The distribution of products, quotients, and powers of two dependent H-function variates

The H-function distribution has been shown to be a powerful addition in the study of the algebra of non-negative random variables. However, most of this work has been restricted to the study of independent H-function variates. This paper introduces a bivariate probability distribution based on the H-function of two variables. The distribution is shown to be a generalization of several known bivariate distributions. Further, it is shown that products, quotients, and powers of bivariate H-function variates are H-function variates. Several examples are given.