Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 4

Bayes estimators and posterior risks under gamma prior.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LLF	PLF	QLF	LLF	PLF	QLF	LLF	PLF	QLF
	Ψ=2
20	2.17527	2.25845	2.12255	2.20418	2.27239	2.16207	2.19255	2.26757	2.14576
	(0.07926)	(0.07640)	(0.05361)	(0.06529)	(0.06207)	(0.04640)	(0.07167)	(0.06851)	(0.04688)
30	2.11988	2.20094	2.06850	2.14805	2.21452	2.10702	2.13672	2.20982	2.09112
	(0.05347)	(0.05154)	(0.03574)	(0.04405)	(0.04188)	(0.03093)	(0.04835)	(0.04622)	(0.02677)
50	2.09161	2.17159	2.04091	2.11941	2.18499	2.07892	2.10823	2.18035	2.06323
	(0.04605)	(0.04438)	(0.02144)	(0.03793)	(0.03606)	(0.01717)	(0.04164)	(0.03980)	(0.01907)
70	2.07006	2.14922	2.01989	2.09757	2.16248	2.05750	2.08651	2.15789	2.04198
	(0.03524)	(0.03397)	(0.01532)	(0.02903)	(0.02760)	(0.01326)	(0.03187)	(0.03046)	(0.01147)
100	2.02771	2.10525	1.98489	2.05268	2.11620	2.02185	2.03131	2.06859	2.00660
	(0.02144)	(0.02141)	(0.01072)	(0.01765)	(0.01740)	(0.00859)	(0.01938)	(0.01921)	(0.00953)
150	2.01890	2.09610	1.97726	2.03760	2.10065	2.01407	2.01687	2.04361	1.99888
	(0.01410)	(0.01419)	(0.00715)	(0.01161)	(0.01153)	(0.00572)	(0.01275)	(0.01272)	(0.00636)
	Ψ=4
20	4.23236	4.39420	4.12978	4.28861	4.42131	4.20668	4.26599	4.41194	4.17495
	(0.13132)	(0.12657)	(0.08882)	(0.10817)	(0.10284)	(0.07687)	(0.11874)	(0.11351)	(0.07766)
30	4.20938	4.37034	4.10736	4.26532	4.39731	4.18384	4.24282	4.38798	4.15228
	(0.08860)	(0.08539)	(0.05922)	(0.07298)	(0.06938)	(0.05125)	(0.08011)	(0.07658)	(0.04435)
50	4.17416	4.33377	4.07299	4.22963	4.36051	4.14883	4.20732	4.35126	4.11753
	(0.07629)	(0.07353)	(0.03553)	(0.06284)	(0.05975)	(0.02845)	(0.06898)	(0.06594)	(0.03159)
70	4.17256	4.33211	4.07143	4.22801	4.35884	4.14725	4.20571	4.34960	4.11596
	(0.05839)	(0.05628)	(0.02538)	(0.04810)	(0.04573)	(0.02196)	(0.05280)	(0.05047)	(0.01901)
100	4.09488	4.25146	4.02825	4.14531	4.27358	4.08304	4.10215	4.17743	4.05224
	(0.03552)	(0.03547)	(0.01776)	(0.02925)	(0.02884)	(0.01423)	(0.03210)	(0.03182)	(0.01579)
150	4.07708	4.23298	4.02560	4.11484	4.24217	4.06733	4.07299	4.12698	4.03665
	(0.02336)	(0.02351)	(0.01184)	(0.01924)	(0.01910)	(0.00948)	(0.02112)	(0.02108)	(0.01053)
	Ψ=6
20	6.53716	6.78713	6.37873	6.62405	6.82902	6.49750	6.58910	6.81453	6.44849
	(0.24950)	(0.24048)	(0.16877)	(0.20553)	(0.19540)	(0.14605)	(0.22561)	(0.21566)	(0.14756)
30	6.50166	6.75028	6.34409	6.58808	6.79193	6.46222	6.55332	6.77753	6.41347
	(0.16833)	(0.16225)	(0.11251)	(0.13867)	(0.13183)	(0.09737)	(0.15221)	(0.14550)	(0.08426)
50	6.44726	6.69379	6.29101	6.53295	6.73511	6.40815	6.49849	6.72082	6.35981
	(0.14495)	(0.13971)	(0.06751)	(0.11940)	(0.11352)	(0.05406)	(0.13107)	(0.12529)	(0.06003)
70	6.38015	6.62412	6.22552	6.46495	6.66500	6.34145	6.43084	6.65086	6.29360
	(0.11094)	(0.10693)	(0.04822)	(0.09139)	(0.08689)	(0.04173)	(0.10032)	(0.09590)	(0.03611)
100	6.19793	6.43493	6.09709	6.27426	6.46841	6.18002	6.20893	6.32288	6.13340
	(0.06748)	(0.06740)	(0.03375)	(0.05557)	(0.05479)	(0.02703)	(0.06100)	(0.06046)	(0.03000)
150	6.12409	6.35826	6.08418	6.18080	6.37206	6.10943	6.11794	6.19903	6.06335
	(0.04439)	(0.04466)	(0.02249)	(0.03656)	(0.03629)	(0.01801)	(0.04013)	(0.04004)	(0.02001)