UZH-Logo

Normal approximation for random sums


Barbour, A 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.

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.

Citations

10 citations in Web of Science®
11 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

20 downloads since deposited on 05 Jan 2010
7 downloads since 12 months
Detailed statistics

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: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:05 Apr 2016 13:23
Publisher:Applied Probability Trust
ISSN:0001-8678
Additional Information:Copyright © 2006 Applied Probability Trust
Publisher DOI:10.1239/aap/1158684998
Permanent URL: http://doi.org/10.5167/uzh-21594

Download

[img]
Preview
Filetype: PDF (Preprint)
Size: 1MB
View at publisher

TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.

Author Collaborations