Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 3

Bayes estimators and posterior risks under exponential prior.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LLF	PLF	QLF	LLF	PLF	QLF	LLF	PLF	QLF
	Ψ=2
20	2.13477	2.21640	2.08304	2.16315	2.23008	2.12182	2.15174	2.22535	2.10582
	(0.08792)	(0.08474)	(0.05947)	(0.07242)	(0.06885)	(0.05146)	(0.07950)	(0.07599)	(0.05199)
30	2.08041	2.15996	2.02999	2.10806	2.17329	2.06779	2.09694	2.16868	2.05219
	(0.05931)	(0.05717)	(0.03964)	(0.04886)	(0.04645)	(0.03431)	(0.05363)	(0.05127)	(0.02969)
50	2.05267	2.13116	2.00292	2.07995	2.14431	2.04022	2.06898	2.13976	2.02482
	(0.05108)	(0.04923)	(0.02379)	(0.04207)	(0.04000)	(0.01905)	(0.04618)	(0.04415)	(0.02115)
70	2.03152	2.10920	1.98229	2.05852	2.12222	2.01920	2.04766	2.11772	2.00397
	(0.03909)	(0.03768)	(0.01699)	(0.03220)	(0.03062)	(0.01470)	(0.03535)	(0.03379)	(0.01272)
100	1.98996	2.06606	1.94794	2.01447	2.07681	1.98421	1.99350	2.03008	1.96924
	(0.02378)	(0.02375)	(0.01189)	(0.01958)	(0.01931)	(0.00952)	(0.02149)	(0.02130)	(0.01057)
150	1.98132	2.05708	1.94045	1.99966	2.06154	1.97658	1.97933	2.00556	1.96167
	(0.01564)	(0.01574)	(0.00793)	(0.01288)	(0.01279)	(0.00635)	(0.01414)	(0.01411)	(0.00705)
	Ψ=4
20	4.15357	4.31239	4.05290	4.20877	4.33901	4.12837	4.18657	4.32980	4.09722
	(0.14566)	(0.14039)	(0.09852)	(0.11999)	(0.11407)	(0.08526)	(0.13171)	(0.12590)	(0.08614)
30	4.13101	4.28898	4.03089	4.18592	4.31544	4.10595	4.16384	4.30629	4.07498
	(0.09827)	(0.09472)	(0.06568)	(0.08095)	(0.07696)	(0.05684)	(0.08886)	(0.08494)	(0.04919)
50	4.09645	4.25309	3.99717	4.15089	4.27934	4.07160	4.12900	4.27026	4.04088
	(0.08462)	(0.08156)	(0.03941)	(0.06971)	(0.06627)	(0.03156)	(0.07652)	(0.07314)	(0.03504)
70	4.09488	4.25146	3.99564	4.14930	4.27770	4.07004	4.12742	4.26862	4.03933
	(0.06477)	(0.06243)	(0.02815)	(0.05335)	(0.05072)	(0.02436)	(0.05857)	(0.05598)	(0.02108)
100	4.01865	4.17231	3.95326	4.06814	4.19402	4.00703	4.02578	4.09966	3.97680; )
	(0.03939)	(0.03935)	(0.01970)	(0.03244)	(0.03198)	(0.01578)	(0.03561)	(0.03530)	(0.01751)
150	4.00118	4.15418	3.95066	4.03824	4.16319	3.99161	3.99717	4.05015	3.96150
	(0.02592)	(0.02607)	(0.01313)	(0.02134)	(0.02119)	(0.01051)	(0.02343)	(0.02338)	(0.01168)
	Ψ=6
20	6.41546	6.66078	6.25998	6.50073	6.70189	6.37654	6.46644	6.68767	6.32844
	(0.27675)	(0.26675)	(0.18720)	(0.22798)	(0.21674)	(0.16200)	(0.25025)	(0.23922)	(0.16367)
30	6.38063	6.62461	6.22599	6.46543	6.66549	6.34192	6.43132	6.65135	6.29407
	(0.18672)	(0.17997)	(0.12480)	(0.15381)	(0.14623)	(0.10800)	(0.16884)	(0.16139)	(0.09346)
50	6.32724	6.56918	6.17389	6.41133	6.60972	6.28886	6.37751	6.59570	6.24141
	(0.16078)	(0.15497)	(0.07488)	(0.13244)	(0.12592)	(0.05996)	(0.14538)	(0.13897)	(0.06658)
70	6.26137	6.50080	6.10962	6.34459	6.54092	6.22339	6.31113	6.52704	6.17644
	(0.12306)	(0.11861)	(0.05348)	(0.10137)	(0.09638)	(0.04629)	(0.11128)	(0.10637)	(0.04006)
100	6.08255	6.31513	5.98359	6.15746	6.34799	6.06497	6.09335	6.20517	6.01921
	(0.07485)	(0.07476)	(0.03744)	(0.06164)	(0.06077)	(0.02998)	(0.06766)	(0.06706)	(0.03328)
150	6.01008	6.23989	5.97091	6.06574	6.25343	5.99570	6.00405	6.08363	5.95047
	(0.04924)	(0.04954)	(0.02495)	(0.04055)	(0.04025)	(0.01998)	(0.04451)	(0.04442)	(0.02219)