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arXiv:0710.3456 [math.PR]AbstractReferencesReviewsResources

On an extreme two-point distribution

V. I. Chebotarev, A. S. Kondrik, K. V. Mikhaylov

Published 2007-10-18Version 1

A bound for functional $\Delta(F)=\sup_{x\in\mathbb R}|F(x)-\Phi(x)|$ is obtained, which is uniform for all distribution functions $F$ of random variables with zero mean-value and unity variance. Moreover, a two-point distribution is found, for which this bound is reached.

Comments: 4 pages, 3 figures
Categories: math.PR
Subjects: 60E15
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