Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 5

Bayes estimators and posterior risks under inverse Levy prior.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LLF	PLF	QLF	LLF	PLF	QLF	LLF	PLF	QLF
	Ψ=2
20	2.15285	2.23518	2.10068	2.18147	2.24897	2.13980	2.16996	2.24420	2.12365
	(0.07731)	(0.07452)	(0.05230)	(0.06369)	(0.06055)	(0.04526)	(0.06991)	(0.06683)	(0.04572)
30	2.09803	2.17826	2.04718	2.12592	2.19170	2.08531	2.11470	2.18705	2.06957
	(0.05216)	(0.05028)	(0.03486)	(0.04297)	(0.04085)	(0.03017)	(0.04717)	(0.04509)	(0.026110)
50	2.07005	2.14921	2.01988	2.09757	2.16247	2.05750	2.08650	2.15788	2.04197
	(0.04492)	(0.04329)	(0.02092)	(0.03700)	(0.03518)	(0.01675)	(0.04061)	(0.03882)	(0.01860)
70	2.04873	2.12707	1.99908	2.07596	2.14020	2.03630	2.06501	2.13566	2.02094
	(0.03438)	(0.03314)	(0.01494)	(0.02832)	(0.02692)	(0.01293)	(0.03109)	(0.02972)	(0.01119)
100	2.00682	2.08355	1.96444	2.03153	2.09440	2.00102	2.01038	2.04728	1.98592
	(0.02091)	(0.02088)	(0.01046)	(0.01722)	(0.01698)	(0.00838)	(0.01890)	(0.01873)	(0.00930)
150	2.00673	2.08346	1.96534	2.02531	2.08798	2.00192	2.00471	2.03128	1.98682
	(0.01376)	(0.01384)	(0.00697)	(0.01133)	(0.01125)	(0.00558)	(0.01243)	(0.01241)	(0.00620)
	Ψ=4
20	4.18874	4.34891	4.08723	4.24442	4.37575	4.16333	4.22203	4.36647	4.13193
	(0.12809)	(0.12346)	(0.08664)	(0.10552)	(0.10032)	(0.07498)	(0.11583)	(0.11072)	(0.07575)
30	4.16600	4.32530	4.06503	4.22137	4.35199	4.14073	4.19910	4.34276	4.10949
	(0.08642)	(0.08330)	(0.05776)	(0.07119)	(0.06768)	(0.04999)	(0.07814)	(0.07470)	(0.04326)
50	4.13114	4.28911	4.03102	4.18605	4.31558	4.10608	4.16397	4.30643	4.07510
	(0.07441)	(0.07173)	(0.03466)	(0.06130)	(0.05828)	(0.02775)	(0.06729)	(0.06432)	(0.03082)
70	4.12956	4.28747	4.02948	4.18445	4.31393	4.10451	4.16237	4.30478	4.07354
	(0.05696)	(0.05490)	(0.02475)	(0.04692)	(0.04461)	(0.02142)	(0.05150)	(0.04923)	(0.01854)
100	4.05268	4.20765	4.02703	4.10259	4.22954	4.07060	4.05988	4.13439	4.03989
	(0.03464)	(0.03460)	(0.01733)	(0.02853)	(0.02813)	(0.01388)	(0.03132)	(0.03104)	(0.01540)
150	4.05250	4.20746	4.00132	4.09003	4.21659	4.04280	4.04843	4.10209	4.01231
	(0.02279)	(0.02293)	(0.01155)	(0.01877)	(0.01863)	(0.00925)	(0.02060)	(0.02056)	(0.01027)
	Ψ=6
20	6.46980	6.71719	6.31300	6.55579	6.75865	6.43055	6.52120	6.74431	6.38204
	(0.24337)	(0.23458)	(0.16462)	(0.20048)	(0.19060)	(0.14246)	(0.22007)	(0.21037)	(0.14393)
30	6.43467	6.68072	6.27872	6.52019	6.72195	6.39563	6.48579	6.70769	6.34738
	(0.16420)	(0.15826)	(0.10975)	(0.13526)	(0.12859)	(0.09498)	(0.14847)	(0.14193)	(0.08219)
50	6.38083	6.62482	6.22618	6.46563	6.66570	6.34212	6.43153	6.65156	6.29427
	(0.14139)	(0.13628)	(0.06585)	(0.11647)	(0.11073)	(0.05273)	(0.12785)	(0.12221)	(0.05855)
70	6.31440	6.55586	6.16137	6.39833	6.59632	6.27610	6.36458	6.58232	6.22875
	(0.10822)	(0.10431)	(0.04703)	(0.08915)	(0.08475)	(0.04070)	(0.09786)	(0.09354)	(0.03522)
100	6.13406	6.36862	6.09523	6.20961	6.40175	6.16118	6.14495	6.25773	6.11471
	(0.06582)	(0.06574)	(0.03292)	(0.05421)	(0.05344)	(0.02637)	(0.05950)	(0.05897)	(0.02926)
150	6.08716	6.31992	6.04748	6.14353	6.33363	6.07259	6.08105	6.16165	6.02679
	(0.04330)	(0.04356)	(0.02194)	(0.03566)	(0.03540)	(0.01757)	(0.03914)	(0.03906)	(0.01952)