Characterizations of Bivariate Pareto and Yule Distributions

This article provides two characterizations of Mardia's Type I bivari-ate Pareto distribution. In particular, it is shown that the distribution of a random vector (X, Y) is uniquely detennined as a Mardia's Type I bivariate Pareto distribution ifits weighted form follows a Mardia's Type I bivariate Pareto distribution. Furthennore, 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.