A characterization of the gamma distribution by the negative binomial distribution

1 March 1980

journal article
research article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 17 (04) , 1138-1144
https://doi.org/10.1017/s0021900200097473

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

GAMMA DISTRIBUTION
NEGATIVE BINOMIAL DISTRIBUTION
CHARACTERIZATION
POISSON PROCESS
GEOMETRIC DISTRIBUTION
EXPONENTIAL DISTRIBUTION
MOMENT PROBLEM

This publication has 2 references indexed in Scilit:

Characterizations of Statistical Distributions: A Supplement to Recent Surveys
International Statistical Review, 1974
Note on a Characterizing Property of the Exponential Distribution
The Annals of Mathematical Statistics, 1971