Empirical Bayes Procedure for Selecting the Best Exponential Population

Assume that there are k ( 2≥k) populations kππ,,1 L such that the distribution of iπ is an exponential distribution with parameter iθ, ki,,1L =. Let 0θ and 0δ be two given controls. We would like to identify the best population whose parameter is mostly closed to 0θ from the qualified subset which is a set that includes populations whose relevant parameter lies between 0θ and 0θ + 0δ. It is clear that this article will involve a parameter and three criteria when exploring the problem of selection. This research is based on the framework of Bayes, using empirical Bayes approach to solve the selection problem. Our main consideration here is to select the so-called best population among the k populations with exponential distribution. The relevant empirical Bayes decision rule has been presented and proven to be asymptotically optimal