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Compound Poisson approximation: a user's guide


Barbour, A D; Chryssaphinou, O (2001). Compound Poisson approximation: a user's guide. Annals of Applied Probability, 11(3):964-1002.

Abstract

Compound Poisson approximation is a useful tool in a variety of applications, including insurance mathematics, reliability theory, and molecu- lar sequence analysis. In this paper, we review the ways in which Stein’s method can currently be used to derive bounds on the error in such approximations. The theoretical basis for the construction of error bounds is systematically discussed, and a number of specific examples are used for illustration.We give no numerical comparisons in this paper, contenting ourselves with references to the literature, where compound Poisson approximations derived using Stein’s method are shown frequently to improve upon bounds obtained from problem specific, ad hoc methods.

Abstract

Compound Poisson approximation is a useful tool in a variety of applications, including insurance mathematics, reliability theory, and molecu- lar sequence analysis. In this paper, we review the ways in which Stein’s method can currently be used to derive bounds on the error in such approximations. The theoretical basis for the construction of error bounds is systematically discussed, and a number of specific examples are used for illustration.We give no numerical comparisons in this paper, contenting ourselves with references to the literature, where compound Poisson approximations derived using Stein’s method are shown frequently to improve upon bounds obtained from problem specific, ad hoc methods.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Compound Poisson, Stein's method, total variation distance, Kolmogorov distance
Language:English
Date:2001
Deposited On:07 Apr 2010 11:46
Last Modified:19 Feb 2018 22:01
Publisher:Institute of Mathematical Statistics
ISSN:1050-5164
OA Status:Green
Publisher DOI:https://doi.org/10.1214/aoap/1015345355

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