Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

Table 8

Average 95% confidence/HPD intervals (in brackets) and bootstrap method along with their width and shape (in square brackets) for bootstrap method for complete sample 𝑛=20, 𝑟=12 with varying parameters.

(𝑛,𝑟)		Asymptotic	Bootstrap	Bayes
				Jeffrey	Gamma-1	Gamma-2
1,1	𝛼	1.80922	2.494413 [3.704015]	1.04609	0.96179	1.03549
		(0.3894311, 2.1986549)	(0.763769, 3.258183)	(0.58521, 1.63130)	(0.65815, 1.61994)	(0.60219, 1.63768)
	𝛽	1.1317	1.440344 [2.899471]	0.58801	0.57383	0.58606
		(0.5780497, 1.7097506)	(0.774531, 2.214875)	(0.79841, 1.38642)	(0.80093, 1.37476)	(0.79897, 1.38503)
1,2	𝛼	1.5505	2.090383 [3.461255]	0.7101	0.6779	0.7043
		(0.4658775, 2.0163793)	(0.772565, 2.862947)	(0.8058, 1.5159)	(0.8171, 1.4950)	(0.8094, 1.5137)
	𝛽	2.26918	2.903446 [2.942088]	0.974	0.9167	0.9661
		(1.159005, 3.428187)	(1.557071, 4.460517)	(1.7172, 2.6912)	(1.7286, 2.6453)	(1.7188, 2.6849)
1,3	𝛼	1.45582	1.948467 [3.381644]	0.5674	0.5473	0.5638
		(0.4942760, 1.9500981)	(0.777498, 2.725965)	(0.8813, 1.4487)	(0.8819, 1.4292)	(0.8827, 1.4465)
	𝛽	3.41489	4.381877 [2.966392]	1.2838	1.1625	1.265
		(1.738521, 5.153412)	(2.341215, 6.723092)	(2.7184, 4.0022)	(2.7368, 3.8993)	(2.7219, 3.9869)
2,1	𝛼	3.10101	4.180747 [3.461238]	1.4143	1.2678	1.3829
		(0.9317525, 4.0327632)	(1.545131, 5.725878)	(1.6060, 3.0203)	(1.6496, 2.9174)	(1.6259, 3.0088)
	𝛽	1.1346	1.451719 [2.942077]	0.4892	0.4771	0.4871
		(0.5795007, 1.7140960)	(0.778536, 2.230255)	(0.8650, 1.3542)	(0.8622, 1.3393)	(0.8651, 1.3522)
2,2	𝛼	2.81147	3.749764 [3.341453]	0.9754	0.9233	0.9672
		(1.018547, 3.830021)	(1.560572, 5.310336)	(1.8490, 2.8244)	(1.8515, 2.7748)	(1.8513, 2.8185)
	𝛽	2.28314	2.936211 [2.984448]	0.771	0.737	0.7653
		(1.158481, 3.441619)	(1.563132, 4.499343)	(1.8684, 2.6394)	(1.8681, 2.6051)	(1.8694, 2.6347)
2,3	𝛼	2.7054	3.594662 [3.297717]	0.7911	0.7575	0.786
		(1.050075, 3.755473)	(1.566362, 5.161024)	(1.9465, 2.7376)	(1.9422, 2.6997)	(1.9466, 2.7326)
	𝛽	3.44036	4.436749 [3.006102]	0.9862	0.9225	0.976
		(1.735746, 5.176104)	(2.348427, 6.785176)	(2.9134, 3.8996)	(2.9127, 3.8352)	(2.9144, 3.8904)
3,1	𝛼	4.36047	5.837303 [3.381616]	1.7022	1.493	1.6623
		(1.479581, 5.840054)	(2.327943, 8.165246)	(2.6367, 4.3389)	(2.6489, 4.1419)	(2.6515, 4.3138)
	𝛽	1.13673	1.458758 [2.966365]	0.4279	0.4164	0.4257
		(0.5787959, 1.7155273)	(0.779418, 2.238177)	(0.9046, 1.3325)	(0.8975, 1.3139)	(0.9042, 1.3299)
3,2	𝛼	4.05809	5.391884 [3.297632]	1.1866	1.108	1.1739
		(1.575106, 5.633193)	(2.349532, 7.741416)	(2.9198, 4.1064)	(2.9066, 4.0146)	(2.9209, 4.0948)
	𝛽	2.29357	2.957763 [3.006009]	0.6575	0.6326	0.653
		(1.157161, 3.450727)	(1.565612, 4.523375)	(1.9423, 2.5998)	(1.9347, 2.5673)	(1.9421, 2.5951)
3,3	𝛼	3.9438	5.227407 [3.269421]	1.0633	1.0157	1.0556
		(1.608629, 5.552424)	(2.356143, 7.583550)	(2.9352, 3.9985)	(2.9191, 3.9348)	(2.9352, 3.9908)
	𝛽	3.45715	4.469468 [3.026892]	0.9317	0.889	0.901
		(1.733091, 5.190240)	(2.351761, 6.821229)	(2.9117, 3.8434)	(2.9027, 3.7917)	(2.9352, 3.8362)