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


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.