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Poisson approximations of multinomial distributions and point processes

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  • Deheuvels, Paul
  • Pfeifer, Dietmar

Abstract

We present an extension to the multinomial case of former estimations for univariate Poisson binomial approximation problems and generalize a result obtained by [1], 805-810). As an application, we evaluate the total variation distance between superpositions of independent Bernoulli point processes and a suitable Poisson process. The main tool will be a multiparameter semigroup approach.

Suggested Citation

  • Deheuvels, Paul & Pfeifer, Dietmar, 1988. "Poisson approximations of multinomial distributions and point processes," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 65-89, April.
    • Handle: RePEc:eee:jmvana:v:25:y:1988:i:1:p:65-89
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    Cited by:

    1. Roos, Bero, 1999. "On the Rate of Multivariate Poisson Convergence," Journal of Multivariate Analysis, Elsevier, vol. 69(1), pages 120-134, April.
    2. Kruopis, Julius & Čekanavičius, Vydas, 2014. "Compound Poisson approximations for symmetric vectors," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 30-42.
    3. Vishal Gupta & Nathan Kallus, 2022. "Data Pooling in Stochastic Optimization," Management Science, INFORMS, vol. 68(3), pages 1595-1615, March.

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