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Compound Poisson process approximation


Barbour, A D; Månsson, M (2002). Compound Poisson process approximation. The Annals of Probability, 30(3):1492-1537.

Abstract

Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.

Abstract

Compound Poisson processes are often useful as approximate models, when describing the occurrence of rare events. In this paper, we develop a method for showing how close such approximations are. Our approach is to use Stein's method directly, rather than by way of declumping and a marked Poisson process; this has conceptual advantages, but entails technical difficulties. Several applications are given to illustrate the procedure.

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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
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Uncontrolled Keywords:Extreme values, point processes, compound Poisson process, Stein's method
Language:English
Date:2002
Deposited On:07 Apr 2010 10:18
Last Modified:29 Jul 2020 19:42
Publisher:Institute of Mathematical Statistics
ISSN:0091-1798
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1214/aop/1029867135

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