Multivariate Pareto Distributions

Abstract

It is well known that the family of Pareto distributions with densities \begin{equation*}\begin{align*}f(x; a, p) = pa^p/x^{p+1},\qquad x > a > 0, \\ = (1.1) \\ 0,\qquad x \leqq a, p > 0,\end{align*}\end{equation*} provides reasonably good fits to many empirical distributions, e.g., to distributions of income and of property values. In most of these cases, ancillary information is present, which could be utilized if an appropriate multivariate Pareto distribution were available. The objects of this note are (i) to suggest two families of bivariate Pareto distributions with the property that both marginal distributions are of univariate Pareto form; (ii) to extend these to multivariate forms; and (iii) to discuss estimation of the parameters in the bivariate distributions.