Comparing between Maximum Likelihood Method and Moments Method to estimation the Fuzzy reliability for Frechet Distribution By using simulation

Abstract

The researcher estimated distribution parameters by using the method of maximum Likelihood estimation and moments when the data of life times are fuzzy numbers. And then use the estimates obtained in the estimation of the fuzzy reliability function of the distribution and then choose the best estimate of this function by comparing in mean square error (MSE) and Mean Absolut Proportional Error (MAPE). The researcher concluded by means of the simulation results the fuzzy reliability by using maximum Likelihood estimation is better than moment's method because is give less mean square error (MSE) and less Mean Absolut Proportional Error (MAPE) . That the estimation of the fuzzy is better than the real for all sample sizes when we estimate of the Frechet distribution parameters by using Maximum Likelihood method.