A bivariate infinitely divisible distribution with exponential and Mittag–Leffler marginals

Abstract

We introduce a bivariate distribution supported on the first quadrant with exponential, and heavy tailed Mittag–Leffer, marginal distributions. Although this distribution belongs to the class of geometric operator stable laws, it is a rather special case that does not follow their general theory. Our results include the joint density and distribution function, Laplace transform, conditional distributions, joint moments, and tail behavior. We also establish infinite divisibility and stability properties of this model, and clarify its connections with operator stable and geometric operator stable laws.