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A joint characterization of the multinomial distribution and the Poisson process
Published online by Cambridge University Press: 14 July 2016
Abstract
It has been recently proved that if N, X1, X2, … are non-constant mutually independent random variables with X1,X2, … identically distributed and N non-negative and integer-valued, then the independence of and implies that X1 is Bernoulli and N is Poisson. A well-known theorem in point process theory due to Fichtner characterizes a Poisson process in terms of a sum of independent thinnings. In the present article, simultaneous generalizations of both of these results are provided, including a joint characterization of the multinomial distribution and the Poisson process.
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- Copyright © Applied Probability Trust 1983
Footnotes
Research partly supported by NSF Grant MCS-8102564.
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