Estimating the Reliability Function for a Family of Exponentiated Distributions
Table 2
Simulation results for “.”
(1, 0.50)
(1, 0.75)
(1, 1.00)
(1, 1.25)
0.6667000
0.5714286
0.500000
0.4444000
(, )
(5, 5)
0.4160
0.4071
0.5196
0.5198
0.4937
0.4925
0.4503
0.4445
−0.2507
−0.2595
−0.0518
−0.0516
−0.0063
−0.0075
0.0058
0.08305567
0.09161194
0.04060813
0.04711423
0.01738566
0.02128741
0.03447488
0.04041304
0.5225
0.5686
0.6963
0.7375
0.4996
0.5469
0.7179
0.7577
92.2467
91.7696
92.6155
91.9685
93.9423
93.6839
93.2283
92.5227
(10, 10)
0.4219
0.4179
0.5324
0.5340
0.5028
0.5029
0.4477
0.4451
−0.2448
−0.2487
−0.0391
−0.0374
0.0028
0.0029
0.0033
0.06910139
0.07194417
0.01062704
0.01145625
0.01023848
0.01128198
0.01168588
0.01284482
0.3560
0.3727
0.3524
0.3698
0.3863
0.4050
0.4024
0.4213
93.4513
93.3550
93.5220
93.4724
94.1638
94.1400
93.2875
93.2019
(15, 15)
0.4507
0.4491
0.5601
0.5620
0.5015
0.5016
0.4499
0.4481
−0.2159
−0.2176
−0.0113
−0.0095
0.0015
0.0016
0.0054
0.0037
0.05200412
0.05309595
0.01157199
0.0122409
0.00717329
0.007664479
0.002471958
0.002628193
0.2739
0.2826
0.4016
0.4130
0.3234
0.3340
0.1911
0.1976
93.2657
93.2813
93.8776
93.8404
94.2206
94.1996
94.6752
94.6696
(25, 25)
0.4676
0.4670
0.5625
0.5637
0.4994
0.4994
0.4466
0.4455
−0.1990
−0.1997
−0.0090
−0.0077
0.0021
0.001
0.04415965
0.0446212
0.002974049
0.003065954
0.004487199
0.004669894
0.004399884
0.004568917
0.2529
0.2578
0.2048
0.2088
0.2579
0.2630
0.266
0.271
93.8839
93.87700
94.2551
94.2501
94.3152
94.3066
95.5079
95.4975
(30, 30)
0.4869
0.4867
0.5740
0.5753
0.4999
0.4999
0.447
0.4461
−0.1798
−0.1800
0.0026
0.0038
0.0025
0.0017
0.03621819
0.03642065
0.003972225
0.004105375
0.003633788
0.003756843
0.00493606
0.005091428
0.2470
0.2511
0.243
0.2468
0.2391
0.243
0.2797
0.2841
95.2267
95.2211
94.5145
94.5023
95.1531
95.1467
95.3624
95.3519
Here, the first row indicates the estimate, the second row indicates the bias, the third row indicates variance, the fourth row indicates 95% bootstrap confidence length, and the fifth row indicates the coverage percentage.
