Empirical bayes estimation of reliability characteristics for an exponential family

This paper considers empirical Bayes (EB) squared‐error‐loss estimations of mean lifetime, variance and reliability function for failure‐time distributions belonging to an exponential family, which includes gamma and Weibull distributions as special cases. EB estimators are proposed when the prior distribution of the lifetime parameter is completely unknown but has a compact (known or unknown) support. Asymptotic optimality and rates of convergence of these estimators are investigated. The rates established here under the compact support restriction are better than the polynomial rates of convergence obtained previously.