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Characterization of life distributions under some generalized stochastic orderings

Part of: Distribution theory - Probability Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

Jun Cai  and
Yanhong Wu
Jun Cai*
Affiliation:
Concordia University
Yanhong Wu*
Affiliation:
University of Alberta
*
∗Postal address: Department of Mathematics and Statistics, Concordia University, Montreal, Quebec, H4B 1R6, Canada.
∗∗Postal address: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
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Abstract

In this paper we investigate the characterizations of life distributions under four stochastic orderings, < p, < (p), < (p) and < L, by a unified method. Conditions for the stochastic equality of two non-negative random variables under the four stochastic orderings are derived. Many previous results are consequences. As applications, we provide characterizations of life distributions by a single value of their Laplace transforms under orderings < p and < (p) and their moment generating functions under orderings < p and < (p). Under ordering < L, a characterization is given by the expected value of a strictly completely monotone function. The conditions for the stochastic equality of two non-negative vectors under the stochastic orderings < (p), < (p) and < L are presented in terms of the Laplace transforms and moment generating functions of their extremes and sample means. Characterizations of the exponential distribution among L and L life distribution classes are also given.

Keywords

CONCAVITYMOMENT GENERATING FUNCTIONSLAPLACE TRANSFORMSTOCHASTIC EQUALITYSTRICTLY COMPLETELY MONOTONE

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 711 - 719
Copyright
Copyright © Applied Probability Trust 1997 

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