On the supremum and its location of the standardized uniform empirical process

Dietmar Ferger

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arXiv · 2512.17674

On the supremum and its location of the standardized uniform empirical process

Dietmar Ferger

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Abstract

We show that the maximizing point and the supremum of the standardized uniform empirical process converge in distribution. Here, the limit variable (Z, Y ) has independent components. Moreover, Z attains the values zero and one with equal probability one half and Y follows the Gumbel-distribution.

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Dietmar Ferger. 2025-12-19. On the supremum and its location of the standardized uniform empirical process. https://arxiv.org/abs/2512.17674

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