The E-Bayesian estimation and its E-MSE of Pareto distribution parameter under different loss functions

Abstract

ABSTRACTThis paper studies the E-Bayesian estimations and their E-MSE of Pareto distribution parameter under different loss functions. In order to measure the estimated error, in the case of the two hyper parameters, the definition of E-MSE (expected mean square error) is introduced based on the definition of E-Bayesian estimation, and the formulas of E-Bayesian estimation and the formulas of E-MSE are given, respectively. Monte Carlo simulations are performed to analysis the performances of the proposed methods, results are compared on the basis of E-MSE. Finally, combined with the golfers income problem are performed to calculated, the maximum likelihood estimations of the shape parameter and scale parameter are given, respectively, and that compared and analysed with the E-Bayesian estimations; moreover, the Bayesian credible intervals of the shape parameter and scale parameter are also given, respectively, by MCMC method.