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Calculation of density for the multivariate Poisson distribution. (English) Zbl 0637.60022
It is known that a density function of Poisson distribution p(k,l) in the bivariate case satisfies two main recurrence relations (r.r.). Conversely, if we need to calculate the density using the r.r.’s, not using the direct calculation, one of the relations would be meaningless except in the usage of its reduced relations. It is also known that in the trivariate case, the density function satisfies three main r.r.’s. But to calculate the density from r.r.’s we need one of the relations and their reduced relations.
The author has obtained the r.r.’s for the multivariate case and shown that only one of the n main r.r.’s and their reduced relations are used to calculate the density function.
Reviewer: V.Thangaraj

MSC:
60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
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[1] JOHNSON, N. L. and Kotz S., Discrete distributions, Houghton MiJllin Co. (1969) · Zbl 0292.62009
[2] KAWAMURA, K., The structure of bivariate Poisson distribution, Kodai Math Sem. Rep., 25(2) (1973), 246-256. · Zbl 0266.60004 · doi:10.2996/kmj/1138846776
[3] KAWAMURA, K., The structure of trivariate Poisson distribution, Kodai Mat Sem. Rep., 28(1) (1976), 1-88. · Zbl 0349.60013 · doi:10.2996/kmj/1138847374
[4] KAWAMURA, K., The structure of multivariate Poisson distribution, Kodai Math J. 2(3) (1979), 337-345. · Zbl 0434.60019 · doi:10.2996/kmj/1138036064
[5] KAWAMURA, K., A note on the recurrence relations for the bivariate Poisso distribution, Kodai Math. J. 8(1) (1985), 70-78. · Zbl 0574.60024 · doi:10.2996/kmj/1138036998
[6] Liu, C., Necessary and sufficient conditions for a Poisson approximation (trivariat case). Kodai Math. J. Vol. 9(3) (1986), 368-384. · Zbl 0633.60033 · doi:10.2996/kmj/1138037265
[7] POLAK, M., Poisson approximation for sums of independent bivariate Bernoull vectors, Kodai Math. J. 8 (1982), 408-415. · Zbl 0522.60026 · doi:10.2996/kmj/1138036608
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