On an extreme two-point distribution

Abstract

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.

4 pages, 3 figures

Cited by in corpus (1)

• On a bound of the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables