The comparative studies on stress-strength reliability for Rayleigh distribution

Abstract

This paper deals with the estimation of the stress-strength parameter R = P(Y X) with three different methods for Rayleigh distribution. We assumed that the stress and strength variables are independent. We derive a maximum likelihood estimator of R and its an asymptotic distribution. We also compute an asymptotic confidence intervals. The bootstrap estimator and confidence intervals are also derived based on maximum likelihood estimator of R. We obtained the Bayes estimator based on inversed gamma priors on scale parameters and its most plausible set for constructing the confidence interval of R which is quiet similar to classical confidence interval unlike the highest posterior density region We compare the performances of three estimators using the mean squared error (MSE) of each estimator.