Bayesian Inference on the Shape Parameter and Future Observation of Exponentiated Family of Distributions
Table 1
(a) The Bayes estimates of the shape parameter under extended prior and the corresponding risk function under three different loss functions for the data set
0.5
4.607
0.0454
4.936
0.0444
4.881
0.0055
4.826
0.0225
4.771
0.0511
1.0
4.387
0.0476
4.717
0.0465
4.662
0.0058
4.607
0.0236
4.551
0.0535
1.5
4.168
0.0541
4.498
0.0531
4.443
0.0066
4.387
0.0269
4.332
0.0611
2.0
3.949
0.0649
4.278
0.0649
4.223
0.0081
4.168
0.0327
4.113
0.0741
5.0
2.632
0.2207
2.962
0.3052
2.907
0.0364
2.852
0.1395
2.796
0.3012
(b) The Bayes estimates of the shape parameter under conjugate prior and the corresponding risk function under three different loss functions for the data set