Comparison Four Methods for Estimating the Fatigue Life Distribution Parameters through Simulation

In this paper we estimated the parameters for two parameter-Birnbaum-Saunders distribution. The paper has estimated the parameters (shape and scale) using (Maximum likelihood, Modified moment, Lindley (1980) Bayesian approximation technique and Shrinkage Bayesian) methods, and then computing the value of the above-mentioned. We consider the Bayesian estimators for the unknown parameters of the Birnbaum_Saunders distribution under the reference prior. The Bayesian estimators cannot be obtained in closed forms. An approximate Bayesian approach is proposed using the idea of Lindley to obtain the Bayesian estimators. We then calculated and estimated all previous parameters, and compared the numerical estimation using statistical indicators mean absolute percentage error among the four considered estimation methods. Results are compared using Monte Carlo simulations studies carried out showed that the Shrinkage method gave us the best estimator.