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--11F1(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.