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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

REFERENCES

(1)Bildikar, S. and Patil, G. P.Multivariate exponential-type distributions. Ann. Math. Statist. 39 (1968), 1316–1326.CrossRefGoogle Scholar
(2)Feller, William.An introduction to probability theory and its applications, vol. I (3rd edn), pp. 286–290 (New York: Wiley, 1968).Google Scholar
(3)Feller, William.An introduction to probability theory and its applications, vol. II (1st edn), pp. 425–427 (New York: Wiley, 1966).Google Scholar
(4)Godambe, A. V. and Patil, G. P. Some characterizations involving additivity and their applications to Poisson mixtures and Poisson sums. Statistical distributions in scientific work, vol. III, pp. 339–351 (Dordrecht-Holland: D. Reidel Publishing Company, 1975).Google Scholar
(5)Gurland, J.Some inter-relations among compound and generalized distributions. Biometrika 44 (1957), 265–268.CrossRefGoogle Scholar
(6)Wani, J. K. and Patil, G. P. Characterizations of linear exponential families. Statistical distributions in scientific work, vol. III, pp. 423–431 (Dordrecht-Holland: D. Reidel Publishing Company, 1975).Google Scholar