Bayesian Inference on the Generalized Gamma Distribution using Conjugate Priors

Abstract

This paper focuses on the three-parameter generalized gamma distribution and uses Bayesian techniques to estimate its parameters. Many authors con-sidered estimating the parameters of the generalized gamma distribution in a Bayesian framework using Jeffrey’s priors. Others used different loss functions and the least squares approach. This study uses Bayesian techniques to estimate the three-parameter generalized gamma distribution by using conjugate priors. The random Metropolis algorithm is used to simulate the Bayesian estimates of the three parameters. Then these estimates are compared to the maximum like-lihood estimates using the mean error through simulation. It has been shown in this paper that the obtained estimates using this approach is more accurate than the traditional methods of estimation such as the Maximum likelihood method. The same approach is then used to estimate the parameters of mixtures of the generalized gamma parameters using conjugate priors.