On the Construction of Preliminary Test Estimators of the Reliability Characteristics for the Exponential Distribution Based on Records

Abstract

SYNOPTIC ABSTRACTThe one-parameter exponential distribution plays an important role in reliability theory. Two measures of reliability for exponential distribution are considered, R(t) = P(X > t) and P = P(X > Y). Sometimes, due to past knowledge or experience, the experimenter may be in a position to make an initial guess on some of the parameters of interest. In such cases, we can provide an improved estimator by incorporating the prior information on the parameters. Preliminary test estimators (PTES) have been developed in the literature for the parameters of various distributions. To the best of the knowledge of the authors, PTES are not available for reliability functions R(t) and P. For record values from exponential distribution, we define PTES based on uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE), and empirical Bayes estimator (EBE) for the powers of the parameter, R(t) and P. Bias and mean square error (MSE) expressions for the proposed estimators are derived to examine their efficiency. A comparative study of different methods of estimation is done through simulations, and it is established that PTES perform better than ordinary UMVUES, MLES, and EBES.