Abstract
A finite mixture of gamma distributions [Finite mixture of certain distributions. Comm. Statist. Theory Methods 31(12), 2123–2137] is used as a conjugate prior, which gives a nice form of posterior distribution. This class of conjugate priors offers a more flexible class of priors than the class of gamma prior distributions. The usefulness of a mixture gamma-type prior and the posterior of uncertain parameters λ for the Poisson distribution are illustrated by using Markov Chain Monte Carlo ( MCMC), Gibbs sampling approach, on hierarchical models. Using the generalized hypergeometric function, the method to approximate maximum likelihood estimators for the parameters of Agarwal and Al-Saleh [Generalized gamma type distribution and its hazard rate function. Comm. Statist. Theory Methods 30(2), 309–318] generalized gamma-type distribution is also suggested.
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