Geodesic
Discrete Multidimensional Distributions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 68-77.

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Polynomial distribution, which is used at present as a generalization for Binomial, in fact, doesn't take into account the specific notion from the probability theory namely independence of events, random variables, tests. Such a generalization can be used in a special case, that is to say when events don't intersect. Eventology deals with various structures of events' dependencies, therefore it is reasonable that in case of arbitrary structure dependency structure question emerges about more harmonious generalization of the Binomial distribution. Besides there is cite about approximation Binomial multivariate distribution with another new one — multivariate analogue of the Poisson distribution. The article brings in definitions for those new objects and also their main characteristics and properties.
Mots-clés : multidimensional polynomial distribution, multidimensional binomial distribution. 
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Oleg Yu. Vorob'ov; Lavrenty S. Golovkov. Discrete Multidimensional Distributions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 1, pp. 68-77. http://geodesic.mathdoc.fr/item/JSFU_2008_1_1_a7/