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 Electronic Journal of Probability > Vol. 13 (2008) > Paper 24 open journal systems 


Symmetric and centered binomial approximation of sums of locally dependent random variables

Adrian Roellin, University of Oxford


Abstract
Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric binomial distribution, serving as a natural alternative to the normal distribution in discrete settings. The bounds are given with respect to the total variation and a local limit metric. Under appropriate smoothness properties of the summands, the same order of accuracy as in the Berry-Essen Theorem is achieved. The approximation of the total number of points of a point processes is also considered. The results are applied to the exceedances of the $r$-scans process and to the Mat'ern hardcore point process type I to obtain explicit bounds with respect to the two metrics.


Full text: PDF

Pages: 756-776

Published on: May 6, 2008
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Electronic Journal of Probability. ISSN: 1083-6489