BAYES ESTIMATION OF THE EXTREME-VALUE RELIABILITY FUNCTION

This paper obtains Bayes estimates of the reliability function of the extreme value distribution by using two Bayes approximation procedures : Lindley (1980), and Tierney & Kadane (1986). These estimates were co mpared to maximum likelihood estimates (MLE) based on a Monte Carlo si mulation study. Jeffreys invariant prior was used in the comparison fo r both Bayes procedures. The MLE am superior to either of the Bayes es timates, except for small values of t; the simpler Lindley Bayes proce dure gives estimates with smaller root-mean-square error than estimate s obtained by the Tierney & Kadane procedure except for large values o f t. From a practical standpoint, the ML method is easiest to use and wore accurate for the extreme value distribution than our two Bayes ap proximation procedures. Both Bayes procedures seem to perform equally. However, the Lindley method is easier to use with little loss of accu racy.