On an extreme two-point distribution

Details On an extreme two-point distribution On an extreme two-point distribution

2007-10-18

arxiv.org/abs/0710.3456v1

Mathematics

Probability

4 pages, 3 figures

Scientific paper

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.

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