## The Annals of Statistics

### A Characterization of the Multivariate Pareto Distribution

#### 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

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