Estimation of the stress–strength reliability for the exponential-Rayleigh distribution

In this current paper, we consider the problem of estimating the stress–strength parameter $\psi =P(X<Y)$. This is done by using Bayesian and non-Bayesian approaches when $X$ and $Y$ are independent random variables from two exponential-Rayleigh distributions with different shape parameters but the same scale parameter. Maximum likelihood and Bayes estimators are used to estimate and construct the asymptotic confidence interval and credible interval of $\psi$. Finally, an intensive simulation study is performed to compare the proposed methods and analyze a real data set for illustrative purposes.