Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21594
Barbour, A D; Xia, A (2006). Normal approximation for random sums. Advances in Applied Probability, 38(3):693-728.
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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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|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|
|Deposited On:||05 Jan 2010 15:34|
|Last Modified:||05 Apr 2016 13:23|
|Publisher:||Applied Probability Trust|
|Additional Information:||Copyright © 2006 Applied Probability Trust|
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