On a Generalization of Bivariate Cauchy Distribution

Abstract

This paper addresses a generalization of the bivariate Cauchy distribution discussed by Fang et al. (1990), derived from a trivariate normal distribution with a general correlation matrix. We obtain explicit expressions for the joint distribution function and joint density function, and show that they reduce in a special case to the corresponding expressions of Fang et al. (1990). Finally, we show that this generalized distribution is useful in determining the orthant probability of a bivariate skew-normal distribution of Azzalini and Dalla Valle (1996).

Keywords:

• Bivariate Cauchy distribution
• Bivariate skew-normal distribution
• Generalized bivariate Cauchy distribution
• Orthant probability
• Trivariate normal distribution

Mathematics Subject Classification:

• Primary 60E05
• Secondary 62H05

Acknowledgments

The authors thank Shahid Bahonar University (Kerman, Iran) and the Natural Sciences and Engineering Research Council of Canada for supporting this research.