Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 1

Bayes estimators and posterior risks under uniform prior.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LLF	PLF	QLF	LLF	PLF	QLF	LLF	PLF	QLF
	Ψ=2
20	2.16360	2.24633	2.11116	2.19235	2.26019	2.15047	2.18079	2.25540	2.13425
	(0.09240)	(0.08906)	(0.06250)	(0.07612)	(0.07236)	(0.05409)	(0.08355)	(0.07987)	(0.05465)
30	2.10850	2.18912	2.05740	2.13652	2.20263	2.09571	2.12525	2.19796	2.07990
	(0.06234)	(0.06009)	(0.04167)	(0.05135)	(0.04882)	(0.03606)	(0.05637)	(0.05389)	(0.03121)
50	2.08038	2.15993	2.02996	2.10803	2.17326	2.06776	2.09691	2.16865	2.05216
	(0.05368)	(0.05174)	(0.02500)	(0.04422)	(0.04204)	(0.02002)	(0.04854)	(0.04640)	(0.02223)
70	2.05895	2.13768	2.00905	2.08631	2.15087	2.04646	2.07531	2.14631	2.03102
	(0.04109)	(0.03960)	(0.01786)	(0.03385)	(0.03218)	(0.01545)	(0.03715)	(0.03551)	(0.01337)
100	2.01683	2.09395	1.97424	2.04167	2.10484	2.01100	2.02041	2.05749	1.99583
	(0.02499)	(0.02496)	(0.01250)	(0.02058)	(0.02029)	(0.01001)	(0.02259)	(0.02239)	(0.01111)
150	2.00807	2.08485	1.96665	2.02666	2.08937	2.00326	2.00605	2.03264	1.98815
	(0.01644)	(0.01654)	(0.00833)	(0.01354)	(0.01344)	(0.00667)	(0.01486)	(0.01483)	(0.00741)
	Ψ=4
20	4.20964	4.37061	4.10762	4.26559	4.39758	4.18411	4.24309	4.38826	4.15254
	(0.15309)	(0.14755)	(0.10355)	(0.12611)	(0.11989)	(0.08961)	(0.13843)	(0.13232)	(0.09054)
30	4.18678	4.34688	4.08531	4.24243	4.37371	4.16139	4.22005	4.36443	4.12999
	(0.10328)	(0.09955)	(0.06903)	(0.08508)	(0.08089)	(0.05974)	(0.09339)	(0.08928)	(0.05170)
50	4.15175	4.31051	4.05113	4.20693	4.33711	4.12657	4.18474	4.32791	4.09543
	(0.08894)	(0.08572)	(0.04142)	(0.07326)	(0.06965)	(0.03317)	(0.08042)	(0.07687)	(0.03683)
70	4.15016	4.30886	4.04958	4.20532	4.33545	4.12499	4.18314	4.32625	4.09387
	(0.06807)	(0.06561)	(0.02959)	(0.05608)	(0.05331)	(0.02560)	(0.06155)	(0.05884)	(0.02216)
100	4.07290	4.22864	4.00663	4.12306	4.25064	4.06113	4.08013	4.15501	4.03049
	(0.04140)	(0.04135)	(0.02071)	(0.03410)	(0.03362)	(0.01658)	(0.03743)	(0.03710)	(0.01841)
150	4.05520	4.21026	4.00399	4.09275	4.21940	4.04550	4.05113	4.10483	4.01498
	(0.02724)	(0.02740)	(0.01380)	(0.02243)	(0.02227)	(0.01105)	(0.02462)	(0.02457)	(0.01228)
	Ψ=6
20	6.50207	6.75070	6.34449	6.58849	6.79236	6.46263	6.55374	6.77796	6.41388
	(0.29086)	(0.28035)	(0.19674)	(0.23960)	(0.22779)	(0.17026)	(0.26301)	(0.25142)	(0.17202)
30	6.46677	6.71405	6.31004	6.55272	6.75548	6.42754	6.51815	6.74115	6.37905
	(0.19624)	(0.18915)	(0.13116)	(0.16166)	(0.15369)	(0.11351)	(0.17745)	(0.16962)	(0.09823)
50	6.41266	6.65787	6.25724	6.49789	6.69896	6.37376	6.46361	6.68475	6.32567
	(0.16898)	(0.16287)	(0.07870)	(0.13920)	(0.13234)	(0.06302)	(0.15280)	(0.14606)	(0.06998)
70	6.41020	6.65532	6.25485	6.49540	6.69639	6.37132	6.46114	6.68219	6.32325
	(0.12934)	(0.12466)	(0.05621)	(0.10654)	(0.10129)	(0.04865)	(0.11695)	(0.11180)	(0.04210)
100	6.29087	6.53142	6.18852	6.36834	6.56540	6.27268	6.30203	6.41769	6.22537
	(0.07867)	(0.07857)	(0.03935)	(0.06478)	(0.06387)	(0.03151)	(0.07111)	(0.07048)	(0.03497)
150	6.26353	6.50303	6.18443	6.32153	6.51714	6.24854	6.25724	6.34018	6.20141
	(0.05175)	(0.05207)	(0.02622)	(0.04262)	(0.04231)	(0.02100)	(0.04678)	(0.04668)	(0.02333)