On the accuracy of poisson approximation

Article

Novak, S. 2019. On the accuracy of poisson approximation. Extremes. 22 (4), pp. 729-748. https://doi.org/10.1007/s10687-019-00350-6
TypeArticle
TitleOn the accuracy of poisson approximation
AuthorsNovak, S.
Abstract

The problem of evaluating the accuracy of Poisson approximation to the distribution of a sum of independent integer-valued random variables has attracted a lot of attention in the past six decades. From a practical point of view, it has important applications in insurance, reliability theory, extreme value theory, etc.; from a theoretical point of view, the topic provides insights into Kolmogorov's problem.
The task of establishing an estimate with the best possible constant at the leading term remained open for decades. The paper presents a solution to that problem. A first-order asymptotic expansion is established as well.
We generalise and sharpen the corresponding inequalities of Prokhorov, LeCam, Barbour, Hall, Deheuvels, Pfeifer, and Roos. A new result is established for the intensively studied topic of Poisson approximation to the binomial distribution.

PublisherSpringer
JournalExtremes
ISSN1386-1999
Electronic1572-915X
Publication dates
Online18 Jun 2019
Print01 Dec 2019
Publication process dates
Deposited17 Jun 2019
Accepted13 May 2019
Output statusPublished
Accepted author manuscript
Copyright Statement

This is a post-peer-review, pre-copyedit version of an article published in Extremes. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10687-019-00350-6

Digital Object Identifier (DOI)https://doi.org/10.1007/s10687-019-00350-6
LanguageEnglish
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