A characterization of the gamma distribution by the negative binomial distribution
- 1 December 1980
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 17 (4) , 1138-1144
- https://doi.org/10.2307/3213228
Abstract
It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.Keywords
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