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On recurrence relations for the probability function of multivariate generalized Poisson distribution. (English) Zbl 0733.60025
Let $$X_ 1,...,X_ m$$ be independent Poisson random variables with parameters $$\lambda_ 1,...,\lambda_ m$$, respectively, and let $$\phi_ 1,...,\phi_ m$$ be different non-zero vectors in $$({\mathbb{N}}\cup \{0\})^ n$$. Then the distribution of the random vector $$X=\phi_ 1X_ 1+...+\phi_ mX_ m$$ is called n-variate m-parametric generalized Poisson distribution. The authors prove recurrence relations for the distribution of X.

##### MSC:
 60E05 Probability distributions: general theory 62H05 Characterization and structure theory for multivariate probability distributions; copulas
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##### References:
 [1] DOI: 10.2996/kmj/1138036064 · Zbl 0434.60019 · doi:10.2996/kmj/1138036064 [2] DOI: 10.2996/kmj/1138036265 · Zbl 0472.62020 · doi:10.2996/kmj/1138036265 [3] DOI: 10.2996/kmj/1138036998 · Zbl 0574.60024 · doi:10.2996/kmj/1138036998 [4] DOI: 10.2996/kmj/1138037418 · Zbl 0637.60022 · doi:10.2996/kmj/1138037418 [5] DOI: 10.2996/kmj/1138038878 · Zbl 0661.62038 · doi:10.2996/kmj/1138038878
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