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Poisson approximation of multivariate Poisson mixtures. (English) Zbl 1028.60011

Summary: We show how good multivariate Poisson mixtures can be approximated by multivariate Poisson distributions and related finite signed measures. Upper bounds for the total variation distance with applications to risk theory and generalized negative multinomial distributions are given. Furthermore, it turns out that the ideas used in this paper also lead to improvements in the Poisson approximation of generalized multinomial distributions.

MSC:

60E05 Probability distributions: general theory
60F05 Central limit and other weak theorems
62E17 Approximations to statistical distributions (nonasymptotic)
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