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Characterizations of life distributions by moments of extremes and sample mean

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

Published online by Cambridge University Press:  14 July 2016

Cai Jun
Cai Jun*
Affiliation:
Yangzhou Teachers College
*
∗ Postal address: Department of Mathematics, Yangzhou Teachers College, Jiangsu 225002, People's Republic of China.
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Abstract

We consider two weaker partial orderings among non-negative random variables. We derive some characterizations of the equivalence of two life distributions under the weaker orderings. These results lead to the characterizations of the equality of two non-negative random vectors in distributions by moments of extremes and sample mean. As the application of these results, we get various characterizations of the exponential distribution among HNBUE and HNWUE life distribution classes. The main results of Bhattacharjee and Sethuraman (1990), and Basu and Kirmani (1986) are special cases of these more general results.

Keywords

PARTIAL ORDERINGHNBUEHNWUE

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 148 - 155
Copyright
Copyright © Applied Probability Trust 1994 

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References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
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