Mixture of Distributions in the Biparametric Exponential Family: A Bayesian Approach

Abstract

In this article we propose mixture of distributions belonging to the biparametric exponential family, considering joint modeling of the mean and variance (or dispersion) parameters. As special cases we consider mixtures of normal and gamma distributions. A novel Bayesian methodology, using Markov Chain Monte Carlo (MCMC) methods, is proposed to obtain the posterior summaries of interest. We include simulations and real data examples to illustrate de performance of the proposal.

Keywords:

• Bayesian methods
• Biparametric exponential family
• MCMC simulation
• Mixture models

Mathematics Subject Classification:

• 62F15
• 62J12

Acknowledgments

The authors thank the reviewers for their comments which contributed to the improvement of this article.