Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples

Table 7

95% posterior predictive intervals under different priors and censoring techniques for Ψ=2.

𝑛	Left censored			Singly type II censored			Doubly type II censored
	LL	UL	UL−LL	LL	UL	UL−LL	LL	UL	UL−LL
	Uniform prior
20	0.49523	13.47175	12.97652	0.54924	13.88351	13.33428	0.54950	14.20442	13.65491
30	0.51144	12.68323	12.17179	0.56744	13.21114	12.64370	0.56500	13.30473	12.73974
50	0.51370	12.37380	11.86010	0.56909	12.99057	12.42147	0.56585	13.00277	12.43692
70	0.52488	11.99177	11.46689	0.58051	12.64354	12.06303	0.57578	12.68553	12.10975
100	0.53920	11.35919	10.81999	0.58614	11.80088	11.21474	0.57939	11.75484	11.17545
150	0.55492	11.03062	10.47570	0.59534	11.43179	10.83645	0.58711	11.37969	10.79258
	Jeffreys prior
20	0.49548	13.40360	12.90812	0.54870	13.68310	13.13440	0.54882	14.01045	13.46163
30	0.51132	12.62235	12.11103	0.56665	13.02328	12.45663	0.56409	13.12565	12.56157
50	0.51347	12.31546	11.80199	0.56823	12.80670	12.23848	0.56488	12.82862	12.26374
70	0.52445	11.93714	11.41269	0.57950	12.46617	11.88667	0.56821	12.40388	11.83566
100	0.53846	11.31051	10.77205	0.58495	11.63757	11.05262	0.56544	11.38658	10.82113
150	0.55396	10.98561	10.43164	0.59400	11.27517	10.68117	0.56840	10.94338	10.37497
	Exponential prior
20	0.49075	13.25962	12.76887	0.54330	13.40106	12.85776	0.54339	13.60054	13.05716
30	0.50637	12.48741	11.98104	0.56101	12.75544	12.19443	0.55846	12.78659	12.22813
50	0.50847	12.18403	11.67556	0.56256	12.54351	11.98094	0.55922	12.89878	12.33956
70	0.51930	11.81020	11.29091	0.57369	12.21035	11.63665	0.56250	12.16650	11.60400
100	0.53311	11.19085	10.65774	0.57905	11.39922	10.82017	0.55973	11.31530	10.75557
150	0.54842	10.86990	10.32148	0.58798	11.04458	10.45660	0.56264	11.01827	10.45563
	Gamma prior
20	0.51282	13.31401	12.80119	0.56189	13.60967	13.04778	0.56092	13.59571	13.03479
30	0.52645	12.56240	12.03595	0.57846	12.97465	12.39619	0.57499	12.80080	12.22581
50	0.52784	12.26493	11.73709	0.57955	12.76555	12.18600	0.57534	12.91904	12.34370
70	0.53765	11.90282	11.36517	0.59010	12.43805	11.84795	0.57799	12.19526	11.61727
100	0.54986	11.30065	10.75079	0.59434	11.62805	11.03371	0.57411	11.35602	10.78191
150	0.56420	10.99298	10.42878	0.60264	11.27800	10.67536	0.57636	11.06816	10.49180
	Inverse Levy prior
20	0.50789	13.17130	12.66342	0.55634	13.36996	12.81362	0.55535	13.19078	12.63544
30	0.52132	12.42838	11.90706	0.57270	12.74670	12.17400	0.56923	12.42004	11.85081
50	0.52267	12.13433	11.61166	0.57376	12.54141	11.96765	0.56957	12.53496	11.96539
70	0.53235	11.77647	11.24412	0.58418	12.22001	11.63583	0.57217	11.83295	11.26078
100	0.54438	11.18133	10.63695	0.58834	11.42461	10.83627	0.56830	11.01905	10.45075
150	0.56126	10.91945	10.35819	0.59931	11.12563	10.52632	0.57315	10.78344	10.21029