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

Table 5

Average 95% confidence/HPD/bootstrap intervals (in brackets) along with their width and shape (in square brackets) for bootstrap method under different Type-II censoring schemes for fixed 𝛼=2 and 𝛽=2.

(𝑛,𝑟)		Asymptotic	Bootstrap	Bayes
				Jeffrey	Gamma-1	Gamma-2
20,20	𝛼	1.42104	1.672185 [2.492175]	0.59304	0.57805	0.59072
		(1.452209, 2.873245)	(1.676250, 3.348435)	(1.82722, 2.42026)	(1.82973, 2.40778)	(1.82818, 2.41890)
	𝛽	1.66567	1.892912 [2.134547]	0.68685	0.66402	0.68298
		(1.320337, 2.986004)	1.548423, 3.441335	(1.77583, 2.46268)	(1.78165, 2.44567)	(1.77731, 2.46029)
20,16	𝛼	1.96999	2.426357 [2.773682]	0.74758	0.72096	0.74375
		(1.270139, 3.240126)	(1.611282, 4.037639)	(1.82464, 2.57222)	(1.82727, 2.54823)	(1.82559, 2.56934)
	𝛽	1.93131	2.301952 [2.467296]	0.72063	0.69357	0.71606
		(1.244336, 3.175642)	(1.545066, 3.847018)	(1.81036, 2.53099)	(1.81423, 2.5078)	(1.81135, 2.52741)
20,12	𝛼	2.81147	3.749764 [3.347512]	0.97546	0.92306	0.96713
		(1.018547, 3.830021)	(1.560572, 5.310336)	(1.84771, 2.82317)	(1.85060, 2.77366)	(1.85008, 2.81721)
	𝛽	2.28314	2.936211 [2.990892]	0.77081	0.73686	0.76509
		(1.158481, 3.441619)	(1.563132, 4.499343)	(1.86734, 2.63815)	(1.86716, 2.60402)	(1.86832, 2.63341)
30,30	𝛼	1.12314	1.247883 [2.056709]	0.4791	0.47062	0.47771
		(1.539796, 2.662935)	(1.692596, 2.940479)	(1.83586, 2.31496)	(1.83784, 2.30846)	(1.83645, 2.31416)
	𝛽	1.32406	1.438015 [1.840961]	0.56098	0.54809	0.55861
		(1.432405, 2.756466)	(1.587448, 3.025463)	(1.79086, 2.35184)	(1.79496, 2.34305)	(1.79186, 2.35047)
30,24	𝛼	1.54929	1.7729 [2.272754]	0.60329	0.58807	0.60117
		(1.392709, 2.942003)	(1.624975, 3.397875)	(1.82805, 2.43134)	(1.83084, 2.41891)	(1.82825, 2.42942)
	𝛽	1.52657	1.706546 [2.06264]	0.58835	0.57302	0.58567
		(1.373484, 2.900058)	(1.578646, 3.285192)	(1.81574, 2.40409)	(1.81937, 2.39239)	(1.81669, 2.40236)
30,21	𝛼	2.15385	2.59599 [2.624895]	0.78178	0.75125	0.77734
		(1.176378, 3.330229)	(1.537144, 4.133134)	(1.80412, 2.58590)	(1.81047, 2.56172)	(1.80539, 2.58273)
	𝛽	1.76257	2.071998 [2.388763]	0.62933	0.60969	0.62606
		(1.297852, 3.060424)	(1.567708, 3.639706)	(1.83298, 2.46231)	(1.83617, 2.44586)	(1.83368, 2.45974)
50,50	𝛼	0.84922	0.902724 [1.740127]	0.36791	0.36381	0.36732
		(1.631801, 2.481019)	(1.726964, 2.629688)	(1.85716, 2.22507)	(1.85882, 2.22263)	(1.85731, 2.22463)
	𝛽	1.00564	1.054286 [1.595255]	0.43445	0.42822	0.43321
		(1.549076, 2.554712)	(1.645654, 2.699940)	(1.82095, 2.25540)	(1.82367, 2.25189)	(1.82162, 2.25483)
50,40	𝛼	1.1557	1.250972 [1.873862]	0.46222	0.45477	0.46123
		(1.505854, 2.661558)	(1.648413, 2.899385)	(1.83026, 2.29248)	(1.83315, 2.28792)	(1.83062, 2.29185)
	𝛽	1.14531	1.222437 [1.735241]	0.45574	0.44818	0.45429
		(1.496150, 2.641461)	(1.621884, 2.844321)	(1.82516, 2.2809)	(1.82774, 2.27592)	(1.82558, 2.27987)
50,30	𝛼	1.6002	1.784637 [2.088423]	0.59843	0.58372	0.59636
		(1.345588, 2.945790)	(1.567841, 3.352478)	(1.81112, 2.40955)	(1.81576, 2.39948)	(1.81225, 2.40861)
	𝛽	1.31418	1.442373 [1.937533]	0.48696	0.47735	0.48517
		(1.442738, 2.756921)	(1.608814, 3.051187)	(1.83724, 2.32420)	(1.83956, 2.31691)	(1.83778, 2.32295)