Hostname: page-component-5b777bbd6c-5mwv9 Total loading time: 0 Render date: 2025-06-22T20:06:43.319Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing. To Begin With, Silver Spring, MD.Google Scholar
Basu, A. P. and Kirmani, S. N. U. A. (1986) Some results involving HNBUE distributions. J. Appl. Prob. 23, 1038–1044.CrossRefGoogle Scholar
Basu, S. K. and Bhattacharjee, M. C. (1984) On weak convergence within the class of HNBUE life distributions. J. Appl. Prob. 21, 654–660.CrossRefGoogle Scholar
Bhattacharjee, M. C. (1991) Some generalized variability orderings among life distributions with reliability applications. J. Appl. Prob. 28, 374–383.CrossRefGoogle Scholar
Bhattacharjee, M. C. and Sethuraman, J. (1990) Families of life distributions characterized by two moments. J. Appl. Prob. 27, 720–725.CrossRefGoogle Scholar
Klefsjö, B. (1982) The HNBUE and HNWUE classes of life distributions. Naval Res. Logist. Quart. 29, 331–344.CrossRefGoogle Scholar