Multivariate Generalization of the Confluent Hypergeometric Function Kind 1 Distribution

Abstract

The confluent hypergeometric function kind 1 distribution with the probability density function (pdf) proportional to x_−1F11(α;β;−x), x>0 occurs as the distribution of the ratio of independent gamma and beta variables. In this article, a multivariate generalization of this distribution is defined and derived. Several pertinent properties of this multivariate distribution are discussed that shed some light on the nature of the distribution.