Bayesian Inference on Mixture of Gamma Distribution via MCMC Optimization

An extended form of gamma distribution is suggested which has two shape parameters (c and u). Introduction of another shape parameter m helps to express the extended gamma distribution not only as an exact form of a mixture of distributions, but also provides extra flexibility to the density function over positive range. In Bayesian setting, extended gamma type distribution is used as a conjugate prior for uncertain parameter y for the poisson distribution. In this paper, we consider an extension of gamma distributions, namely mixture of gamma distributions as a conjugate prior, which gives a nice form of posterior distribution than the gamma prior distributions. With the help of a simulation data set, the usefulness of mixture gamma type distribution is illustrated by using Markov Chain Monte Carlo (MCMC).

Keywords:

Bayesian analysis , Markov Chain Monte Carlo , Metropolis-Hasting sampling , Mixture gamma distributions