Comparison of Estimation Methods for the Parameters of the Frechet Distribution - using Simulation.

Probability distributions are mathematical functions that describe the likelihood of different outcomes in random process estimates for the scale parameters and the shape parameter according to the type of data that can determine the appropriate probability distribution. In this paper, an experimental study is presented to compare a number of estimation methods for the parameters of the Frechet distribution, which is one of the most important probability distributions in the fields of determining failure times. The estimation Methods are (Maximum Likelihood, Moments and Bayesian methods) were adopted. Through the simulation method, the comparison process was carried out, where the experimental samples were determined (n = 15, 25, 50, 75, 100) with the assumption of four default values ​​for each of the shape parameter (λ =1.1, 1.5, 2, 2.5) and the scale parameter (θ=1.4, 1.8, 2.3, 3). Through this method, the paper was able to determine the appropriate method for estimation by adopting the Mean square error criterion. The experimental results showed the superiority of the Bayes method. Then the method of Maximum likelihood.