Empirical bayes shrinkage estimation of reliability in the exponential distribution

Abstract

In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life.

Keywords:

• Empirical Bayes shrinkage estimator
• preliminary test estimator
• shrinkage testimator
• mean square error
• relative efficiency
• effective interval