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

Table 7

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=16 with varying parameters.

(𝑛,𝑟)		Asymptotic	Bootstrap	Bayes
				Jeffrey	Gamma-1	Gamma-2
1,1	𝛼	1.13535	1.441475 [3.029834]	0.6736	0.6537	0.6704
		(0.5924266, 1.7277759)	(0.802400, 2.243875)	(0.7505, 1.4241)	(0.7568, 1.4105)	(0.7517, 1.4221)
	𝛽	1.0079	1.195897 [2.431916]	0.5714	0.5585	0.5693
		(0.6011738, 1.6090738)	(0.756660, 1.952557)	(0.7766, 1.3480)	(0.7786, 1.3371)	(0.7772, 1.3465)
1,2	𝛼	1.03659	1.290073 [2.861497]	0.5053	0.4943	0.5036
		(0.6210150, 1.6576012)	(0.805222, 2.095295)	(0.8404, 1.3457)	(0.8421, 1.3364)	(0.8409, 1.3445)
	𝛽	1.96599	2.336601 [2.444149]	0.9327	0.8825	0.9249
		(1.226844, 3.192829)	(1.531410, 3.868011)	(1.6816, 2.6143)	(1.6950, 2.5775)	(1.6844, 2.6093)
1,3	𝛼	1.00217	1.238806 [2.801578]	0.4245	0.4145	0.423
		(0.6305741, 1.632746)	(0.805794, 2.044599)	(0.8848, 1.3093)	(0.8848, 1.2993)	(0.8849, 1.3079)
	𝛽	2.91598	3.471131 [2.45426]	1.2101	1.10717	1.194
		(1.856743, 4.772727)	(2.309851, 5.780982)	(2.6382, 3.8483)	(2.66343, 3.7706)	(2.6429, 3.8369)
2,1	𝛼	2.07318	2.580142 [2.861492]	1.0107	0.9546	1.0023
		(1.242028, 3.315206)	(1.610445, 4.190587)	(1.6808, 2.6915)	(1.6934, 2.6480)	(1.6835, 2.6858)
	𝛽	0.983	1.168299 [2.444144]	0.4663	0.4571	0.4646
		(0.6134203, 1.5964171)	(0.765705, 1.934004)	(0.8408, 1.3071)	(0.8407, 1.2978)	(0.8413, 1.3059)
2,2	𝛼	1.96999	2.426357 [2.768508]	0.7477	0.7211	0.7439
		(1.270139, 3.240126)	(1.611282, 4.037639)	(1.8255, 2.5732)	(1.8280, 2.5491)	(1.8264, 2.5703)
	𝛽	1.93131	2.301952 [2.461984]	0.7208	0.6938	0.7162
		(1.244336, 3.175642)	(1.545066, 3.847018)	(1.8113, 2.5321)	(1.8151, 2.5089)	(1.8123, 2.5285)
2,3	𝛼	1.93619	2.37571 [2.731208]	0.6222	0.6938	0.6192
		(1.278243, 3.214431)	(1.609624, 3.985334)	(1.8946, 2.5168)	(1.8942, 2.4972)	(1.8948, 2.5140)
	𝛽	2.87555	3.434175 [2.475603]	0.9124	0.8621	0.9042
		(1.877916, 4.753462)	(2.327609, 5.761784)	(2.8180, 3.7304)	(2.8259, 3.6880)	(2.8200, 3.7242)
3,1	𝛼	3.00653	3.716418 [2.801586]	1.2737	1.172	1.258
		(1.891721, 4.898246)	(2.417387, 6.133805)	(2.6544, 3.9281)	(2.6668, 3.8388)	(2.6585, 3.9165)
	𝛽	0.972	1.157043 [2.454261]	0.40339	0.39493	0.40167
		(0.6189131, 1.5909124)	(0.769952, 1.926994)	(0.8794, 1.28279)	(0.8769, 1.27183)	(0.8794, 1.28107)
3,2	𝛼	2.90428	3.56358 [2.73123]	0.9335	0.8884	0.9265
		(1.917364, 4.821645)	(2.414436, 5.978016)	(2.8418, 3.7753)	(2.8420, 3.7304)	(2.8427, 3.7692)
	𝛽	1.91703	2.289456 [2.475615]	0.6083	0.5889	0.6047
		(1.251943, 3.168972)	(1.551738, 3.841194)	(1.8787, 2.4870)	(1.8784, 2.4673)	(1.8795, 2.4842)
3,3	𝛼	2.87151	3.514358 [2.704448]	0.7726	0.7435	0.7682
		(1.924054, 4.795567)	(2.411125, 5.925483)	(2.9299, 3.7025)	(2.9263, 3.6698)	(2.9299, 3.6981)
	𝛽	2.8594	3.42188 [2.488985]	0.7619	0.7293	0.7564
		(1.886973, 4.746374)	(2.335907, 5.757787)	(2.9074, 3.6693)	(2.9074, 3.6367)	(2.9086, 3.6650)