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September, 1982 A Characterization of the Multivariate Pareto Distribution
P. E. Jupp, K. V. Mardia
Ann. Statist. 10(3): 1021-1024 (September, 1982). DOI: 10.1214/aos/1176345894


For a random vector $\mathbf{X}$ on $\mathbf{X} > \mathbf{b}$ whose mean exists, the mean residual lifetime $E(\mathbf{X} - \mathbf{c}\mid \mathbf{X} > \mathbf{c})$ is an affine function of $\mathbf{c}$ on $\mathbf{c} > \mathbf{b}$ if and only if $\mathbf{X}$ can be partitioned into independent random vectors which have shifted multivariate Pareto or exponential distributions. An interpretation in terms of income-distribution is suggested for the Pareto case. It is also shown that every multivariate distribution whose mean exists is determined by its mean residual lifetime.


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P. E. Jupp. K. V. Mardia. "A Characterization of the Multivariate Pareto Distribution." Ann. Statist. 10 (3) 1021 - 1024, September, 1982.


Published: September, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0485.62041
MathSciNet: MR663455
Digital Object Identifier: 10.1214/aos/1176345894

Primary: 62H05
Secondary: 62F10 , 62P20

Keywords: characterization , mean residual lifetime , multivariate Pareto distribution

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 3 • September, 1982
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