Bayesian Estimation of the parameters of the Weibull-Weibull Length-Biased mixture distributions using time censored data
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4 x x. h Gs sl os y hoosg so l vlus whh w wll o y 0 0 fo h s. hs y sol vlu of h w ws fo h wo ool suos h followg squ: 0 x x x x.. - x x hs squ of ws osus Mov h us h vlus s o h vlus s -. hs lgoh sly gl o h - s. Fo h h o: 3 x K 3 x K. 3 x K Wh: 3 x K K s h full ool suo of h gv ll h oh s -x - h. -- Ilo of h Gs sl h Gs sl ou usg h BUGS og Bys f Usg Gs Slg whh s fly owlol fo h s h: Wh BUGS w oly o so gl sfo ou h ol of s h sofw wll ous ll h qu uv gl's. 3- Bys so u y I so : Assu h o sl of s s u o s o sv ul fuho h lfs of h fl s follow h W-
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6 hs ool os' hv y s fo h w hv o ov oly h s log-ov fuo wh s o h xg ooo. g h so vv of h logh of h ool suo 3-3 wh s o "" s gv y l s s sly gv h h ool suo 3-3 s log-ov h xg ooo h h g usg h v jo slg ou of Gls Wl 99. As sl s wh ol oso s h ool suo of h xg ooo s o us fo hs suo g ly usg s o u go s of h v jo hqu h ool suo of h sl ' ' Igog ll s 3- whh ul o h sl " " w f: l x 3-4 h ool suo of sl os' hv x s suo howv s fo suggs usg G suo sou λ G wh λ s whh o y solvg h sl o ol x λ λ A wh λ A s h s f y h o of h ool suo s gv 3-4 o h o suo sou whh s hs s g h logh of hs o s gv y: λ λ λ l l l A Dffg l λ A wh s o λ u qug h suls o o suls h h ol vlu of h λ s wh solvs h ol quo: 0
7 Fo h ol sl h ool suo gv 3-4 s g suo G [s sos E.G.004] h ool suo of h sl ' ' l x 3-5 By h s wy h fo of hs ool suggs usg g suo sou λ G usg h s ss s fo w f h h ol vlu of h λ s wh solvs h followg ol quo: 0 h g usg h -jo slg ou usg g suo sou. Fo 3-5 wll u o g suo G h - jo hqu s o h ool suo of h sh ' ' ovg ll s 3- whh ul o h sh w g h followg ool suo: l l x 3-6 S h fo of h ool os' s o y s fo w o g suo sou λ G w hoos λ suh h gvs h xu ws fou h h ol vlu of h λ s wh solvs h followg ol quo: 0 l l h g usg h -jo slg ou usg g suo sou. Fo h ool suo 3-6 s lso os.
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9 f Wh f gv svly y -4-5 s o fuo s gv y: > f f 0 Du o h olo of h llhoo fuo fo h s of ulssf osvos h xu suo s - o foul s ws o ou y Ds l. 977 y gg s ssg ol oug fo h o " " s of y l vls " j " sg whh oo h xu gv s o h of h os suh h: Ohws j j oo j j 0 Wh j. hs s h f gv o s g fo h oo "j" h h l vl s o h vlu o o f o. h l vls h s uow s whh us s fo h ol o g y gvg h s ol suo. hs foulo wll gly slfy h llhoo fuo whh s gv y: j j j j j f f f lg h sy fuo of h oo h ov llhoo ullyg y h o gv 3- gvs h followg jo oso: Γ l x l l x 3-8 Wh: j j j j j j j j j j Fo hs oso w g h followg ool suos: x
10 l x l x Γ l l x h wo fs ools hv s fos B G svly whl w us g sou o sl fo h h h fouh ool suos xol o o sl fo h ls o usg h jo ho. 4- Nul xls: o llus h ov hos wo ul xls gv low: 4-- Poso : A sl of s 00 ws g fo h W-WB xu suo wh s h s w s usg h g WBUGS ovg ws o usg 0000 os h fs 000 os w s h ol ws oh 9000 os. h suls gv h x fo whh w g: l : h Bys ss of h s of h W-WB xu suo wh v s squ o fo oso. P u vlu Es V Bs MSE P
11 Fo l o h ll h ss los o h u vlus us o g h sl ll h s ovs x h sl of h Wull oulo. 4-- No-oso : A sl of s 80 ws g fo h W-WB xu suo wh s h g sl ws so wo os of. &.4. h s w s usg h Bys ho h s y I so usg h WBUGS g. h suls gv h x fo whh h vs ss squ os w lul h followg suls w o: l : h Bys ss of h s of h W-WB xu suo wh v s squ o fo so o-oso. u..4 P P vlu Es V Bs MSE Es V Bs MSE P Fo hs l h suls gv h x w olu: - h v h squ o s wh sg h s o. - h u of os f ovg ss wh sg h s o. 3- Fo. ll h s ovs x h sl of h
12 Wull oulo. 4- Fo.4 h sl s h xg ooo us Ax h sh s ovs. - Poso : o s MC o.5% 97.5% s sl P[] E [] [] h[] h[] P[] sl: [] sl: [] sl: h[] sl: h[] sl: P[] o
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16 P[] [] o [] o o h[] o h[] o
17 fs: [] w BUGS : Bys Usg Gs Slg 000 : h: [] Ds A. P. N. M. & u D. B Mxu llhoo fo ol v h EM lgoh wh susso Joul of oyl Ssl Soy B [3] Gls W.. & Wl P. 99. Av jo slg fo Gs slg. Al Sss [4] Gu. C. & A H. O O h lly sus of wgh vs Guss ol. Joul of Ssl Plg If [5] Ms G. & Bhg. M A ouo o h DA- Gs sl fo wo- logs P ol yo. Ps-Colog [6] Mhll W. & H Eso of s of x xolly su flu suos fo so lf s. Bo [7] Pl G. P. & o C Wgh suos s-s slg wh los o wllf oulos hu fls. Bos [8] ouh E. C A f vw of Gs sl IBC sss suy. [9] Sh S. A. & Bouss N. A h Wull lgh-s suo: Pos so. Is vll fo owlo : h:s.sjouls.yea007ls07000.f [0] Sh S. A. & Bouss N. A O h lly of h Wull lgh-s suo. F Es Joul of hol Sss 3-7 Push Pulshg Hous. [] sose.g Bys f fo ulv g suo. Sss Coug.vol.0 ssu 4
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