Bayesian Estimation of Gumbel Type-II Distribution under Type-II Censoring with Medical Applications
Table 1
Average ML and Bayesain estimates with corresponding MSEs (within parenthesis) using different percentages of failures for α = 1.5 (when a = b = c = d = 2, k = 1).
n
Percent
ML
BSELF
BGELF
BLINEX
25
40
1.7162 (0.2808)
1.7948 (0.3524)
1.4560 (0.0989)
1.4666 (0.0981)
60
1.6408 (0.1565)
1.6893 (0.1822)
1.4633 (0.0794)
1.4708 (0.0758)
80
1.6160 (0.1090)
1.6527 (0.1231)
1.4883 (0.0645)
1.4947 (0.0620)
50
40
1.6263 (0.0985)
1.6580 (0.1112)
1.5114 (0.0587)
1.5179 (0.0565)
60
1.5610 (0.0579)
1.5826 (0.0624)
1.4836 (0.0429)
1.4891 (0.0416)
80
1.5667 (0.0412)
1.5840 (0.0446)
1.5084 (0.0308)
1.5126 (0.0303)
80
40
1.5708 (0.0521)
1.5889 (0.0561)
1.5042 (0.0384)
1.5095 (0.0375)
60
1.5516 (0.0348)
1.5648 (0.0369)
1.5041 (0.0278)
1.5080 (0.0274)
80
1.5269 (0.0223)
1.5373 (0.0233)
1.4926 (0.0196)
1.4958 (0.0193)
100
40
1.5540 (0.0420)
1.5681 (0.0445)
1.5023 (0.0334)
1.5069 (0.0328)
60
1.5345 (0.0278)
1.5448 (0.0289)
1.4975 (0.0237)
1.5008 (0.0234)
80
1.5292 (0.0176)
1.5374 (0.0184)
1.5020 (0.0155)
1.5045 (0.0154)
150
40
1.5327 (0.0243)
1.5448 (0.0253)
1.4992 (0.0210)
1.5026 (0.0207)
60
1.5234 (0.0162)
1.5381 (0.0167)
1.4991 (0.0146)
1.5016 (0.0145)
80
1.5143 (0.0128)
1.5208 (0.0131)
1.4977 (0.0119)
1.4995 (0.0118)
200
40
1.5317 (0.0188)
1.5384 (0.0195)
1.5067 (0.0165)
1.5092 (0.0164)
60
1.5220 (0.0114)
1.5271 (0.0117)
1.5040 (0.0104)
1.5058 (0.0103)
80
1.5119 (0.0089)
1.5160 (0.0091)
1.4987 (0.0084)
1.5001 (0.0083)
ML: maximum likelihood estimators, BSELF: Bayesian estimators under squared error loss function, BGELF: Bayesian estimators under general entropy loss function, and BLINEX: Bayesian estimators under linear exponential loss function.
