A pooling procedure for the exponential distribution

Abstract

If two censored samples come from the same exponential distribution, it is advantageous to pool the two samples for estimating the scale parameter. In practice, when there are two censored samples available and it is uncertain whether these two samples come from the same distribution, the question of whether to pool these two samples is usually determined via a preliminary test. In this paper we propose an empirical Bayes pooling procedure and study its properties. Under the uniform prior distribution and the inverted gamma prior distribution the empirical Bayes shrinkage estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. Two empirical Bayes shrinkage estimators under the inverted gamma prior distribution are shown to be preferable to the preliminary test estimator and the shrinkage testimator when the scale parameters may be similar in size.

Keywords:

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