Inference on Pr(X Y ) Based on Record Values from the Burr Type X Distribution

Our interest is in estimating the stress-strength reliability Pr(X > Y ) based on lower record values when X and Y are two independent but not identically distributed Burr type X random variables. The maximum likelihood estimator, Bayes and empirical Bayes estimators using Lindleys approximations, are obtained and their properties are studied. The exact confidence interval, as well as the Bayesian credible sets are obtained. Two examples are presented in order to illustrate the inferences discussed in the previous sections. A Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper and to compare them with some bootstrap intervals.