Bayesian Analysis of the Survival Function and Failure Rate of Weibull Distribution with Censored Data

Table 3

MSEs and Abs. Biases (in parenthesis) for the survival function 𝑆(𝑡) using GNP.

		𝛼=0.5		𝛼=1.5
𝑛		𝛽=0.8	𝛽=1.2	𝛽=0.8	𝛽=1.2
		𝑎=5, [3]		𝑎=5, [3]
25	BS	0.01671 (0.10237)	0.01731 (0.10550)	0.01553 (0.09804)	0.01740 (0.10389)
		[0.01528 (0.09853)]	[0.01733 (0.10441)]	[0.01632 (0.10123)]	[0.01861 (0.10795)]
	BL (𝑐=1)	0.01736 (0.01025)	0.01608 (0.10052)	0.01531 (0.09805)	0.01694 (0.10227)
		[0.01559 (0.09876)]	[0.01726 (0.10385)]	[0.01585 (0.09796)]	[0.01755 (0.10476)]
	BL (𝑐=−1)	0.01756 (0.10315)	0.01655 (0.10308)	0.01614 (0.10075)	0.01748 (0.10470)
		[0.01544 (0.09803)]	[0.01806 (0.10735)]	[0.01680 (0.10254)]	[0.01727 (0.10453)]
	BL (𝑐=2)	0.01797 (0.10635)	0.01649 (0.10116)	0.01467 (0.09588)	0.01718 (0.10317)
		[0.01716 (0.10194)]	[0.01806 (0.10617)]	[0.01506 (0.09667)]	[0.01793 (0.10640)]
	BL (𝑐=−2)	0.01756 (0.10499)	0.01637 (0.10090)	0.01571 (0.09796)	0.01748 (0.10551)
		[0.01554 (0.09817)]	[0.01732 (0.10397)]	[0.01602 (0.10003)]	[0.01857 (0.10914)]
	BG (𝑘=1)	0.01645 (0.10157)	0.01659 (0.10271)	0.01587 (0.09919)	0.01719 (0.10355)
		[0.01519 (0.09767)]	[0.01741 (0.10468)]	[0.01649 (0.10107)]	[0.01782 (0.10583)]
	BG (𝑘=−1)	0.01660 (0.10067)	0.01734 (0.10515)	0.01621 (0.09978)	0.01808 (0.10817)
		[0.01554 (0.09757)]	[0.01609 (0.10096)]	[0.01539 (0.09644)]	[0.01793 (0.10731)]
	BG (𝑘=2)	0.01794 (0.10643)	0.01773 (0.10477)	0.01653 (0.10009)	0.01688 (0.10393)
		[0.01551 (0.09821)]	[0.01690 (0.10249)]	[0.01518 (0.09757)]	[0.01667 (0.10306)]
	BG (𝑘=−2)	0.01623 (0.10158)	0.01730 (0.10519)	0.01562 (0.09759)	0.01748 (0.10465)
		[0.01654 (0.10175)]	[0.01773 (0.10552)]	[0.01636 (0.10043)]	[0.01822 (0.10797)]
50	BS	0.01178 (0.08765)	0.01299 (0.09209)	0.01174 (0.08754)	0.01312 (0.09343)
		[0.01163 (0.08629)]	[0.01255 (0.09154)]	[0.01163 (0.08679)]	[0.01272 (0.09223)]
	BL (𝑐=1)	0.01092 (0.08456)	0.01259 (0.09203)	0.01134 (0.08587)	0.01276 (0.09198)
		[0.01128 (0.08459)]	[0.01284 (0.09326)]	[0.01181 (0.08617)]	[0.01289 (0.09290)]
	BL (𝑐=−1)	0.01201 (0.08874)	0.01266 (0.09119)	0.01149 (0.08649)	0.01270 (0.09149)
		[0.01118 (0.08561)]	[0.01274 (0.09196)]	[0.01126 (0.08554)]	[0.01251 (0.09036)]
	BL (𝑐=2)	0.01126 (0.08480)	0.01288 (0.09267)	0.01164 (0.08756)	0.01307 (0.09326)
		[0.01149 (0.08640)]	[0.01261 (0.09249)]	[0.01106 (0.08521)]	[0.01335 (0.09481)]
	BL (𝑐=−2)	0.01119 (0.08567)	0.01304 (0.09343)	0.01135 (0.08484)	0.01299 (0.09379)
		[0.01158 (0.08676)]	[0.01234 (0.09038)]	[0.01209 (0.08853)]	[0.01310 (0.09310)]
	BG (𝑘=1)	0.01109 (0.08496)	0.01322 (0.09375)	0.01137 (0.08565)	0.01309 (0.09474)
		[0.01111 (0.08467)]	[0.01287 (0.09549)]	[0.01176 (0.08690)]	[0.01279 (0.09197)]
	BG (𝑘=−1)	0.01187 (0.08821)	0.01365 (0.09533)	0.01191 (0.08832)	0.01263 (0.09130)
		[0.01147 (0.08608)]	[0.01289 (0.09229)]	[0.01126 (0.08621)]	[0.01298 (0.09259)]
	BG (𝑘=2)	0.01135 (0.08535)	0.01307 (0.09349)	0.01126 (0.08878)	0.01361 (0.09489)
		[0.01197 (0.08815)]	[0.01257 (0.09113)]	[0.01145 (0.08588)]	[0.01251 (0.09138)]
	BG (𝑘=−2)	0.01199 (0.08802)	0.01325 (0.09363)	0.01232 (0.08958)	0.01259 (0.09138)
		[0.01166 (0.08674)]	[0.01299 (0.09296)]	[0.01138 (0.08564)]	[0.01302 (0.09359)]
100	BS	0.00967 (0.08273)	0.01069 (0.08780)	0.00935 (0.08153)	0.01107 (0.08928)
		[0.00936 (0.08143)]	[0.01087 (0.08831)]	[0.00929 (0.08039)]	[0.01084 (0.08928)]
	BL (𝑐=1)	0.00984 (0.08327)	0.01084 (0.08875)	0.00867 (0.07797)	0.01061 (0.08743)
		[0.00961 (0.08267)]	[0.01090 (0.08894)]	[0.00969 (0.08240)]	[0.01093 (0.08894)]
	BL (𝑐=−1)	0.00951 (0.08128)	0.01051 (0.08688)	0.00975 (0.08276)	0.01119 (0.08929)
		[0.00925 (0.08078)]	[0.01043 (0.08648)]	[0.00963 (0.08201)]	[0.01110 (0.08923)]
	BL (𝑐=2)	0.00937 (0.08062)	0.01064 (0.08733)	0.00929 (0.08096)	0.01105 (0.08896)
		[0.00973 (0.08233)]	[0.01101 (0.08887)]	[0.00969 (0.08302)]	[0.01118 (0.09015)]
	BL (𝑐=−2)	0.00952 (0.08184)	0.01098 (0.08906)	0.00966 (0.08244)	0.01087 (0.08856)
		[0.00994 (0.08372)]	[0.01102 (0.08887)]	[0.00938 (0.08141)]	[0.01094 (0.08877)]
	BG (𝑘=1)	0.00895 (0.07874)	0.01091 (0.08838)	0.00946 (0.08088)	0.01059 (0.08729)
		[0.00926 (0.08019)]	[0.01093 (0.08855)]	[0.00955 (0.08214)]	[0.01108 (0.08918)]
	BG (𝑘=−1)	0.00914 (0.08047)	0.01093 (0.08833)	0.00956 (0.08156)	0.01078 (0.08802)
		[0.00897 (0.07956)]	[0.01091 (0.08844)]	[0.00985 (0.08260)]	[0.01001 (0.08491)]
	BG (𝑘=2)	0.00929 (0.08071)	0.01106 (0.08889)	0.00921 (0.07979)	0.01142 (0.09069)
		[0.00963 (0.08220)]	[0.01111 (0.08947)]	[0.00975 (0.08284)]	[0.01092 (0.08865)]
	BG (𝑘=−2)	0.00936 (0.08122)	0.01128 (0.09042)	0.00990 (0.08379)	0.01111 (0.08941)
		[0.00961 (0.08213)]	[0.01072 (0.08811)]	[0.00947 (0.08152)]	[0.01132 (0.09072)]

GNP: generalised nonInformative prior, BG: general entropy loss function, BL: LINEX loss function, BS: squared error loss function.