Hierarchical Bayesian and E-Bayesian Statistical Inference of Reliability of Geometric Distribution

Abstract

Geometric distribution is a very important distribution in reliability area. The aim of this paper is to study the estimation problem of reliability of Geometric distribution. Hierarchical Bayesian method is more robust than ordinary Bayesian method. A new Hierarchical Bayesian and E-Bayesian estimation methods are put forward under scaled squared error loss function. First, we develop a new hierarchical prior distribution of reliability of Geometric distribution on the basis of negative logarithm gamma distribution, which can fit all kinds of density functions on the interval (0, 1) when changing values of it’s parameters. Then we derive hierarchical Bayesian and E-Bayesian estimators under scaled squared error loss function. Finally, Monte Carlo simulations prove that the hierarchical Bayesian estimation is more robust than E-Bayeisan estimation.