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August, 1974 On a Characterization of the Family of Distributions with Constant Multivariate Failure Rates
Prem S. Puri, Herman Rubin
Ann. Probab. 2(4): 738-740 (August, 1974). DOI: 10.1214/aop/1176996616

Abstract

Let $f(t_1, \cdots, t_k)$ be the probability density function of a vector $(Y_1, \cdots, Y_k)$ of nonnegative random variables. Let the multivariate failure rate (M.F.R.) $r(t_1, \cdots, t_k)$ be defined by the ratio $f(t_1, \cdots, t_k)/P(Y_i > t_i, i = 1, 2, \cdots, k)$, for $t_i \geqq 0, i = 1, \cdots, k$. It is shown that $r(t_1, \cdots, t_k)$ is constant if and only if the distribution of $(Y_1, \cdots, Y_k)$ is a mixture of exponential distributions. Analogous results hold for the nonnegative integer valued random vector with mixture being of geometric distributions.

Citation

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Prem S. Puri. Herman Rubin. "On a Characterization of the Family of Distributions with Constant Multivariate Failure Rates." Ann. Probab. 2 (4) 738 - 740, August, 1974. https://doi.org/10.1214/aop/1176996616

Information

Published: August, 1974
First available in Project Euclid: 19 April 2007

zbMATH: 0286.60007
MathSciNet: MR436463
Digital Object Identifier: 10.1214/aop/1176996616

Subjects:
Primary: 60E05

Keywords: characterization of distributions , exponential distribution , geometric distribution , mixture of distribution , Multivariate failure rate

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 4 • August, 1974
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