## Electronic Journal of Probability

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

#### 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.

#### Article information

Source
Electron. J. Probab., Volume 13 (2008), paper no. 24, 756-776.

Dates
Accepted: 6 May 2008
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819097

Digital Object Identifier
doi:10.1214/EJP.v13-503

Mathematical Reviews number (MathSciNet)
MR2399295

Zentralblatt MATH identifier
1189.60053

Subjects
Primary: 60F05: Central limit and other weak theorems

Rights

#### Citation

Roellin, Adrian. Symmetric and centered binomial approximation of sums of locally dependent random variables. Electron. J. Probab. 13 (2008), paper no. 24, 756--776. doi:10.1214/EJP.v13-503. https://projecteuclid.org/euclid.ejp/1464819097

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