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A Characterization of Positive Poisson Distribution and its Statistical Application

Jagbir Singh
SIAM Journal on Applied Mathematics
Vol. 34, No. 3 (May, 1978), pp. 545-548
Stable URL: http://www.jstor.org/stable/2100953
Page Count: 4
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A Characterization of Positive Poisson Distribution and its Statistical Application
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Abstract

Let X1, X2, ⋯, Xn be mutually independent nonnegative random variables taking on integral values. It is known that for each of these variables to have a Poisson distribution it is necessary and sufficient that their joint conditional distribution for each fixed sum ∑ Xi be a multinomial distribution. An analogous characterization for a positive Poisson distribution is given in this paper. A statistical application of the characterization and a numerical example to illustrate it are discussed.

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