The Annals of Statistics

A Characterization of the Multivariate Pareto Distribution

P. E. Jupp and K. V. Mardia

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 10, Number 3 (1982), 1021-1024.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345894

Digital Object Identifier
doi:10.1214/aos/1176345894

Mathematical Reviews number (MathSciNet)
MR663455

Zentralblatt MATH identifier
0485.62041

JSTOR
links.jstor.org

Subjects
Primary: 62H05: Characterization and structure theory
Secondary: 62F10: Point estimation 62P20: Applications to economics [See also 91Bxx]

Keywords
Characterization mean residual lifetime multivariate Pareto distribution

Citation

Jupp, P. E.; Mardia, K. V. A Characterization of the Multivariate Pareto Distribution. Ann. Statist. 10 (1982), no. 3, 1021--1024. doi:10.1214/aos/1176345894. https://projecteuclid.org/euclid.aos/1176345894


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