BAYES EMPIRICAL BAYES APPROACH TO ESTIMATION OF THE FAILURE RATE IN EXPONENTIAL DISTRIBUTION

ABSTRACT

In the empirical Bayes (EB) decision problem consisting of squared error estimation of the failure rate in exponential distribution, a prior Λ is placed on the gamma family of prior distributions to produce Bayes EB estimators which are admissible. A subclass of such estimators is shown to be asymptotically optimal (a.o.). The results of a Monte Carlo study are presented to demonstrate the a.o. property of the Bayes EB estimators.

Keywords:

• Admissible
• Asymptotic optimality
• Empirical Bayes
• Exponential distribution
• Failure rate

ACKNOWLEDGMENTS

The author is grateful to the editor and referees for the valuable suggestions for the improvement on this paper.