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Normal approximation for random sums


Barbour, Andrew D; Xia, A (2006). Normal approximation for random sums. Advances in Applied Probability, 38(3):693-728.

Abstract

In this paper, we adapt the very effective Berry-Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples: in a rather general model of the insurance collective; in problems in geometrical probability involving stabilizing functionals; and in counting the maximal points in a two-dimensional region.

Abstract

In this paper, we adapt the very effective Berry-Esseen theorems of Chen and Shao (2004), which apply to sums of locally dependent random variables, for use with randomly indexed sums. Our particular interest is in random variables resulting from integrating a random field with respect to a point process. We illustrate the use of our theorems in three examples: in a rather general model of the insurance collective; in problems in geometrical probability involving stabilizing functionals; and in counting the maximal points in a two-dimensional region.

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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
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Stein's method, Berry-Esseen bound, point process, random field, local dependence, two-dimensional maximum
Language:English
Date:2006
Deposited On:05 Jan 2010 15:34
Last Modified:07 Apr 2024 03:41
Publisher:Cambridge University Press
ISSN:0001-8678
Additional Information:Copyright © 2006 Applied Probability Trust
OA Status:Hybrid
Publisher DOI:https://doi.org/10.1239/aap/1158684998
  • Content: Accepted Version
  • Language: English
  • Description: Preprint