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

Table 2

MSEs and Abs. Biases (in parenthesis) for the failure rate 𝐹(𝑡).

𝑛		𝛼=0.5		𝛼=1.5
		𝛽=0.8	𝛽=1.2	𝛽=0.8	𝛽=1.2
25	ML	3.68099 (0.54756)	0.67105 (0.70131)	0.32433 (0.22685)	0.08476 (0.24458)
	BS	3.68274 (0.54755)	0.67104 (0.70129)	0.32525 (0.22687)	0.08476 (0.24581)
	BL (𝑐=1)	2.90228 (0.64591)	0.73442 (0.73753)	0.22901 (0.21768)	0.08163 (0.24202)
	BL (𝑐=−1)	3.26232 (0.65045)	0.73879 (0.72318)	0.83318 (0.22460)	0.07709 (0.23813)
	BL (𝑐=2)	2.82598 (0.65421)	0.73698 (0.73324)	0.46876 (0.21809)	0.07626 (0.23769)
	BL (𝑐=−2)	2.05587 (0.66813)	0.71049 (0.71956)	0.28028 (0.22308)	0.07876 (0.23947)
	BG (𝑘=1)	3.45630 (0.64855)	0.70479 (0.72267)	0.51944 (0.21948)	0.07729 (0.23826)
	BG (𝑘=−1)	3.38251 (0.66240)	0.68825 (0.71194)	0.43598 (0.21791)	0.07829 (0.23991)
	BG (𝑘=2)	2.74521 (0.68257)	0.68329 (0.70471)	0.53684 (0.22410)	0.07949 (0.24022)
	BG (𝑘=−2)	2.63739 (0.67368)	0.64373 (0.69148)	0.32230 (0.21216)	0.08217 (0.24390)
50	ML	2.74229 (0.54756)	0.55963 (0.66088)	0.10479 (0.18498)	0.05991 (0.21456)
	BS	2.74207 (0.54755)	0.55962 (0.66087)	0.10482 (0.18497)	0.05991 (0.21246)
	BL (𝑐=1)	2.06952 (0.56294)	0.55590 (0.66412)	0.09266 (0.18624)	0.06056 (0.21627)
	BL (𝑐=−1)	2.07558 (0.55519)	0.54833 (0.65331)	0.10693 (0.18579)	0.06066 (0.21665)
	BL (𝑐=2)	1.66649 (0.56345)	0.54094 (0.64491)	0.08616 (0.18786)	0.06103 (0.21764)
	BL (𝑐=−2)	1.48847 (0.56854)	0.57137 (0.66531)	0.11013 (0.18562)	0.05871 (0.21287)
	BG (𝑘=1)	2.35703 (0.57154)	0.55850 (0.65845)	0.09676 (0.18616)	0.05904 (0.21293)
	BG (𝑘=−1)	1.06927 (0.56011)	0.54374 (0.64790)	0.16384 (0.18465)	0.06124 (0.21868)
	BG (𝑘=2)	1.05864 (0.55842)	0.56163 (0.66459)	0.08869 (0.18615)	0.06057 (0.21822)
	BG (𝑘=−2)	0.85649 (0.55619)	0.52414 (0.63780)	0.08375 (0.18829)	0.06088 (0.21713)
100	ML	0.67729 (0.53509)	0.50136 (0.64635)	0.05015 (0.17142)	0.05539 (0.21498)
	BS	0.67733 (0.53509)	0.50136 (0.64635)	0.05015 (0.17142)	0.05539 (0.21498)
	BL (𝑐=1)	0.45556 (0.52062)	0.49361 (0.64479)	0.06047 (0.17411)	0.05607 (0.21656)
	BL (𝑐=−1)	0.42816 (0.52640)	0.47733 (0.63167)	0.09317 (0.17839)	0.05342 (0.21074)
	BL (𝑐=2)	0.48344 (0.52865)	0.49163 (0.64201)	0.04895 (0.17618)	0.05405 (0.21265)
	BL (𝑐=−2)	0.47254 (0.52719)	0.49932 (0.64575)	0.05123 (0.17538)	0.05406 (0.21182)
	BG (𝑘=1)	0.44526 (0.52608)	0.50362 (0.65328)	0.05159 (0.17252)	0.05432 (0.21427)
	BG (𝑘=−1)	0.51433 (0.53095)	0.48884 (0.63931)	0.06519 (0.17545)	0.05395 (0.21272)
	BG (𝑘=2)	0.44763 (0.51844)	0.50123 (0.64629)	0.07165 (0.17638)	0.05428 (0.21193)
	BG (𝑘=−2)	0.46723 (0.51550)	0.48396 (0.63387)	0.05236 (0.17513)	0.05526 (0.21548)

ML: maximum likelihood, BG: general entropy loss function, BL: LINEX loss function, BS: squared error loss function.