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An elementary proof for the Rao-Rubin characterization of the Poisson distribution

Published online by Cambridge University Press:  14 July 2016

D. N. Shanbhag
D. N. Shanbhag*
Affiliation:
University of Sheffield
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Abstract

This note gives elementary proofs for the characterizations of the Poisson distribution given by Rao and Rubin (1964) and Talwalker (1970) and disproves a conjecture of R. C. and A. B. L. Srivastava (1970).

Keywords

CHARACTERIZATIONPOISSON DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 1 , March 1974 , pp. 211 - 215
Copyright
Copyright © Applied Probability Trust 1974 

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References

Aczel, J. (1972) On a characterization of Poisson distributions J. Appl. Prob. 9, 852–856.CrossRefGoogle Scholar
Rao, C. R. and Rubin, H. (1964) On a characterization of the Poisson distribution Sankhya A 26, 295–298.Google Scholar
Srivastava, R. C. and Srivastava, A. B. L. (1970) On a characterization of the Poisson distribution J. Appl. Prob. 7, 495–501.CrossRefGoogle Scholar
Talwalker, Sheela (1970) A characterization of the double Poisson distribution Sankya A 32, 265–270.Google Scholar
Van Der Vaart, H. R. (1972) Anote on a functional equation for the generating function of the Poisson distribution Sankhya A 34, 191–193.Google Scholar