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Some results involving HNBUE distributions

Published online by Cambridge University Press:  24 August 2016

A. P. Basu  and
S. N. U. A. Kirmani
A. P. Basu*
Affiliation:
University of Missouri — Columbia
S. N. U. A. Kirmani*
Affiliation:
University of Northern Iowa
*
∗Postal address: Department of Statistics, University of Missouri, 222 Math. Sci. Building, Columbia, MO 65201, USA.
∗∗Postal address: Department of Mathematics and Computer Science, University of Northern Iowa, Cedar Falls, IA 50614, USA.
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Abstract

A characterization of the exponential distribution in the class of all distributions which are HNBUE or HNWUE is proved. An upper (a lower) bound is obtained on the renewal function of a renewal process when the underlying distribution is HNBUE (HNWUE).

Keywords

CHARACTERIZATIONEXPONENTIAL DISTRIBUTIONRENEWAL FUNCTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 1038 - 1044
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

This research was supported in part by a Weldon Spring Grant and in part by the Research Council of the Graduate School, University of Missouri — Columbia.

References

Basu, A. P. (1981) The estimation of P (X < Y) for distributions useful in life testing. Nav. Res. Logist. Quart. 28, 383–392.Google Scholar
Barlow, R. E. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Basu, A. P., Ebrahimi, N. and Klefsjö, B. (1983) Multivariate harmonic new better than used in expectation distributions. Scand. J. Statist. 10, 19–25.Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Galambos, J. and Kotz, S. (1978) Characterizations of Probability Distributions. Springer-Verlag, Berlin.Google Scholar
Klefsjö, B. (1982) The HNBUE and HNWUE classes of Life Distributions. Nav. Res. Logist. Quart. 29, 331–344.Google Scholar
Klefsjö, B. (1983) A useful ageing property based on the Laplace transform. J. Appl. Prob. 20, 615–626.Google Scholar
Rolski, T. (1975) Mean residual life. Bull. Internat. Statist. Inst. 46, 266–270.Google Scholar