In this study, we discuss the problem of estimating ρ = P(X > Y), when X and Y are two independent power Lindley random variables, based on progressively type II right censored order statistics. The maximum likelihood estimator of ρ and its asymptotic distribution, asymptotic interval estimator of ρ, Bayesian point estimators for ρ under symmetric and asymmetric loss functions as well as credible intervals for ρ are achieved when X and Y have a common parameter. Since it seems that the integrals pertaining to the Bayes estimation cannot be obtained in explicit forms, we propose the Metropolis-Hastings within Gibbs algorithm to find the approximate Bayes estimates of ρ. A simulation study is given in order to evaluate the proposed estimators and compare the different methods, developed in the paper. The corresponding results for the general case (when X and Y have no common parameters), as well as two examples, are also provided. The paper finishes with some remarks.
