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Another characteristic property of the Poisson distribution

Published online by Cambridge University Press:  24 October 2008

D. N. Shanbhag
D. N. Shanbhag
Affiliation:
University of Western Australia
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Extract

1. Introduction: In (4) Moran considers two independent random variables X and Y taking non-negative integral values to give a characterization of the Poisson distribution. He establishes that the conditional distribution of X, given the total X + Y, is binomial for all given values of X + Y and there exists at least one i so that P(x = i) > 0, P( Y = i) > 0 if and only if X and Y have Poisson distributions. A slightly improved version of this result is given by Chatterji (1). For a comprehensive bibliography on the Poisson distribution the reader is referred to (3).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 1 , July 1970 , pp. 167 - 169
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Chatterji, S. D.Some elementary characterizations of the Poisson distribution. Amer. Math. Monthly 70 (1963), 958–964.CrossRefGoogle Scholar
(2)Dahiya, R. C. and Gurland, J.Functions of the sample mean and sample variance. Bio-metrics 26 (1969), 171–173.Google Scholar
(3)Haight, A. H.Handbook of the Poisson distribution (Wiley and Sons, 1967).Google Scholar
(4)Moran, P. A. P.A characteristic property of the Poisson distribution. Proc. Cambridge Philos. Soc. 48 (1952), 206–207.CrossRefGoogle Scholar