A Characteristic Property of the Poisson Distribution

Authors
Gerber, Hans U.
Citation
U. Gerber, Hans, A Characteristic Property of the Poisson Distribution, American statistician , 33(2), 1979, pp. 85-86
Journal title
American statistician → ACNP
ISSN journal
00031305
Volume
33
Issue
2
Year of publication
1979
Pages
85 - 86
Database
ACNP
SICI code
Abstract
Suppose that N is a nonnegative, integer-valued random variable and that the conditional distribution of N 1, ···, N m (given N) is multinomial.Then, according to a result by Moran and Rényi, N 1 and N 2 are independent if and only if N has a Poisson distribution.A new proof is given that uses only the generating function of a single variable.