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

Table 6

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 with varying parameters.

(𝑛,𝑟)		Asymptotic	Bootstrap	Bayes
				Jeffrey	Gamma-1	Gamma-2
1,1	𝛼	0.84323	1.024972 [2.695397]	0.51464	0.506	0.51346
		(0.6923179, 1.5355495)	(0.836569, 1.861541)	(0.81088, 1.32552)	(0.81256, 1.31856)	(0.81082, 1.32428)
	𝛽	0.94998	1.086861 [2.203492]	0.56244	0.5504	0.56069
		(0.6150548, 1.5650366)	(0.750772, 1.837632)	(0.76999, 1.33243)	(0.77297, 1.32337)	(0.77060, 1.33129)
1,2	𝛼	0.79894	0.9567911 [2.582233]	0.40899	0.40252	0.40818
		(0.7039037, 1.5028432)	(0.836280, 1.793071)	(0.86641, 1.27540)	(0.86717, 1.26969)	(0.86644, 1.27462)
	𝛽	1.80953	2.068489 [2.192656]	0.90842	0.86205	0.9015
		(1.272122, 3.081648)	(1.528995, 3.597484)	(1.66685, 2.57527)	(1.68082, 2.54287)	(1.66961, 2.57111)
1,3	𝛼	0.78582	0.9352116 [2.53492]	0.3523	0.3457	0.35143
		(0.7063879, 1.4922066)	(0.834733, 1.769945)	(0.89762, 1.24992)	(0.89777, 1.24347)	(0.89765, 1.24908)
	𝛽	2.65059	3.034498 [2.197503]	1.17065	1.07699	1.15653
		(1.937839, 4.588432)	(2.314114, 5.348612)	(2.61358, 3.78423)	(2.63980, 3.71679)	(2.61865, 3.77518)
2,1	𝛼	1.59788	1.913583 [2.582236]	0.81799	0.78679	0.81391
		(1.407806, 3.005689)	(1.672561, 3.586144)	(1.73282, 2.55081)	(1.73930, 2.52609)	(1.73389, 2.54780)
	𝛽	0.90477	1.034245 [2.19266]	0.45421	0.44617	0.45288
		(0.6360592, 1.5408260)	(0.764498, 1.798743)	(0.83341, 1.28762)	(0.83447, 1.28064)	(0.83390, 1.28678)
2,2	𝛼	1.56103	1.851625 [2.507755]	0.63	0.6128	0.6276
		(1.413654, 2.974686)	(1.666304, 3.517929)	(1.8373, 2.4673)	(1.8391, 2.4519)	(1.8379, 2.4655)
	𝛽	1.74157	1.996533 [2.203399]	0.6938	0.6703	0.6904
		(1.303866, 3.045431)	(1.551394, 3.547927)	(1.7936, 2.4874)	(1.7980, 2.4683)	(1.7945, 2.4849)
2,3	𝛼	1.55385	1.836112 [2.47468]	0.5332	0.52	0.5314
		(1.412461, 2.966312)	(1.660960, 3.497072)	(1.8912, 2.4244)	(1.8915, 2.4115)	(1.8919, 2.4233)
	𝛽	2.56731	2.948256 [2.214166]	0.8724	0.8288	0.866
		(1.977191, 4.544503)	(2.343578, 5.291834)	(2.7883, 3.6607)	(2.7967, 3.6255)	(2.7900, 3.6560)
3,1	𝛼	2.35746	2.805634 [2.534927]	1.05692	0.99444	1.04846
		(2.119162, 4.476625)	(2.504204, 5.309838)	(2.69286, 3.74978)	(2.70190, 3.69634)	(2.69436, 3.74282)
	𝛽	0.88353	1.0115 [2.197506]	0.39022	0.38322	0.389
		(0.6459449, 1.5294797)	(0.771372, 1.782872)	(0.87118, 1.26140)	(0.87031, 1.25353)	(0.87132, 1.26032)
3,2	𝛼	2.33077	2.754159 [2.474687]	0.7998	0.7697	0.7957
		(2.118684, 4.449453)	(2.491433, 5.245592)	(2.8368, 3.6366)	(2.8381, 3.6078)	(2.8379, 3.6336)
	𝛽	1.71154	1.965495 [2.214164]	0.5816	0.5654	0.5791
		(1.318121, 3.029657)	(1.562379, 3.527874)	(1.8589, 2.4405)	(1.8589, 2.4243)	(1.8591, 2.4382)
3,3	𝛼	2.32879	2.743817 [2.44709]	0.6713	0.6509	0.6685
		(2.114429, 4.443215)	(2.482841, 5.226658)	(2.9086, 3.5799)	(2.9071, 3.5580)	(2.9090, 3.5775)
	𝛽	2.53128	2.910998 [2.225123]	0.7242	0.6965	0.7202
		(1.994582, 4.525857)	(2.357619, 5.268617)	(2.8734, 3.5976)	(2.8744, 3.5709)	(2.8739, 3.5941)