Bayes estimators for the extreme-value reliability function

Bayes estimates under both modified symmetric and asymmetric loss functions are obtained for the reliability function of the extreme value distribution (EV1) using Lindley's approximation procedure. These estimates are compared to each others and to maximum likelihood estimates (MLE) using simulation study. A noninformative prior (Jeffreys invariant prior) is used in the comparisons. The Bayes estimator under asymmetric loss function compared to the posterior mean, it incorporates additional information about possible consequences of overestimation and underestimation of the true value of the reliability function. The MLE is superior to either of the Bayes estimates, except for small values of time t the Bayes estimates consistently perform well. While the Bayes approach is computationally intensive, the calculations can be easily computerized.