Inference on P(X < Y) in Bivariate Lomax model based on progressive type II censoring

This article considers the estimation of the stress-strength reliability parameter, θ = P ( X < Y ), when both the stress ( X ) and the strength ( Y ) are dependent random variables from a Bivariate Lomax distribution based on a progressive type II censored sample. The maximum likelihood, the method of moments and the Bayes estimators are all derived. Bayesian estimators are obtained for both symmetric and asymmetric loss functions, via squared error and Linex loss functions, respectively. Since there is no closed form for the Bayes estimators, Lindley's approximation is utilized to derive the Bayes estimators under these loss functions. An extensive simulation study is conducted to gauge the performance of the proposed estimators based on three criteria, namely, relative bias, mean squared error, and Pitman nearness probability. A real data application is provided to illustrate the performance of our proposed estimators through bootstrap analysis.