Inference on P r(X > Y ) Based on Record Values from the Burr Type X Distribution

Abstract

Our interest is in estimating the stress-strength reliability P r(X > Y )based on lower record values when X and Y are two independent butnot identically distributed Burr type X random variables. The maximum likelihood estimator, Bayes and empirical Bayes estimators usingLindleys approximations, are obtained and their properties are studied. The exact confidence interval, as well as the Bayesian credible setsare obtained. Two examples are presented in order to illustrate theinferences discussed in the previous sections. A Monte Carlo simulation study is conducted to investigate and compare the performance ofdifferent types of estimators presented in this paper and to comparethem with some bootstrap intervals.