On an extreme two-point distribution

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

On an extreme two-point distribution

Authors

Chebotarev, V. I.

Kondrik, A. S.

Mikhaylov, K. V.

Description

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.
4 pages, 3 figures