A bivariate extension of the beta generated distribution derived from copulas

ABSTRACT

In this paper, we introduce a new class of bivariate distributions whose marginals are beta-generated distributions. Copulas are employed to construct this bivariate extension of the beta-generated distributions. It is shown that when Archimedean copulas and convex beta generators are used in generating bivariate distributions, the copulas of the resulting distributions also belong to the Archimedean family. The dependence of the proposed bivariate distributions is examined. Simulation results for beta generators and an application to financial risk management are presented.

KEYWORDS:

• Archimedean copula Beta-generated distribution
• Bivariate joint distribution
• Clayton copula
• Gumbel copula
• Kendall’s τ
• Tail dependence.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05

Acknowledgments

The authors thank two anonymous referees for careful reading and the useful comments and suggestions that improved the presentation of the paper.