Uniform estimates for order statistics and Orlicz functions

TL;DR

This paper derives uniform bounds for the order statistics of i.i.d. log-concave random variables using Orlicz norms linked to their distribution functions.

Contribution

It introduces new uniform estimates connecting order statistics with Orlicz norms for log-concave distributions.

Findings

Established bounds for order statistics using Orlicz norms.

Extended the understanding of distributional properties of log-concave variables.

Provided tools for analyzing extremal behavior in probabilistic models.

Abstract

We establish uniform estimates for order statistics of sequences of independent identically distributed random variables with log-concave distribution in terms of Orlicz norms associated with the distribution function of the random variables.