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

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

2006-08-05

arxiv.org/abs/math/0608138v1

Mathematics

Probability

Scientific paper

Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. 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.

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