Bayesian Estimation of the Parameter of the Exponential Distribution with Different Priors under Symmetric and Asymmetric Loss Functions

The objective of this study is to compare the performance of some Bayesian estimators for the shape parameter of the exponential distribution. We considered three priors: the extension of Jeffreys as non- informative prior information, as well as the inverted gamma conjugate prior and the inverted chi square prior as informative prior information's. Bayes estimators have been obtained under symmetric and asymmetric loss functions: the quadratic loss function QLF and the general entropy loss function GELF, which is a modified version of the linear exponential loss function loss function LINEX. The comparison of Bayes estimators was made through a Monte Carlo simulation study on the performance of these estimators with respect to the mean square error MSE as a measure of performance. The results of comparison showed that Bayes estimators of the shape parameter under the GELF with proper choice of γ, is a suitable alternative to the QLF when the loss is asymmetric in nature. Comparison also show that the informative priors performed better than the non-informative prior. Accordingly; if adequate information is available about the parameters it is preferable to use conjugate informative priors, otherwise the extension of Jeffreys prior gives quite reasonable results.