A Comparative Study for the Quasi E-Bayesian Estimation Method

Abstract

This research aims to introduce a development and comparative study to the E-Bayesian method of estimation against three other methods; Bayesian estimation, hierarchical Bayesian estimation and empirical Bayesian estimation in either complete or censored samples. First, this study compared the previous four methods in estimating the shape parameter and hazard function corresponding to the Gompertz distribution in censored data and deducted that the E-Bayesian criteria is more efficient than the other three techniques. Moreover, this study modified the E-Bayesian method of estimation to present a new method so called the quasi-E-Bayesian estimation (or briefly QE-Bayesian estimation) and then compared this new method with three other techniques; quasi-Bayesian estimation, quasi-hierarchical estimation and quasi-empirical estimation in estimating the scale parameter of the Erlang distribution in complete samples and concluded that the new criteria is superior than the other three methods in producing more efficient estimates. Finally, this research compared the suggested criteria; QE-Bayesian estimation with the original E-Bayesian method of estimation in estimating the scale parameter associated to the Frechet distribution based on complete samples and deducted that the new method is better than the classical method in producing more efficient estimates. This research used simulated random numbers that obtained by using the MATHCAD package. This study recommends to develop the theory of E-Bayesian estimation to allow estimating more than one parameter. Also, develop the QE-Bayesian technique to use in censored samples and estimating more than one parameter. Finally, study how to expand the area of using E-Bayesian vi and QE-Bayesian methods in different models such as mixture distributions and generalized order statistics.