Abstract
This paper addresses a generalization of the bivariate Cauchy distribution discussed by Fang et al. (Citation1990), 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. (Citation1990). 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 (Citation1996).
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Acknowledgments
The authors thank Shahid Bahonar University (Kerman, Iran) and the Natural Sciences and Engineering Research Council of Canada for supporting this research.