Noninformative Priors for Estimating P(X < Y) in Pareto Distributions

In this paper, we develop noninformative priors that are used for estimating the reliability of stress-strength system under the Pareto model. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible interval with the corresponding frequentist coverage probabilities. It turns out that the reference prior as well as the Jeffreys prior are the second order matching prior. The propriety of posterior under the noninformative priors is proved. The frequentist coverage probabilities are investigated for small samples via simulation study.