Bayesian Estimation for the shape parameter of Exponentiated Rayleigh distribution

Abstract

The paper is concerned with Bayesian analysis of Exponentiated Rayleigh distribution for complete samples. The Bayes estimators expressions for the shape parameter of the distribution have been derived under different priors and loss functions. The Gamma, Exponential, Chi-Square and Jeffrey prior have been assumed for posterior analysis. The Bayes estimation has been obtained under eight different loss functions (Squared error, Quadratic, Weighted, Linear exponential, Precautionary, Entropy, De Groot and non-Linear exponential loss functions). The study aims to find out a suitable estimator of the unknown shape parameter. The simulation study has been conducted to compare by mean square error (MSE) for the performance of various estimators.