Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 2

Bayes estimators and posterior risks under Jeffreys prior.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LLF	PLF	QLF	LLF	PLF	QLF	LLF	PLF	QLF
	Ψ=2
20	2.15700	2.23948	2.10472	2.18567	2.25330	2.14392	2.17414	2.24852	2.12774
	(0.09013)	(0.08687)	(0.06096)	(0.07425)	(0.07059)	(0.05276)	(0.08150)	(0.07791)	(0.05330)
30	2.10207	2.18245	2.05113	2.13001	2.19592	2.08932	2.11878	2.19126	2.07356
	(0.06081)	(0.05861)	(0.04064)	(0.05009)	(0.04762)	(0.03517)	(0.05499)	(0.05256)	(0.03044)
50	2.07404	2.15335	2.02377	2.10161	2.16664	2.06146	2.09052	2.16204	2.04591
	(0.05236)	(0.05047)	(0.02439)	(0.04313)	(0.04101)	(0.01953)	(0.04735)	(0.04526)	(0.02168)
70	2.05268	2.13117	2.00293	2.07996	2.14432	2.04022	2.06899	2.13977	2.02483
	(0.04008)	(0.03863)	(0.01742)	(0.03301)	(0.03139)	(0.01507)	(0.03624)	(0.03464)	(0.01304)
100	2.01068	2.08757	1.96822	2.03545	2.09843	2.00487	2.01425	2.05122	1.98975
	(0.02438)	(0.02435)	(0.01219)	(0.02007)	(0.01979)	(0.00976)	(0.02204)	(0.02184)	(0.01084)
150	2.00195	2.07850	1.96066	2.02049	2.08301	1.99716	1.99994	2.02645	1.98209
	(0.01604)	(0.01613)	(0.00813)	(0.01321)	(0.01311)	(0.00651)	(0.01449)	(0.01447)	(0.00723)
	Ψ=4
20	4.19681	4.35729	4.09510	4.25259	4.38418	4.17136	4.23016	4.37488	4.13988
	(0.14933)	(0.14393)	(0.10101)	(0.12301)	(0.11695)	(0.08741)	(0.13503)	(0.12907)	(0.08831)
30	4.17403	4.33363	4.07286	4.22950	4.36038	4.14870	4.20719	4.35113	4.11741
	(0.10075)	(0.09711)	(0.06734)	(0.08299)	(0.07890)	(0.05827)	(0.09110)	(0.08708)	(0.05043)
50	4.13910	4.29737	4.03879	4.19411	4.32389	4.11399	4.17199	4.31472	4.08295
	(0.08675)	(0.08362)	(0.04040)	(0.07146)	(0.06794)	(0.03235)	(0.07844)	(0.07499)	(0.03593)
70	4.13752	4.29573	4.03724	4.19251	4.32224	4.11242	4.17039	4.31307	4.08139
	(0.06640)	(0.06400)	(0.02886)	(0.05470)	(0.05200)	(0.02497)	(0.06004)	(0.05739)	(0.02161)
100	4.06049	4.21575	3.99442	4.11049	4.23769	4.04875	4.06770	4.14235	4.01821
	(0.04039)	(0.04034)	(0.02020)	(0.03326)	(0.03279)	(0.01618)	(0.03651)	(0.03618)	(0.01795)
150	4.04284	4.19743	3.99179	4.08028	4.20654	4.03317	4.03879	4.09232	4.00275
	(0.02657)	(0.02673)	(0.01346)	(0.02188)	(0.02172)	(0.01078)	(0.02402)	(0.02397)	(0.01198)
	Ψ=6
20	6.48226	6.73013	6.32516	6.56842	6.77167	6.44294	6.53377	6.75730	6.39433
	(0.28372	(0.27346)	(0.19191)	(0.23372)	(0.22220)	(0.16608)	(0.25655)	(0.24524)	(0.16779)
30	6.44706	6.69359	6.29081	6.53275	6.73489	6.40795	6.49829	6.72061	6.35961
	(0.19142	(0.18450)	(0.12794)	(0.15768)	(0.14991)	(0.11072)	(0.17309)	(0.16546)	(0.09582)
50	6.39312	6.63758	6.23817	6.47809	6.67854	6.35434	6.44391	6.66438	6.30640
	(0.16483	(0.15887)	(0.07676)	(0.13578)	(0.12909)	(0.06147)	(0.14905)	(0.14247)	(0.06826)
70	6.32657	6.56848	6.17324	6.41065	6.60902	6.28819	6.37684	6.59500	6.24075
	(0.12616	(0.12160)	(0.05483)	(0.10393)	(0.09880)	(0.04745)	(0.11408)	(0.10905)	(0.04106)
100	6.14588	6.38089	6.04589	6.22157	6.41409	6.12811	6.15679	6.26978	6.08189
	(0.07673	(0.07664)	(0.03838)	(0.06319)	(0.06230)	(0.03074)	(0.06936)	(0.06875)	(0.03411)
150	6.07266	6.30486	6.03308	6.12889	6.31854	6.05813	6.06656	6.14697	6.01243
	(0.05048	(0.05079)	(0.02558)	(0.04158)	(0.04127)	(0.02048)	(0.04563)	(0.04554)	(0.02275)