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The American Statistician Volume 33, 1979 - Issue 2
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The Teacher's Corner

A Characteristic Property of the Poisson Distribution

Hans U. Gerber The University of Michigan, Ann Arbor, MI, 48109, USA
Pages 85-86 | Received 25 Oct 1977, Published online: 26 Mar 2012
 
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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.

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