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Families of life distributions characterized by two moments

Published online by Cambridge University Press:  14 July 2016

Manish C. Bhattacharjee  and
Jayaram Sethuraman
Manish C. Bhattacharjee*
Affiliation:
New Jersey Institute of Technology
Jayaram Sethuraman*
Affiliation:
Florida State University
*
∗Postal address: Center for Applied Mathematics and Statistics, Department of Mathematics, New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗Postal address: Deparment of Statistics, Florida State University, Tallahassee, FL 32306-3033, USA.
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Abstract

We consider several classical notions of partial orderings among life distributions which have been used to describe ageing properties and tail domination. We show that if a distribution G dominates another distribution F in one of these partial orderings introduced here, and if two moments of G agree with those of F, including the moment that describes this partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper.

Keywords

LIFE DISTRIBUTIONSAGEING CLASSESCHARACTERIZATION
Type
Short Communications
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 720 - 725
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Research supported by SBR Grant 4-2-1710-1008 from the NJIT Foundation.

Research supported by Contract No. DAAL03-90-G-0103 from the U.S. Army Research Office.

References

Barlow, R. E. and Proschan, F. (1981) Statistical Theory of Reliability and Life Testing: Probability Models. To Begin With, Silver Spring, MD.Google 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. (1981) A note on a Maximin disposal policy under NWUE pricing. Naval Res. Logist. Quart. 28, 341–345.Google Scholar
Ibragimov, I. A. (1956) On the composition of unimodal distributions. Theory Prob. Appl. 1.Google Scholar
Keilson, J. (1979) Markov Chain Models, Rarity and Exponentiality. Springer Verlag, New York.CrossRefGoogle Scholar
Klefsjö, B. (1982) The HNBUE and HNWUE classes of life distributions. Naval Res. Logist. Quart. 29, 331–344.Google Scholar
Kochar, S. C. and Wiens, D. P. (1987) Partial orderings of life distributions with respect to their aging properties. Naval Res. Logist. 34, 823–829.Google Scholar
Rolski, T. (1975) Mean residual life. Proc. 40th Session, Internat. Statist. Inst. 4, 266–270.Google Scholar
Stoyan, D. (1983) Comparison Methods for Queues and other Stochastic Models. Wiley, New York.Google Scholar