A COMPARISON OF BAYESIAN APPROACH WITH Maximum Likelihood Method To Estimate Parameter For Rayleigh Distribution

Abstract

The main objective of this study is to obtain and compare the performance of "Maximum likelihood estimator (MLE) and Bayesian estimators of the scale parameter of the Rayleigh distribution. In order to get better understanding in our Bayesian analysis we consider informative prior as well as non-informative prior using Jeffery prior information under loss functions (modified squred error loss function, Quadratic error loss function) to find the best method for estimation, which used the samples size ( 10, 20, 30, 50, 100). The comparison of the estimators, based on their mean squared errors (MSE's), we obtain that, MinMSE is the best estimator, while the performance of Bayes estimator under modified squared error loss function with non-informative prior with a value of the scale parameter ( ) is the best estimator comparing to other for all simple size.