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arXiv · 0710.3456

On an extreme two-point distribution

V. I. Chebotarev·A. S. Kondrik·K. V. Mikhaylov
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Abstract

A bound for functional $Δ(F)=\sup_{x\in\mathbb R}|F(x)-Φ(x)|$ 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.

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V. I. Chebotarev, A. S. Kondrik, K. V. Mikhaylov. 2007-10-18. On an extreme two-point distribution. https://arxiv.org/abs/0710.3456

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