Journal of Multivariate Analysis
Pairwise likelihood estimation for multivariate mixed Poisson models generated by Gamma intensities
Statistics and Computing
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If I=(I"1,...,I"d) is a random variable on [0,~)^d with distribution @m(d@l"1,...,d@l"d), the mixed Poisson distribution MP(@m) on N^d is the distribution of (N"1(I"1),...,N"d(I"d)) where N"1,...,N"d are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,~)^d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v"0+v"1Y"1+...+v"qY"q for some q=