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

Part of:Multiplicative number theoryCombinatorial probabilityCombinatoricsFinite fields and commutative rings (number-theoretic aspects)Limit theorems

Published online by Cambridge University Press:  01 July 2016

Hsien-Kuei Hwang
Hsien-Kuei Hwang*
Affiliation:
Academia Sinica
*
∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan. Email address: hkhwang@stat.sinica.edu.tw
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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.

Keywords

Poisson approximationEwens sampling formulaconvolution methodsingularity analysisarithmetic functionscombinatorial structuresgenerating functions

MSC classification

Primary:60C05: Combinatorial probability60F99: None of the above, but in this section
Secondary:11N60: Distribution functions associated with additive and positive multiplicative functions11T06: Polynomials05A99: None of the above, but in this section

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 2 , June 1999, pp. 448 - 491
Copyright
Copyright © Applied Probability Trust 1999 

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Footnotes

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

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