Permanent URL to this publication: http://dx.doi.org/10.5167/uzh21767
Barbour, A D; Choi, K (2004). A nonuniform bound for translated Poisson approximation. Electronic Journal of Probability, 9(2):1836.

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Abstract
Let $X_1, ldots , X_n$ be independent, integer valued random variables, with $p^{text{th}}$ moments, $p >2$, and let $W$ denote their sum. We prove bounds analogous to the classical nonuniform estimates of the error in the central limit theorem, but now, for approximation of $law(W)$ by a translated Poisson distribution. The advantage is that the error bounds, which are often of order no worse than in the classical case, measure the accuracy in terms of total variation distance. In order to have good approximation in this sense, it is necessary for $law(W)$ to be sufficiently smooth; this requirement is incorporated into the bounds by way of a parameter $al$, which measures the average overlap between $law(X_i)$ and $law(X_i+1), , 1 le i le n.$
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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 
Language:  English 
Date:  4 February 2004 
Deposited On:  16 Nov 2009 20:34 
Last Modified:  27 Nov 2013 18:04 
Publisher:  Institute of Mathematical Statistics 
ISSN:  10836489 
Official URL:  http://www.emis.de/journals/EJPECP/_ejpecp/viewarticle671b.html?id=1425 
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