Empirical E-Bayesian estimation for the parameter of Poisson distribution

Abstract

This paper introduces a new method of estimation, empirical E-Bayesian estimation. In this method, we consider the hyperparameters of E-Bayesian estimation are unknown. We compute the E-Bayesian and empirical E-Bayesian estimates for the parameter of Poisson distribution based on a complete sample. For our purpose, we consider the case of the squared error loss function. The E-posterior risk and empirical E-posterior risk are computed. A comparison between E-Bayesian and empirical E- Bayesian methods with the corresponding maximum likelihood estimation is made using the Monte Carlo simulation. A relevant application is utilized to illustrate the applicability of multiple estimators.

Keywords

• poisson distribution
• e-bayesian estimation
• empirical e-bayesian estimation
• e-posterior risk
• empirical e-posterior risk