Inference of R=P(Y<X) for two-parameter Rayleigh distribution based on progressively censored samples

Based on independent progressively Type-II censored samples from two-parameter Rayleigh distributions with the same location parameter but different scale parameters, the UMVUE and maximum likelihood estimator of $R=P(Y<X)$ are obtained. Also the exact, asymptotic and bootstrap confidence intervals for $R$ are evaluated. Using Gibbs {sampling,} the Bayes estimator and corresponding credible interval for $R$ are obtained too. Applying Monte Carlo {simulations,} we compare the performances of the different estimation methods. Finally we make use of simulated data and two real data sets to show the competitive performance of our method.