Posterior analysis of the compound truncated Weibull under different loss functions for censored data.

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1 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 oso yss of h oou u Wu u ff oss fuos fo so. Khw BOUDJRDA Ass CHADI Ho FAG. As I hs h Bys yss of gh u Wu suo s os u y II so. Bys sos osog ss hv v usg sy sy oss fuos. Bys sos of h s hv o x fos so w o sov yy h's why w h Mo-Co hos o f h sus sy h Moos-Hsgs goh. Fy w us osss o g squ o IM o o Bys hoo sos M. Kywos Bys sos gz qu oss fuo x oss fuo Rs oss fuo o Moos- Hsgs goh. I. INRODUCION RUNCAD ss suos s wh o v X foows ow suo o x h oo of h s s o osv. If vus of h o v fg ow ow o osv h suo s s o u o h f. A u suo s f s oo suo h sus fo sg h o of h ss suo. H u suos us ss wh ous o vus whh ov o ow gv hsho o wh sf g. If ous o vus whh ow gv hsho h ow f u suo s o. y f ous o vus whh ov gv hsho h u gh u suo ss s.g Dus Coh 984. Wgo 988 oos o so of s fo ouy u Wu suo. M 989 vsg h o of xs of h M fo h u Wu suo wh h uo o s ssu o ow. Mz 99 su h M of s of h u u Wu suo. hy -Yousf 993 s ys ss of s fo ouy u Wu suo hy 993 suss h Bys s of h so. Yooy 993 Khw Bouj HD su ooy Bj Moh uvsy A Ag. - : Ass Ch ofsso ooy Bj Moh uvsy A Ag. - Ho Fg ooy f u hs Mouou M Uvsy of z-ouzou Ag - : vo s ous so ho fo h Wu u Wu s. Bsh M h M goh o s h s of Wu suo wh h o s u f gh so. h Wu suo s vy ou suo fo og f. I f uo gh sog of osv f. Fo x fus ug h wy o y o ou. Is y so f foowg h oy so h fus of h go. Aso h u Wu suo us sv gg fs s Zu 986 Mo 4 h 7. v uhos hv su h so of h u Wu suo s o. Zhg X su h hss of h u u Wu suo so y gh oh. K Us 5 oos fo h fs h us of u-u Wu suo og w s so sg w ow sy. Usg w s su vous gos of uy u-u Wu suo v fo us h ssss of w gy o. I hs w suy h so of h gh-u Wu suo whh s o h s. wo ohs oos. h fs o s h ss xu hoo so M. h so o s h Bys ou fo u h gz qu h oy h x oss fuos. Usg xhusv Mo- Co suy w o h Bys sos wh s h oso ss R. h w s h s so gv y h oss fuo. hs h ys sos o o h xu hoo so M usg osss o h g squ o IM. h s of hs s ogz s foows. I so w s h o h o. h so 3 s wh h xu hoo so. I so 4 w oos h Bys sos u vous oss fuos ff o suos. A Mo -Co suy s oos so 5. IN:

2 II. H MOD Cos o v su og o h gh u Wu suo wh h s α > β> h sy gv y:. g h osog y fuo s f s foows G R h fu s R g h : 3 h h o of h gh u Wu suo s gv y h foowg fou 3... g III. IKIHOOD IMAION Cos -s... g fo gh-u Wu o fx os {... }. h ssu o so wh y II... h osvos... osv oy. h hoo fuo s h!! W oos h foowg oos A h w hv.!! N s 4 A h osog ogh s!! 5 h M sos of h h s α souos of h vo quo h h hoo quos s foows 3 3 Af g sfoos w o h foowg o sys. ù : h s o y souo of hs sys. h w u hos o o ox vus of h xu hoo sos α M M M of h s α svy. I hs w w us h R g BB whh hs hgh s fo sovg o sys of quos Vh G 9. INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 IN:

3 III BAYIAN IMAION UNDR DIFFRN O FUNCION o oso suos I hs so w os h o suo of α hy -Youssf 993 f s foows Moov w hoos h o o of whh o o α gv y π=/. h h o of α Is. Moov w o h oso sy K 6 Wh. K A. oss fuos W os h gz qu h x h oy oss fuos. h foowg ss hs oss fuos h xssos of h Bys sos wh h osog oso ss R. U h gz qu oss fuo ssug τθ=θ β- h Bys sos gv y h fous CQ CQ CQ h osog oso ss h R R R No h wh β= w hv h s qu oss. U h oy oss fuo w o h foowg sos h oso ss R R R foowg sos U h x oss fuo w o h K K INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 IN:

4 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 K h osog oso ss R Q R Q R Q w o u h y xssos of hs sos w w us MCMC ous s Moos-Hsgs goh h foowg Mo Co so. IV MON CARO UDY I hs so w oos o fo Mo Co suy ssug h = = = α = =. =.5. h usg N = ss of h gh u o w o h foowg sus. A. hoo so y fous o v o o h xu hoo sos w o us u ous. I hs so w w us h R g BB whh ss vy hgh fos fo o syss. I u w h fuo BB sovs BB fo ou o. hs fuo offs ow-os ho o sov g-s o syss of quos Vh G 9. h sus s foows: 7 α 3 α 5 35 α 7 α 4 α : h M of h s wh qu o s W h h s vus of α os o h u vus of s. Howv h so of Is o os o h u vu. B. Bys so h ys sos o wh fog h MCMC hos. h ss h ys sos h osog oso ss s u h gz qu oss fuo. W h h vu β= gvs us h s oso s h ov h s qu s. Aso w o h ss su oso s wh s hgh. hs s us y h fgu. IN:

5 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 Fgu. oso ss of α u gz qu oss fuo Wh h oy oss fuo w o h foowg wh w o h h vu =.5 h ss = = ov h s oso s. h foowg fgu uss w hs suo. IN:

6 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 Fgu. oso ss of α u x oss fuo U h x oss fuo h sus gv h foowg. O o h h vu =.5 ovs h s R s fgu 3. Fgu. oso ss of α u h oy oss fuo If w o h h oss fuos w o h h oy oss fuo ovs h s Bys so of α. hs Is us y h foowg IN:

7 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 A. Coso wh h hoo sos I hs so w oos o o h s Bys sos o ov wh h xu hoo so. Fo hs w oos o us h foowg os: h osss 937 Fu 98 Joz h g squ o IM f s foows: Dfo 5. A so θ of θ os h ss of osss o oh so θ f fo θ Θ Cos h ss θ = N O wh N ss of h o. Dfo 5. h g squ o s f s N IM N I h foowg w s h vus of h os whh ows us o o h ys sos wh h M u h oss fuos wh β= =.5 =.5. h 5 shou s foows : wh h oy Is g h.5 h ys so Is h h M so. h w o h og o hs o - Wh s o hgh h Bys sos α B B of α h h M s α M M. h gz qu oss fuo ovs h s vus. Howv M s os o h u vu h h ys sos. - Wh s hgh h M of h h s fo h h Bys sos. h 6 ss h vus of g squ o IM of h sos Bys of h s u h oss fuo h xu hoo sos. Aog o hs o wh Is s h Bys sos α B B ov h ss IM fo α ovy o α M M. Aso h vus ov y h gz qu oss fuo vy quv o h oy x. Bu h IM of M s s h h IM of h Bys sos. If Is hgh h h Bys sos fo h h M sos h gz qu oss fuo ovs h s vus of h IM. IN:

8 INRNAIONA JOURNA OF MAHMAIC AND COMUR IN IMUAION Vou 6 IV. CONCUION I hs w o ys sos of h ghu Wu suo u ff oss fuos. I h Bys so fo h oss fuo w o h su whh oz h ys so. h ou Mo Co suy show h h oy oss fuo ovs h ss oso ss. hs s ys sos o o h xu hoo sos of h s usg h osss o h g squ o. h usg ou xhusv Mo Co ou w show h wh Is s h Bys sos fo α o fo. If s ough hgh h M s os o h u vus u ov h hghs IM h h ys sos. o ov hs o suy h ousss ss of hs sos o hs oso. M. Mo so of s sy s sg s y x sz suo fuos Rs vo vo M. h Coso of Johso s Wu u Wu fuos fo og h suo of fos ss Co oh s of s u J Fos Rs vo R. VAh A R g fo sovg g sys of o quos fo ozg hgh-so No ojv ojv fuo Jou of ss sofw vo Zhg M. X ON h u u wu suo s y os Ry gg sys sfy vo BshN. M f u gh so Wu hoo f wh uso ouo sss yss vo M.J. Joz A o o s su of osss wh oss fuo ss Y.M K I. Us Ayss of h u u Wu suo fo w s gy ovso g vo RFRNC.J.G. h oss ss of ss s o. Cg h. o vo W.A Fu Cosss of sos yo of ss vo C. Dus A.C Coh so h sgy u Wu suo wh uow uo o Couos sss-hoy hos vo Issu.7. 4 R.B. Zu Chzg suos wh of ys fos of h Wu suos Fos s vo D.R Wgo o so fo ouy u Wu suo Moo. R vo D.R Wgo h f-u Wu suo hoy ouos. s s vo M.M M R.C Dhy sg of u Wu suo Cou -hoy Mho vo Mz O s fo gz u u Wu suos. o. vo Yooy ous so of h Wu suo Moo. R 993 vo O.A hy h Bys s fo h ouy u Wu suo Moo. R vo O.A hy youf Bys yss of h s of ouy u Wu suo Moo.R vo IN:

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