Using Different Loss Function to Estimate the Parameters of Birnbaum-Saunders Distribution by Bayesian Method with Application

Abstract

The Birnbaum-Saunders distribution is one of the most important distributions that explain fatigue time in general, as it has many engineering and industrial applications. In our Paper we introduce three estimation methods to estimate the parameters of Birnbaum-Saunders parameters, first is the Maximum Likelihood Estimator MLE and second, is Bayes estimation with quadratic loss function BQ and last is the Bayes estimator with weighted loss function BW. simulated data were used as well as real data used which represented by the fatigue time of a concrete block under pressure before its final collapse. It was concluded that the Bayes estimator with squared loss function BQ is the best.