Pitman estimator for the parameter and reliability function of the exponential distribution

Abstract

The easiest and most essential distribution in reliability studies is the exponential distribution. An important issue in this area is to seek for a good estimator to estimate the parameter and reliability function of this distribution. So in this article, The Pitman method is used to derive an estimator for the parameter and reliability function of the exponential distribution, then a comparison was made with the usual methods such as maximum likelihood estimator and Bayes estimator through simulation studies with different sizes of samples. The results showed that the Pitman estimator has a good performance for the parameter of exponential distribution compared with other methods by relying on the statistical measure Mean square error. Also it showed that the Bayes estimator has a good performance compared with the other methods in estimating the reliability function by relying on the statistical measure integral mean square error.