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Representation of multivariate discrete distributions by probability generating functions. (English) Zbl 0916.62041
Summary: This text presents an overview on multivariate discrete distributions such as the multivariate Poisson or Pascal distributions. The paper summarizes uniform representations by probability generating functions to obtain similar expressions as compared to the univariate distribution analogues.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
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References:
[1] Johnson, N.L.; Kotz, S.; Balakrishnan, N., Discrete multivariate distributions, (1997), Wiley New York · Zbl 0868.62048
[2] Kocherlakota, S.; Kocherlakota, K., Bivariate discrete distributions, (1992), Marcel Dekker New York · Zbl 0794.62002
[3] Krummenauer, F., Limit theorems for multivariate discrete distributions, Metrika, (1998), to appear · Zbl 1092.60504
[4] Marshall, A.W.; Olkin, I., A family of bivariate distributions generated by the bivariate Bernoulli distribution, J. amer. statist. assoc., 80, 332-338, (1985) · Zbl 0575.60023
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