Bayesian Estimation for Two Parameters of Exponential Distribution under Different Loss Functions

Abstract

In this paper, two parameters for the Exponential distribution were estimated using the Bayesian estimation method under three different loss functions: the Squared error loss function, the Precautionary loss function, and the Entropy loss function. The Exponential distribution prior and Gamma distribution have been assumed as the priors of the scale γ and location δ parameters respectively. In Bayesian estimation, Maximum likelihood estimators have been used as the initial estimators, and the Tierney-Kadane approximation has been used effectively. Based on the MonteCarlo simulation method, those estimators were compared depending on the mean squared errors (MSEs).The results showed that the Bayesian estimation under the Entropy loss function, assuming Exponential distribution and Gamma distribution priors for the scale and location parameters, respectively, is the best estimator for the scale parameter. The best estimation method for location is the Bayesian estimation under the Entropy loss function in case of a small value of the scale γ (say γ 1).