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A joint characterization of the multinomial distribution and the Poisson process

Published online by Cambridge University Press:  14 July 2016

George Kimeldorf*
Affiliation:
The University of Texas at Dallas
Peter F. Thall*
Affiliation:
George Washington University
*
Postal address: Programs in Mathematical Sciences, University of Texas at Dallas, Box 688, Richardson, TX 75080, U.S.A.
∗∗ Postal address: Department of Statistics, Bldg. C, Room 304, George Washington University, Washington, DC 20052, U.S.A.

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.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Research partly supported by NSF Grant MCS-8102564.

References

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