Bayesian estimation for parameters and reliability characteristic of the Weibull Rayleigh distribution

In this paper we obtain Bayes' estimators under symmetric and asymmetric loss functions for the unknown parameters of Weibull Rayleigh distribution. When all the three parameters are unknown, the closed-form expressions of the Bayes estimators cannot be obtained. We use Lindley's approximation to compute the Bayes estimates. The estimators have been compared through their simulated risks. We also obtain the Bayes estimators of the reliability characteristic using both symmetric as well as asymmetric loss functions and compare its performance based on a Monte Carlo simulation study. Finally, a numerical study is provided to illustrate the results.