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September, 1962 Multivariate Pareto Distributions
K. V. Mardia
Ann. Math. Statist. 33(3): 1008-1015 (September, 1962). DOI: 10.1214/aoms/1177704468


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.


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K. V. Mardia. "Multivariate Pareto Distributions." Ann. Math. Statist. 33 (3) 1008 - 1015, September, 1962.


Published: September, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0109.13303
MathSciNet: MR150885
Digital Object Identifier: 10.1214/aoms/1177704468

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 3 • September, 1962
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