Exponential families of mixed Poisson distributions
Abstract
If I=(I1,...,Id) is a random variable on [0,[infinity])d with distribution [mu](d[lambda]1,...,d[lambda]d), the mixed Poisson distribution MP([mu]) on is the distribution of (N1(I1),...,Nd(Id)) where N1,...,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,[infinity])d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+...+vqYq for some q[less-than-or-equals, slant]d, for some vectors v0,...,vq of [0,[infinity])d with disjoint supports and for independent standard real gamma random variables Y1,...,Yq.Download Info
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Article provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 98 (2007)
Issue (Month): 6 (July)
Pages: 1283-1292
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Related research
Keywords: Natural exponential families Multivariate gamma Overdispersion;References
References listed on IDEASPlease report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bobecka, Konstancja & Wesolowski, Jacek, 2004. "Multivariate Lukacs theorem," Journal of Multivariate Analysis, Elsevier, vol. 91(2), pages 143-160, November.
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