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The structure of trivariate Poisson distribution. (English) Zbl 0349.60013

In this paper the author has defined the trivariate Poisson distribution and he has clarified the structure of random high vector which has the trivariate distribution law. The discussion is constructed by the next three parts:
1. definition of the trivariate Bernoulli distribution
2. definition of the trivariate binomial distribution
3. definition of the trivariate Poisson distribution and the relation of the trivariate Poisson distribution and the trivariate binomial distribution.
In the last part some characters of the trivariate Poisson distribution and the notion of the generalization to the multivariate Poisson distribution are stated.
Reviewer: Kazutomo Kawamura

MSC:

60E05 Probability distributions: general theory
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References:

[1] FELLER, W., An introduction to probability theory and its applications, Vol. 1, sec. ed. 6th print (1961).
[2] KAWAMURA, K., The structure of bivariate Poisson distribution, Vol. 25, No 2, 246-256 (1973).Kdai Math. Sem. Rep. · Zbl 0266.60004 · doi:10.2996/kmj/1138846776
[3] KENDALL, M. G. and A. STUART, The advanced theory of statistics, Vol. 1 Distribution theory, second ed. Criffin (1963). · Zbl 0353.62013
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