The Annals of Mathematical Statistics

Multivariate Pareto Distributions

K. V. Mardia

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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.

Article information

Source
Ann. Math. Statist., Volume 33, Number 3 (1962), 1008-1015.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177704468

Digital Object Identifier
doi:10.1214/aoms/1177704468

Mathematical Reviews number (MathSciNet)
MR150885

Zentralblatt MATH identifier
0109.13303

JSTOR
links.jstor.org

Citation

Mardia, K. V. Multivariate Pareto Distributions. Ann. Math. Statist. 33 (1962), no. 3, 1008--1015. doi:10.1214/aoms/1177704468. https://projecteuclid.org/euclid.aoms/1177704468


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Corrections

  • See Correction: K. V. Mardia. Correction Notes: Correction to "Multivariate Pareto Distributions". Ann. Math. Statist., Volume 34, Number 4 (1963), 1603--1603.