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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
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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