Characterizations of Bivariate Pareto and Yule Distributions

Abstract

This article provides two characterizations of Mardia's Type I bivariate Pareto distribution. In particular, it is shown that the distribution of a random vector (X, Y) is uniquely determined as a Mardia's Type I bivariate Pareto distribution if its weighted form follows a Mardia's Type I bivariate Pareto distribution. Furthermore, this distribution is characterized by a condition on its tail probabilities. Analogous results hold for the bivariate extension of the Yule distribution which can be considered as the discrete analogue of the distribution under study.