Comparison of the Bayesian Estimations under Different Loss Function and Maximum Likelihood Estimation for Rayleigh Distribution

Abstract

This paper is concerned with the comparison of some estimators for the scale parameter è of the Rayleigh distribution by applying the Bayes' estimators under different loss functions (using Jeffrey prior information) in addition of the Maximum likelihood estimator (ML). The comparison was based on a Monte Carlo study. Through the simulation study comparison was made on the performance of these estimators with respect to the mean square error (MSE) and reach to, if c is small, the Bayes estimator with modified El- Sayyad loss function is the best estimator with small and medium samples size and ML with large samples size. As c become large based upon the squared error loss function was the best estimator then ML.