Bayesian Estimation of Shape Parameter of Gamma Family under Kullback-Leibler Type Loss

Abstract

In statistical decision-making, the Kullback-Leibler divergence is used as distance measure that depicts the error while measuring the discrepancy between the actual and approximated distributions. In this study, this measure is employed to determine the loss function in case of two-parameter gamma distribution. The Bayes estimate and the associated risk function of the shape parameter alpha are obtained under the derived loss function. In this context, the truncated Poisson distribution has been chosen as the prior knowledge for the unknown parameter. An extensive simulation study is carried out to verify the performance of the Bayes estimator based on the risk values. Additionally, three real life datasets have been analyzed to investigate the applicability of the proposed procedure and the Bayes estimator has shown its efficacy.