Markov Chain Monte Carlo simulation for estimation problem of P(X> Y) in power Lindley model

Although conceptually appealing and well-founded theoretically, the Bayesian approach to statistical inference for the stress-strength model R P=(X > Y ) has not been widely developed, essentially because of complicated forms of posterior distributions for which simple closed forms are not available. In this paper, we propose to employ Markov Chain Monte Carlo algorithm for approximating the Bayes estimate of R . We assume that the stress and strength variables follow power Lindley model in which progressively type II censored samples are observed. To assess the accuracy of the proposed procedure, a simulation study is carried out. Finally, a real data set is analyzed for illustration purposes.

Keywords:

Bayesian approach , Stress-strength model , Power Lindley model , Progressive type II censoring , Markov Chain Monte Carlo algorithm.