A gamma-mixture class of distributions with Bayesian application

ABSTRACT

In this article, a subjective Bayesian approach is followed to derive estimators for the parameters of the normal model by assuming a gamma-mixture class of prior distributions, which includes the gamma and the noncentral gamma as special cases. An innovative approach is proposed to find the analytical expression of the posterior density function when a complicated prior structure is ensued. The simulation studies and a real dataset illustrate the modeling advantages of this proposed prior and support some of the findings.

KEYWORDS:

• Bayesian inference
• Hypergeometric gamma
• Mixture of gamma
• Normal-gamma
• Normal-inverse gamma
• Variance

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62H12
• 62H10
• 60E05

Acknowledgments

The authors would like to thank the reviewers and the associate editor for the valuable comments and recommendations.

Funding

The authors would like to hereby acknowledge the support of the StatDisT group. This work is based upon research supported by the National Research foundation, Grant (Re:CPRR13090132066 No 91497) and the vulnerable discipline-academic statistics (STAT) fund.