 9 used use VERB iajs-3377 107 10 in in ADP iajs-3377 107 11 determining determine VERB iajs-3377 107 12 the the DET iajs-3377 107 13 cytotoxicity cytotoxicity NOUN iajs-3377 107 14 of of ADP iajs-3377 107 15 each each DET iajs-3377 107 16 drug drug NOUN iajs-3377 107 17 towards towards ADP iajs-3377 107 18 the the DET iajs-3377 107 19 receptor receptor NOUN iajs-3377 107 20 responsible responsible ADJ iajs-3377 107 21 for for ADP iajs-3377 107 22 hiv hiv PROPN iajs-3377 107 23 . . PUNCT iajs-3377 108 1 failure failure NOUN iajs-3377 108 2 of of ADP iajs-3377 108 3 most most ADJ iajs-3377 108 4 drugs drug NOUN iajs-3377 108 5 in in ADP iajs-3377 108 6 clinical clinical ADJ iajs-3377 108 7 experiments experiment NOUN iajs-3377 108 8 is be AUX iajs-3377 108 9 a a DET iajs-3377 108 10 result result NOUN iajs-3377 108 11 of of ADP iajs-3377 108 12 there there PRON iajs-3377 108 13 poor poor ADJ iajs-3377 108 14 adme adme NOUN iajs-3377 108 15 ( ( PUNCT iajs-3377 108 16 absorption absorption NOUN iajs-3377 108 17 , , PUNCT iajs-3377 108 18 distribution distribution NOUN iajs-3377 108 19 , , PUNCT iajs-3377 108 20 metabolism metabolism NOUN iajs-3377 108 21 and and CCONJ iajs-3377 108 22 excretion excretion NOUN iajs-3377 108 23 ) ) PUNCT iajs-3377 108 24 properties property NOUN iajs-3377 108 25 , , PUNCT iajs-3377 108 26 hence hence ADV iajs-3377 108 27 for for SCONJ iajs-3377 108 28 a a DET iajs-3377 108 29 ligand ligand NOUN iajs-3377 108 30 to to PART iajs-3377 108 31 be be AUX iajs-3377 108 32 chosen choose VERB iajs-3377 108 33 as as ADP iajs-3377 108 34 a a DET iajs-3377 108 35 drug drug NOUN iajs-3377 108 36 candidate candidate NOUN iajs-3377 108 37 with with ADP iajs-3377 108 38 good good ADJ iajs-3377 108 39 adme adme NOUN iajs-3377 108 40 properties property NOUN iajs-3377 108 41 hbd hbd PROPN iajs-3377 108 42 must must AUX iajs-3377 108 43 be be AUX iajs-3377 108 44 less less ADJ iajs-3377 108 45 than than ADP iajs-3377 108 46 five five NUM iajs-3377 108 47 , , PUNCT iajs-3377 108 48 hba hba NOUN iajs-3377 108 49 must must AUX iajs-3377 108 50 be be AUX iajs-3377 108 51 less less ADJ iajs-3377 108 52 than than ADP iajs-3377 108 53 ten ten NUM iajs-3377 108 54 and and CCONJ iajs-3377 108 55 its its PRON iajs-3377 108 56 molecular molecular ADJ iajs-3377 108 57 weight weight NOUN iajs-3377 108 58 in in ADP iajs-3377 108 59 g g PROPN iajs-3377 108 60 / / SYM iajs-3377 108 61 mol mol NOUN iajs-3377 108 62 must must AUX iajs-3377 108 63 be be AUX iajs-3377 108 64 below below ADP iajs-3377 108 65 500 500 NUM iajs-3377 108 66 , , PUNCT iajs-3377 108 67 any any DET iajs-3377 108 68 ligand ligand NOUN iajs-3377 108 69 that that PRON iajs-3377 108 70 violates violate VERB iajs-3377 108 71 this this DET iajs-3377 108 72 set set NOUN iajs-3377 108 73 of of ADP iajs-3377 108 74 rules rule NOUN iajs-3377 108 75 might might AUX iajs-3377 108 76 result result VERB iajs-3377 108 77 to to ADP iajs-3377 108 78 the the DET iajs-3377 108 79 problem problem NOUN iajs-3377 108 80 if if SCONJ iajs-3377 108 81 ingested ingest VERB iajs-3377 108 82 [ [ X iajs-3377 108 83 19 19 NUM iajs-3377 108 84 ] ] PUNCT iajs-3377 108 85 . . PUNCT iajs-3377 109 1 polar polar ADJ iajs-3377 109 2 surface surface NOUN iajs-3377 109 3 area area NOUN iajs-3377 109 4 ( ( PUNCT iajs-3377 109 5 psa psa NOUN iajs-3377 109 6 ) ) PUNCT iajs-3377 109 7 gives give VERB iajs-3377 109 8 information information NOUN iajs-3377 109 9 about about ADP iajs-3377 109 10 the the DET iajs-3377 109 11 ability ability NOUN iajs-3377 109 12 of of ADP iajs-3377 109 13 a a DET iajs-3377 109 14 drug drug NOUN iajs-3377 109 15 - - PUNCT iajs-3377 109 16 like like ADJ iajs-3377 109 17 compound compound NOUN iajs-3377 109 18 to to PART iajs-3377 109 19 penetrate penetrate VERB iajs-3377 109 20 into into ADP iajs-3377 109 21 the the DET iajs-3377 109 22 cell cell NOUN iajs-3377 109 23 membrane membrane NOUN iajs-3377 109 24 . . PUNCT iajs-3377 110 1 it it PRON iajs-3377 110 2 has have AUX iajs-3377 110 3 been be AUX iajs-3377 110 4 established establish VERB iajs-3377 110 5 that that SCONJ iajs-3377 110 6 ligands ligand NOUN iajs-3377 110 7 with with ADP iajs-3377 110 8 high high ADJ iajs-3377 110 9 psa psa NOUN iajs-3377 110 10 value value NOUN iajs-3377 110 11 greater great ADJ iajs-3377 110 12 than than ADP iajs-3377 110 13 140Γ₯2 140Γ₯2 NUM iajs-3377 110 14 will will AUX iajs-3377 110 15 have have VERB iajs-3377 110 16 poor poor ADJ iajs-3377 110 17 penetrating penetrating NOUN iajs-3377 110 18 power power NOUN iajs-3377 110 19 into into ADP iajs-3377 110 20 the the DET iajs-3377 110 21 cell cell NOUN iajs-3377 110 22 membrane membrane NOUN iajs-3377 110 23 . . PUNCT iajs-3377 111 1 on on ADP iajs-3377 111 2 the the DET iajs-3377 111 3 other other ADJ iajs-3377 111 4 hand hand NOUN iajs-3377 111 5 , , PUNCT iajs-3377 111 6 molecules molecule NOUN iajs-3377 111 7 with with ADP iajs-3377 111 8 psa psa NOUN iajs-3377 111 9 value value NOUN iajs-3377 111 10 below below ADP iajs-3377 111 11 60Γ₯2 60Γ₯2 NUM iajs-3377 111 12 will will AUX iajs-3377 111 13 have have VERB iajs-3377 111 14 high high ADJ iajs-3377 111 15 penetrating penetrating NOUN iajs-3377 111 16 power power NOUN iajs-3377 111 17 [ [ X iajs-3377 111 18 20 20 NUM iajs-3377 111 19 ] ] PUNCT iajs-3377 111 20 . . PUNCT iajs-3377 112 1 hence hence ADV iajs-3377 112 2 , , PUNCT iajs-3377 112 3 we we PRON iajs-3377 112 4 are be AUX iajs-3377 112 5 expecting expect VERB iajs-3377 112 6 high high ADJ iajs-3377 112 7 penetrating penetrate VERB iajs-3377 112 8 power power NOUN iajs-3377 112 9 into into ADP iajs-3377 112 10 the the DET iajs-3377 112 11 cell cell NOUN iajs-3377 112 12 membrane membrane NOUN iajs-3377 112 13 from from ADP iajs-3377 112 14 abacavir abacavir NOUN iajs-3377 112 15 and and CCONJ iajs-3377 112 16 nevirapine nevirapine ADJ iajs-3377 112 17 , , PUNCT iajs-3377 112 18 and and CCONJ iajs-3377 112 19 these these PRON iajs-3377 112 20 are be AUX iajs-3377 112 21 used use VERB iajs-3377 112 22 to to PART iajs-3377 112 23 determine determine VERB iajs-3377 112 24 if if SCONJ iajs-3377 112 25 a a DET iajs-3377 112 26 particular particular ADJ iajs-3377 112 27 compound compound NOUN iajs-3377 112 28 is be AUX iajs-3377 112 29 good good ADJ iajs-3377 112 30 drug drug NOUN iajs-3377 112 31 candidate candidate NOUN iajs-3377 112 32 . . PUNCT iajs-3377 113 1 the the DET iajs-3377 113 2 docking docking NOUN iajs-3377 113 3 result result NOUN iajs-3377 113 4 used use VERB iajs-3377 113 5 for for ADP iajs-3377 113 6 stochastic stochastic ADJ iajs-3377 113 7 dominance dominance NOUN iajs-3377 113 8 in in ADP iajs-3377 113 9 order order NOUN iajs-3377 113 10 to to PART iajs-3377 113 11 determine determine VERB iajs-3377 113 12 the the DET iajs-3377 113 13 most most ADV iajs-3377 113 14 effective effective ADJ iajs-3377 113 15 drugs drug NOUN iajs-3377 113 16 that that PRON iajs-3377 113 17 perform perform VERB iajs-3377 113 18 actively actively ADV iajs-3377 113 19 in in ADP iajs-3377 113 20 curing cure VERB iajs-3377 113 21 the the DET iajs-3377 113 22 diseases disease NOUN iajs-3377 113 23 shows show VERB iajs-3377 113 24 better well ADJ iajs-3377 113 25 binding bind VERB iajs-3377 113 26 affinity affinity NOUN iajs-3377 113 27 and and CCONJ iajs-3377 113 28 inhibition inhibition VERB iajs-3377 113 29 constant constant ADJ iajs-3377 113 30 from from ADP iajs-3377 113 31 nevirapine nevirapine ADJ iajs-3377 113 32 as as SCONJ iajs-3377 113 33 compared compare VERB iajs-3377 113 34 to to ADP iajs-3377 113 35 abacavir abacavir NOUN iajs-3377 113 36 and and CCONJ iajs-3377 113 37 this this PRON iajs-3377 113 38 is be AUX iajs-3377 113 39 an an DET iajs-3377 113 40 indication indication NOUN iajs-3377 113 41 that that SCONJ iajs-3377 113 42 nevirapine nevirapine ADJ iajs-3377 113 43 drug drug NOUN iajs-3377 113 44 is be AUX iajs-3377 113 45 more more ADV iajs-3377 113 46 potent potent ADJ iajs-3377 113 47 for for ADP iajs-3377 113 48 curing cure VERB iajs-3377 113 49 the the DET iajs-3377 113 50 disease(hiv disease(hiv NOUN iajs-3377 113 51 ) ) PUNCT iajs-3377 113 52 . . PUNCT iajs-3377 114 1 5 5 X iajs-3377 114 2 . . X iajs-3377 114 3 conclusion conclusion NOUN iajs-3377 114 4 a a DET iajs-3377 114 5 new new ADJ iajs-3377 114 6 family family NOUN iajs-3377 114 7 of of ADP iajs-3377 114 8 distribution distribution NOUN iajs-3377 114 9 ( ( PUNCT iajs-3377 114 10 double double ADJ iajs-3377 114 11 exponential exponential NOUN iajs-3377 114 12 - - PUNCT iajs-3377 114 13 x x SYM iajs-3377 114 14 family family NOUN iajs-3377 114 15 ) ) PUNCT iajs-3377 114 16 has have AUX iajs-3377 114 17 been be AUX iajs-3377 114 18 introduced introduce VERB iajs-3377 114 19 . . PUNCT iajs-3377 115 1 two two NUM iajs-3377 115 2 distinct distinct ADJ iajs-3377 115 3 sub sub NOUN iajs-3377 115 4 - - NOUN iajs-3377 115 5 models model NOUN iajs-3377 115 6 of of ADP iajs-3377 115 7 the the DET iajs-3377 115 8 distribution distribution NOUN iajs-3377 115 9 were be AUX iajs-3377 115 10 discussed discuss VERB iajs-3377 115 11 . . PUNCT iajs-3377 116 1 it it PRON iajs-3377 116 2 is be AUX iajs-3377 116 3 shown show VERB iajs-3377 116 4 that that SCONJ iajs-3377 116 5 the the DET iajs-3377 116 6 two two NUM iajs-3377 116 7 special special ADJ iajs-3377 116 8 models model NOUN iajs-3377 116 9 ' ' PART iajs-3377 116 10 densities density NOUN iajs-3377 116 11 can can AUX iajs-3377 116 12 generally generally ADV iajs-3377 116 13 be be AUX iajs-3377 116 14 skewed skew VERB iajs-3377 116 15 to to ADP iajs-3377 116 16 the the DET iajs-3377 116 17 left left NOUN iajs-3377 116 18 or or CCONJ iajs-3377 116 19 right right ADJ iajs-3377 116 20 , , PUNCT iajs-3377 116 21 symmetrical symmetrical ADJ iajs-3377 116 22 , , PUNCT iajs-3377 116 23 reverse reverse ADJ iajs-3377 116 24 j j NOUN iajs-3377 116 25 - - PUNCT iajs-3377 116 26 shaped shaped ADJ iajs-3377 116 27 , , PUNCT iajs-3377 116 28 and and CCONJ iajs-3377 116 29 can can AUX iajs-3377 116 30 also also ADV iajs-3377 116 31 have have AUX iajs-3377 116 32 both both PRON iajs-3377 116 33 growing grow VERB iajs-3377 116 34 and and CCONJ iajs-3377 116 35 decreasing decrease VERB iajs-3377 116 36 , , PUNCT iajs-3377 116 37 as as ADV iajs-3377 116 38 well well ADV iajs-3377 116 39 as as ADP iajs-3377 116 40 , , PUNCT iajs-3377 116 41 of of ADP iajs-3377 116 42 course course NOUN iajs-3377 116 43 , , PUNCT iajs-3377 116 44 unimodal unimodal ADJ iajs-3377 116 45 . . PUNCT iajs-3377 117 1 the the DET iajs-3377 117 2 maximum maximum ADJ iajs-3377 117 3 likelihood likelihood NOUN iajs-3377 117 4 estimation estimation NOUN iajs-3377 117 5 approach approach NOUN iajs-3377 117 6 is be AUX iajs-3377 117 7 used use VERB iajs-3377 117 8 to to PART iajs-3377 117 9 estimate estimate VERB iajs-3377 117 10 the the DET iajs-3377 117 11 parameters parameter NOUN iajs-3377 117 12 . . PUNCT iajs-3377 118 1 a a DET iajs-3377 118 2 molecular molecular ADJ iajs-3377 118 3 simulation simulation NOUN iajs-3377 118 4 study study NOUN iajs-3377 118 5 that that PRON iajs-3377 118 6 compares compare VERB iajs-3377 118 7 the the DET iajs-3377 118 8 newly newly ADV iajs-3377 118 9 ihjpas ihjpa NOUN iajs-3377 118 10 . . PUNCT iajs-3377 119 1 36 36 NUM iajs-3377 119 2 ( ( PUNCT iajs-3377 119 3 3 3 NUM iajs-3377 119 4 ) ) PUNCT iajs-3377 119 5 2023 2023 NUM iajs-3377 119 6 448 448 NUM iajs-3377 119 7 built build VERB iajs-3377 119 8 model model NOUN iajs-3377 119 9 's 's PART iajs-3377 119 10 performance performance NOUN iajs-3377 119 11 to to PART iajs-3377 119 12 previous previous ADJ iajs-3377 119 13 well well ADV iajs-3377 119 14 - - PUNCT iajs-3377 119 15 known know VERB iajs-3377 119 16 distributions distribution NOUN iajs-3377 119 17 is be AUX iajs-3377 119 18 presented present VERB iajs-3377 119 19 . . PUNCT iajs-3377 120 1 there there PRON iajs-3377 120 2 are be VERB iajs-3377 120 3 derived derive VERB iajs-3377 120 4 and and CCONJ iajs-3377 120 5 explained explain VERB iajs-3377 120 6 several several ADJ iajs-3377 120 7 fundamental fundamental ADJ iajs-3377 120 8 mathematical mathematical ADJ iajs-3377 120 9 characteristics characteristic NOUN iajs-3377 120 10 of of ADP iajs-3377 120 11 the the DET iajs-3377 120 12 new new ADJ iajs-3377 120 13 family family NOUN iajs-3377 120 14 . . PUNCT iajs-3377 121 1 finally finally ADV iajs-3377 121 2 , , PUNCT iajs-3377 121 3 reallife reallife PROPN iajs-3377 121 4 applications application NOUN iajs-3377 121 5 of of ADP iajs-3377 121 6 the the DET iajs-3377 121 7 model model NOUN iajs-3377 121 8 to to ADP iajs-3377 121 9 data datum NOUN iajs-3377 121 10 sets set NOUN iajs-3377 121 11 on on ADP iajs-3377 121 12 the the DET iajs-3377 121 13 effectiveness effectiveness NOUN iajs-3377 121 14 of of ADP iajs-3377 121 15 various various ADJ iajs-3377 121 16 antiretroviral antiretroviral ADJ iajs-3377 121 17 medications medication NOUN iajs-3377 121 18 were be AUX iajs-3377 121 19 provided provide VERB iajs-3377 121 20 , , PUNCT iajs-3377 121 21 and and CCONJ iajs-3377 121 22 they they PRON iajs-3377 121 23 compare compare VERB iajs-3377 121 24 favorably favorably ADV iajs-3377 121 25 to to ADP iajs-3377 121 26 other other ADJ iajs-3377 121 27 well well ADV iajs-3377 121 28 - - PUNCT iajs-3377 121 29 known know VERB iajs-3377 121 30 distributions distribution NOUN iajs-3377 121 31 in in ADP iajs-3377 121 32 terms term NOUN iajs-3377 121 33 of of ADP iajs-3377 121 34 data datum NOUN iajs-3377 121 35 fit fit ADJ iajs-3377 121 36 , , PUNCT iajs-3377 121 37 and and CCONJ iajs-3377 121 38 the the DET iajs-3377 121 39 efficacy efficacy NOUN iajs-3377 121 40 of of ADP iajs-3377 121 41 the the DET iajs-3377 121 42 pharmaceuticals pharmaceutical NOUN iajs-3377 121 43 utilized utilize VERB iajs-3377 121 44 was be AUX iajs-3377 121 45 compared compare VERB iajs-3377 121 46 using use VERB iajs-3377 121 47 the the DET iajs-3377 121 48 stochastic stochastic ADJ iajs-3377 121 49 dominance dominance NOUN iajs-3377 121 50 approach approach NOUN iajs-3377 121 51 . . PUNCT iajs-3377 122 1 references reference NOUN iajs-3377 122 2 1 1 NUM iajs-3377 122 3 . . PUNCT iajs-3377 123 1 eugene eugene NOUN iajs-3377 123 2 , , PUNCT iajs-3377 123 3 n. n. PROPN iajs-3377 123 4 ; ; PUNCT iajs-3377 123 5 lee lee PROPN iajs-3377 123 6 , , PUNCT iajs-3377 123 7 c c X iajs-3377 123 8 ; ; PUNCT iajs-3377 123 9 famoye famoye PROPN iajs-3377 123 10 , , PUNCT iajs-3377 123 11 f. f. PROPN iajs-3377 123 12 beta beta NOUN iajs-3377 123 13 - - PUNCT iajs-3377 123 14 normal normal ADJ iajs-3377 123 15 distribution distribution NOUN iajs-3377 123 16 and and CCONJ iajs-3377 123 17 its its PRON iajs-3377 123 18 applications application NOUN iajs-3377 123 19 . . PUNCT iajs-3377 124 1 communications communication NOUN iajs-3377 124 2 in in ADP iajs-3377 124 3 statistic statistic NOUN iajs-3377 124 4 : : PUNCT iajs-3377 124 5 theory theory NOUN iajs-3377 124 6 and and CCONJ iajs-3377 124 7 methods method NOUN iajs-3377 124 8 , , PUNCT iajs-3377 124 9 2002 2002 NUM iajs-3377 124 10 ; ; PUNCT iajs-3377 124 11 31(4 31(4 NUM iajs-3377 124 12 ) ) PUNCT iajs-3377 124 13 , , PUNCT iajs-3377 124 14 497 497 NUM iajs-3377 124 15 - - SYM iajs-3377 124 16 512 512 NUM iajs-3377 124 17 . . PUNCT iajs-3377 125 1 2 2 NUM iajs-3377 125 2 . . X iajs-3377 125 3 jones jones PROPN iajs-3377 125 4 , , PUNCT iajs-3377 125 5 m. m. PROPN iajs-3377 125 6 c. c. PROPN iajs-3377 125 7 families family NOUN iajs-3377 125 8 of of ADP iajs-3377 125 9 distributions distribution NOUN iajs-3377 125 10 arising arise VERB iajs-3377 125 11 from from ADP iajs-3377 125 12 distributions distribution NOUN iajs-3377 125 13 of of ADP iajs-3377 125 14 orderstatistics orderstatistic NOUN iajs-3377 125 15 . . PUNCT iajs-3377 126 1 test test NOUN iajs-3377 126 2 , , PUNCT iajs-3377 126 3 ( ( PUNCT iajs-3377 126 4 2004 2004 NUM iajs-3377 126 5 ) ) PUNCT iajs-3377 126 6 13 13 NUM iajs-3377 126 7 : : SYM iajs-3377 126 8 1 1 NUM iajs-3377 126 9 – – SYM iajs-3377 126 10 42 42 NUM iajs-3377 126 11 . . PUNCT iajs-3377 127 1 3 3 X iajs-3377 127 2 . . X iajs-3377 128 1 zografos zografos PROPN iajs-3377 128 2 , , PUNCT iajs-3377 128 3 k. k. PROPN iajs-3377 128 4 ; ; PUNCT iajs-3377 129 1 balakrishnan balakrishnan PROPN iajs-3377 129 2 , , PUNCT iajs-3377 129 3 n. n. NOUN iajs-3377 129 4 on on ADP iajs-3377 129 5 families family NOUN iajs-3377 129 6 of of ADP iajs-3377 129 7 betaand betaand NOUN iajs-3377 129 8 generalized generalize VERB iajs-3377 129 9 gamma gamma NOUN iajs-3377 129 10 - - PUNCT iajs-3377 129 11 generated generate VERB iajs-3377 129 12 distributions distribution NOUN iajs-3377 129 13 and and CCONJ iajs-3377 129 14 associated associated ADJ iajs-3377 129 15 inference inference NOUN iajs-3377 129 16 . . PUNCT iajs-3377 130 1 statistical statistical ADJ iajs-3377 130 2 methodology methodology NOUN iajs-3377 130 3 . . PUNCT iajs-3377 131 1 2009 2009 NUM iajs-3377 131 2 , , PUNCT iajs-3377 131 3 6 6 NUM iajs-3377 131 4 , , PUNCT iajs-3377 131 5 344–362 344–362 NUM iajs-3377 131 6 . . NOUN iajs-3377 132 1 4 4 NUM iajs-3377 132 2 . . X iajs-3377 133 1 alexander alexander PROPN iajs-3377 133 2 c c PROPN iajs-3377 133 3 ; ; PUNCT iajs-3377 133 4 cordeiro cordeiro PROPN iajs-3377 133 5 g.m g.m PROPN iajs-3377 133 6 ; ; PUNCT iajs-3377 133 7 ortega ortega PROPN iajs-3377 133 8 e.m.m e.m.m PROPN iajs-3377 133 9 . . PROPN iajs-3377 133 10 ; ; PUNCT iajs-3377 133 11 sara sara PROPN iajs-3377 133 12 - - PUNCT iajs-3377 133 13 bia bia PROPN iajs-3377 133 14 j.m j.m PROPN iajs-3377 133 15 . . PROPN iajs-3377 133 16 generalized generalize VERB iajs-3377 133 17 beta beta NOUN iajs-3377 133 18 - - PUNCT iajs-3377 133 19 generated generate VERB iajs-3377 133 20 distributions distribution NOUN iajs-3377 133 21 . . PUNCT iajs-3377 134 1 computational computational ADJ iajs-3377 134 2 statistics statistic NOUN iajs-3377 134 3 and and CCONJ iajs-3377 134 4 data datum NOUN iajs-3377 134 5 analysis analysis NOUN iajs-3377 134 6 . . PUNCT iajs-3377 134 7 , , PUNCT iajs-3377 134 8 2012 2012 NUM iajs-3377 134 9 , , PUNCT iajs-3377 134 10 56:1880 56:1880 NUM iajs-3377 134 11 – – PUNCT iajs-3377 134 12 1897 1897 NUM iajs-3377 134 13 . . PUNCT iajs-3377 135 1 5 5 X iajs-3377 135 2 . . X iajs-3377 135 3 amini amini PROPN iajs-3377 135 4 , , PUNCT iajs-3377 135 5 m. m. NOUN iajs-3377 135 6 ; ; PUNCT iajs-3377 135 7 mir mir PROPN iajs-3377 135 8 mostafaee mostafaee PROPN iajs-3377 135 9 ; ; PUNCT iajs-3377 136 1 s.m s.m PROPN iajs-3377 136 2 . . PROPN iajs-3377 136 3 t.k t.k PROPN iajs-3377 136 4 . . PROPN iajs-3377 136 5 ; ; PUNCT iajs-3377 136 6 ahmadi ahmadi PROPN iajs-3377 136 7 , , PUNCT iajs-3377 136 8 j. j. PROPN iajs-3377 136 9 ( ( PUNCT iajs-3377 136 10 2012 2012 NUM iajs-3377 136 11 ) ) PUNCT iajs-3377 136 12 . . PUNCT iajs-3377 137 1 log log NOUN iajs-3377 137 2 - - PUNCT iajs-3377 137 3 gamma gamma NOUN iajs-3377 137 4 - - PUNCT iajs-3377 137 5 generated generate VERB iajs-3377 137 6 families family NOUN iajs-3377 137 7 of of ADP iajs-3377 137 8 distributions distribution NOUN iajs-3377 137 9 . . PUNCT iajs-3377 138 1 statistics statistic NOUN iajs-3377 138 2 , , PUNCT iajs-3377 138 3 ifirst.doi:10.1008/02331888.2012.748775 ifirst.doi:10.1008/02331888.2012.748775 PROPN iajs-3377 138 4 6 6 NUM iajs-3377 138 5 . . PUNCT iajs-3377 138 6 torabi torabi NOUN iajs-3377 138 7 , , PUNCT iajs-3377 138 8 h. h. PROPN iajs-3377 138 9 ; ; PUNCT iajs-3377 138 10 montazari montazari PROPN iajs-3377 138 11 , , PUNCT iajs-3377 138 12 n.h n.h PROPN iajs-3377 138 13 .. .. PUNCT iajs-3377 138 14 the the DET iajs-3377 138 15 gamma gamma NOUN iajs-3377 138 16 - - PUNCT iajs-3377 138 17 uniform uniform NOUN iajs-3377 138 18 distribution distribution NOUN iajs-3377 138 19 and and CCONJ iajs-3377 138 20 its its PRON iajs-3377 138 21 application application NOUN iajs-3377 138 22 . . PUNCT iajs-3377 139 1 kybernetika kybernetika PROPN iajs-3377 139 2 2012 2012 NUM iajs-3377 139 3 , , PUNCT iajs-3377 139 4 48:16 48:16 NUM iajs-3377 139 5 - - SYM iajs-3377 139 6 30 30 NUM iajs-3377 139 7 7 7 NUM iajs-3377 139 8 . . PUNCT iajs-3377 139 9 alzaatreh alzaatreh NOUN iajs-3377 139 10 , , PUNCT iajs-3377 139 11 a. a. NOUN iajs-3377 139 12 ; ; PUNCT iajs-3377 139 13 famoye famoye PROPN iajs-3377 139 14 , , PUNCT iajs-3377 139 15 f. f. PROPN iajs-3377 139 16 ; ; PUNCT iajs-3377 139 17 lee lee PROPN iajs-3377 139 18 , , PUNCT iajs-3377 139 19 c. c. PROPN iajs-3377 139 20 the the DET iajs-3377 139 21 gamma gamma NOUN iajs-3377 139 22 - - PUNCT iajs-3377 139 23 normal normal ADJ iajs-3377 139 24 distribution distribution NOUN iajs-3377 139 25 : : PUNCT iajs-3377 139 26 properties property NOUN iajs-3377 139 27 and and CCONJ iajs-3377 139 28 applications application NOUN iajs-3377 139 29 . . PUNCT iajs-3377 140 1 computational computational ADJ iajs-3377 140 2 statistics statistic NOUN iajs-3377 140 3 and and CCONJ iajs-3377 140 4 data datum NOUN iajs-3377 140 5 analysis analysis NOUN iajs-3377 140 6 . . PUNCT iajs-3377 140 7 2014 2014 NUM iajs-3377 140 8 , , PUNCT iajs-3377 140 9 69 69 NUM iajs-3377 140 10 , , PUNCT iajs-3377 140 11 67–80 67–80 NOUN iajs-3377 140 12 . . NOUN iajs-3377 140 13 8 8 NUM iajs-3377 140 14 . . PUNCT iajs-3377 141 1 tahir tahir PROPN iajs-3377 141 2 , , PUNCT iajs-3377 141 3 m.h m.h PROPN iajs-3377 141 4 . . 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