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On a characterization of Poisson distribution

Published online by Cambridge University Press:  14 July 2016

R. C. Srivastava  and
A. B. L. Srivastava
R. C. Srivastava
Affiliation:
Ohio State University, Columbus
A. B. L. Srivastava
Affiliation:
National Council of Educational Research and Training, New Delhi
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Extract

Recently Rao (1963) has considered discrete models where an original observation produced by nature is subjected to a destructive process and we observe the undestroyed part of the original observation. Suppose the original observation produced by nature is distributed according to a Poisson distribution with parameter λ and the probability that the original observation n is reduced to r due to the destructive process is Now if Y denotes the resulting random variable (r.v.), then it is easily seen that Let us call this condition the *-condition. Later Rao and Rubin ({1964),Theorem 1) proved that the *-condition is a characterizing property of the Poisson distribution.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 2 , August 1970 , pp. 497 - 501
Copyright
Copyright © Applied Probability Trust 1970 

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References

Raikov, D. (1937) On the composition of Poisson laws. C. R. Acad. Sci. U.S.S.R. 14, 8–11.Google Scholar
Rao, C. R. (1963) On discrete distributions arising out of methods of ascertainment. Internat. Symp. on Discrete Distributions, McGill University. 320–332.Google Scholar
Rao, C. R. and Rubin, H. (1964) On a characterization of the Poisson distribution. Sankhya A 26, 295–298.Google Scholar
Teicher, H. (1954) On the multivariate Poisson distributions. Skand. Aktuartidskr. 37, 1–9.Google Scholar