Inference on P(X less than Y) in bivariate Lomax model

Abstract

In this article we consider the estimation of the stress-strength reliability parameter, R = P(X < Y ) when the stress (X) and the strength (Y ) are dependent random variables distributed as bivariate Lomax model. The maximum likelihood, moment and Bayes estimators are derived. We obtained Bayes estimators using symmetric and asymmetric loss functions via squared error loss and Linex loss functions respectively. Since there are no closed forms for the Bayes estimators, we used an approximation based on Lindley's method to obtain Bayes estimators under these loss functions. An extensive computer simulation is used to compare the performance of the proposed estimators using three criteria, namely, relative bias, mean squared error and Pitman nearness (PN) probability. Real data application is provided to illustrate the performance of our proposed estimators.