Estimation Of Pr(X>Y) For Exponentiated Gumbel Distribution Based On Lower Record Values

Abstract

In this paper, we consider the estimation of R = Pr(X > Y ) based on lower record values when X and Y are independently but not identically exponentiated Gumbel distributed random variables. The maximum likelihood, Bayes and empirical Bayes estimators of R are obtained and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for R are obtained. A simulation study is conducted to investigate and compare the performance of the intervals.