Exponential families of mixed Poisson distributions

A. Ferrari, G. Letac and J.-Y. Tourneret

Journal of Multivariate Analysis, 2007, vol. 98, issue 6, 1283-1292

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.

Keywords: Natural; exponential; families; Multivariate; gamma; Overdispersion (search for similar items in EconPapers)
Date: 2007
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