Comparison Between Methods Estimation of Rayleigh Distribution

We have estimated the parameters of a Rayleigh distribution using different ways, including traditional methods (classical), such as (Least Squares Method, Maximum Likelihood Method, White Method and Ridge Regression Method). The Robust methods we used are (Robustfit Method, M-estimator Method and Robust Ridge Regression Method). These methods are used to find the estimators of the parameters of this distribution we adopt an experimental study to design a number of simulation experiments (Simulation) using the software package Matlab. Default values for the parameters of the distribution and different sample sizes are used. The experiment is repeated 1000 times to get a high homogeneity. For comparison between estimators to determine which is better Several scales, including the scale Mean Squares Error (MSE) and the measure of the Mean Squares Error of Parameters (MSEth) and II measure the coefficient of determination R2, have been used. It has been found that the least squares method is the best method of estimation among classical methods Robustfit is the best method among the Robust methods in both simulation experiments and field study of the real data.