Poisson approximation in terms of the Gini-Kantorovich distance

Novak, Serguei ORCID logoORCID: https://orcid.org/0000-0001-7929-7641 (2021) Poisson approximation in terms of the Gini-Kantorovich distance. Extremes, 24 (1) . pp. 64-87. ISSN 1386-1999 [Article] (doi:10.1007/s10687-020-00392-1)

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It is long known that the distribution of a sum Sn of independent non-negative integer-valued random variables can often be approximated by a Poisson law: Sn≈πλ, where . The problem of evaluating the accuracy of such approximation has attracted a lot of attention in the past six decades. From a practical point of view, the problem has important applications in insurance, reliability theory, extreme value theory, etc.; from a theoretical point of view, it provides insights into Kolmogorov’s problem.

Among popular metrics considered in the literature is the Gini–Kantorovich distance dG. The task of establishing an estimate of dG(Sn;πλ) with correct (the best possible) constant at the leading term remained open for a long while.

The paper presents a solution to that problem. A first-order asymptotic expansion is established as well. We show that the accuracy of approximation can be considerably better if the random variables obey an extra condition involving the first two moments. A sharp estimate of the accuracy of shifted (translated) Poisson approximation is established as well.

Item Type: Article
Research Areas: A. > School of Science and Technology
Item ID: 32963
Notes on copyright: This file is a Preprint - short version of an article published in Extremes. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10687-020-00392-1
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Depositing User: Serguei Novak
Date Deposited: 23 Apr 2021 07:50
Last Modified: 03 Feb 2023 11:20
URI: https://eprints.mdx.ac.uk/id/eprint/32963

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