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Poisson perturbations


Barbour, A D; Xia, A (1999). Poisson perturbations. ESAIM: Probability and Statistics, 3:131-150.

Abstract

Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Cekanavicius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.

Abstract

Stein's method is used to prove approximations in total variation to the distributions of integer valued random variables by (possibly signed) compound Poisson measures. For sums of independent random variables, the results obtained are very explicit, and improve upon earlier work of Kruopis (1983) and Cekanavicius (1997); coupling methods are used to derive concrete expressions for the error bounds. An example is given to illustrate the potential for application to sums of dependent random variables.

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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:Stein's method, signed compound Poisson measure, total variation, coupling
Language:English
Date:1999
Deposited On:25 Mar 2010 11:05
Last Modified:05 Apr 2016 13:26
Publisher:EDP Sciences
ISSN:1262-3318
Additional Information:© Copyright EDP Sciences, SMAI
Publisher DOI:https://doi.org/10.1051/ps:1999106

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