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On a characterization of gamma distributions via exponential mixtures

Published online by Cambridge University Press:  14 July 2016

Manish C. Bhattacharjee
Manish C. Bhattacharjee*
Affiliation:
Indian Institute of Management Calcutta
*
∗Postal address: Indian Institute of Management Calcutta, Joka, Diamond Harbour Road, P.O. Box 16757, Alipore Post Office, Calcutta 700 027, India.
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Abstract

A new and simpler proof of Morrison's result that within exponential mixtures only IFR gamma mixing produces linearly increasing mean residual life functions is given. A parallel and new characterization of the DFR gamma laws follows as a consequence. The method of proof used suggests a general result on the infinite divisibility of the mixing distributions in exponential mixtures.

Keywords

MEAN RESIDUAL LIFEEXPONENTIAL MIXTURESRELIABILITY THEORYINFINITE DIVISIBILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 2 , June 1980 , pp. 574 - 576
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported by NRC Grant number A-8218 of the National Research Council of Canada, while the author was visiting Laurentian University.

References

Morrison, D. G. (1978) On linearly increasing mean residual lifetimes. J. Appl. Prob. 15, 617–620.CrossRefGoogle Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. 2. Wiley, New York.Google Scholar