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Asymptotics of poisson approximation to random discrete distributions: an analytic approach

  • Hsien-Kuei Hwang (a1)

Abstract

A general analytic scheme for Poisson approximation to discrete distributions is studied in which the asymptotic behaviours of the generalized total variation, Fortet-Mourier (or Wasserstein), Kolmogorov and Matusita (or Hellinger) distances are explicitly characterized. Applications of this result include many number-theoretic functions and combinatorial structures. Our approach differs from most of the existing ones in the literature and is easily amended for other discrete approximations; arithmetic and combinatorial examples for Bessel approximation are also presented. A unified approach is developed for deriving uniform estimates for probability generating functions of the number of components in general decomposable combinatorial structures, with or without analytic continuation outside their circles of convergence.

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Corresponding author

Postal address: Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan. Email address: hkhwang@stat.sinica.edu.tw

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Part of the work was done while the author was visiting University of the Witwatersrand, Johannesburg.

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References

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Asymptotics of poisson approximation to random discrete distributions: an analytic approach

  • Hsien-Kuei Hwang (a1)

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