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Short Communications

On the normal approximation to symmetric binomial distributions

Ch. Hipp^a, L. Mattner<sup>b

a</sup> Universität Karlsruhe
^b University Lübeck

Abstract: The optimal constant over the square root of $n$ error bound in the central limit theorem for distribution functions of sums of independent symmetric Bernoulli random variables is $1/\sqrt{2\pi n}$.

Keywords: binomial distribution, central limit theorem, optimal error bound, symmetric Bernoulli variables.

Received: 04.05.2006

Language: English

DOI: 10.4213/tvp82

 English version: Theory of Probability and its Applications, 2008, 52:3, 516–523

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