Bayes estimation of the extreme-value reliability function

The authors obtain Bayes estimates of the reliability function of the extreme value distribution by using two Bayes approximation procedures: Lindley (1980), and Tierney and Kadane (1986). These estimates were compared to maximum-likelihood estimates (MLE) based on a Monte Carlo simulation study. Jeffreys invariant prior was used in the comparison for both Bayes procedures. The MLE are superior to either of the Bayes estimates, except for small values of t. The simpler Lindley Bayes procedure gives estimates with smaller root-mean-square error than estimates obtained by the Tierney and Kadane procedure except for large values of t. From a practical standpoint, the ML method is easiest to use and more accurate for the extreme value distribution than the two Bayes approximation procedures. Both Bayes procedures seem to perform equally. However, the Lindley method is easier to use with little loss of accuracy