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Characterizations of the exponential distribution by relevation-type equations

Published online by Cambridge University Press:  14 July 2016

E. Grosswald ,
Samuel Kotz  and
N. L. Johnson
E. Grosswald*
Affiliation:
Temple University
Samuel Kotz
Affiliation:
Temple University
N. L. Johnson*
Affiliation:
University of North Carolina
*
∗Postal address: Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A.
∗∗∗Postal address: Department of Statistics, University of North Carolina, Chapel Hill, NC 27514, U.S.A.
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Abstract

In this note characterizations of the exponential distribution are discussed, based on a generalization of the lack of memory property. The result was motivated by the notion of ‘relevation of distributions' introduced by Krakowski (1973).

Keywords

EXPONENTIAL DISTRIBUTIONCHARACTERIZATIONRELEVATIONCONVOLUTIONPOWER SERIES EXPANSIONLAPLACE TRANSFORMNON-NEGATIVE RANDOM VARIABLESREPLACEMENT PROCEDURES
Type
Short Communications
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 874 - 877
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

∗∗

Present address: Department of Management and Statistics, University of Maryland, College Park, MD 20742, U.S.A.

Research supported by U.S. Air Force Office of Scientific Research Grant No. 78–3673.

Research supported by U.S. Army Research Office under Contract No. DAAG29–77–C–0035.

References

Krákowski, ?. (1973) The relevation transform and a generalization of the gamma distribution function. Rev. Française Automat. Informat. Recherche Opérationnelle 7, Sér. V–2, 107–120.Google Scholar