On Poisson approximation

Article

Novak, S. 2024. On Poisson approximation. Journal of Theoretical Probability. https://doi.org/10.1007/s10959-023-01310-4
TypeArticle
TitleOn 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.
The task of establishing an estimate of the accuracy of Poisson approximation with a correct (the best possible) constant at the leading term remained open for decades.
We present a solution to that problem in the case where the accuracy of approximation is evaluated in terms of the point metric.
We generalise and sharpen the corresponding inequalities established by preceding authors.
A new result is established for the intensively studied topic of compound Poisson approximation to the distribution of a sum of integer-valued random variables.

KeywordsPoisson approximation; Compound Poisson approximation; Point metric
Sustainable Development Goals15 Life on land
Middlesex University ThemeHealth & Wellbeing
PublisherSpringer
JournalJournal of Theoretical Probability
ISSN0894-9840
Electronic1572-9230
Publication dates
Online28 Feb 2024
Publication process dates
Submitted09 Jun 2023
Accepted01 Dec 2023
Deposited27 Mar 2024
Output statusPublished
Publisher's version
License
File Access Level
Open
Digital Object Identifier (DOI)https://doi.org/10.1007/s10959-023-01310-4
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