Bimatrix variate gamma-beta distributions

ABSTRACT

Two bimatrix distributions with beta and gamma marginals are introduced. Various properties (including product moments of determinants and traces, entropies, marginal distributions) are derived. Parameter estimation by the method of maximum likelihood is discussed. The performance and efficiencies of the maximum likelihood estimators and the associated confidence intervals are assessed by simulation. The efficiencies are compared versus those for the maximum likelihood estimators and the associated confidence intervals based on matrix variate gamma distributions. A discussion of possible applications of the bimatrix distributions is given.

KEYWORDS:

• Bimatrix beta-gamma distribution
• Maximum likelihood
• Moment-generating function
• Zonal polynomial

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F10, 62C20
• Secondary 62H12, 62J07

Acknowledgments

The authors would like to thank the editor, the associate editor, and the two referees for carefully reading and for their comments which greatly improved the article.

Funding

The research work of DKN was supported by the Sistema Universitario de Investigación, Universidad de Antioquia under the project no. IN10182CE.