QE-Bayesian and E-Bayesian Estimation of the Frechet Model

Abstract

This paper proposes a new technique namely QE-Bayesian estimation, which is a new modification to the E-Bayesian method of estimation. The suggested approach based on replacing the quasi-likelihood function instead of the likelihood function in the E-Bayesian technique. This study is concerned with evaluating the performance of the QE-Bayesian method versus the original E-Bayesian approach in estimating the scale parameter of the Frechet distribution. The QE-Bayes and E-Bayes estimates are obtained under symmetric loss function [squared error loss (SELF)] and three different asymmetric loss functions [entropy loss function (ELF), weighted balanced loss function (WBLF) and minimum expected loss function (MELF)]. The properties of the QE-Bayesian and E-Bayesian estimates are also studied. Comparisons among all estimators are performed in terms of absolute bias(ABias) and mean square error (MSE) via Monte Carlo simulation. Numerical results show that the QE-Bayes estimates are more efficient as compared with the E-Bayes estimates.