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On representation of Poisson mixtures as Poisson sums and a characterization of the gamma distribution

Published online by Cambridge University Press:  24 October 2008

A. V. Godambe
A. V. Godambe
Affiliation:
Rutgers University, Camden, New Jersey
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Abstract

A necessary and sufficient condition for a Poisson mixture with an exponential type mixing distribution to be equivalently represented as a Poisson sum is obtained. The problem of deriving a similar condition under any mixing distribution on (0, ∞) is discussed. Finally, a characterization of the gamma distribution is obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 297 - 300
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

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