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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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[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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