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Zbl 0699.62010
Fagnola, Franco
Une caractérisation des lois exponentielles et géométriques. (A characterization of the exponential and geometric laws). (French)
[J] Rend. Semin. Mat. Univ. Padova 82, 157-161 (1989). ISSN 0041-8994

Given a probability law $\mu$ on (0,$\infty)$ (resp. ${\bbfN}\sp*)$, we give a necessary and sufficient condition $\mu$ to be the exponential (resp. geometric) probability law. This condition is expressed by a proportionality relation between the average number of jumps of the counting process associated with $\mu$ in a certain random time interval and the average length of this interval.
[F.Fagnola]

MSC 2000:: *62E10 Structure theory of statistical distributions
60G55 Point processes
60E05 General theory of probability distributions

Keywords: characterization; exponential distribution; geometric distribution; proportionality relation; average number of jumps; counting process

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