On the convergence of entropy for K-th extreme

TL;DR

This paper investigates the conditions under which the entropy of the k-th largest order statistic converges under linear normalization, providing a theoretical foundation for understanding entropy behavior in extreme value theory.

Contribution

It establishes necessary and sufficient conditions for the convergence of entropy of k-th extremes, advancing the theoretical understanding of entropy in order statistics.

Findings

Identifies conditions for entropy convergence of k-th extremes.

Provides a theoretical framework for entropy limits in order statistics.

Enhances understanding of entropy behavior in extreme value analysis.

Abstract

Let recall that the term 'k-th extreme' was introduced in a limiting sense. That is, if $X_{r:n}$ denote the r-th order statistic then for fix k, as $n\to\infty$, $X_{n-k+1:n}$ is called the k-th extremes or k-th largest order statistics. In this paper, we study entropy limit theorems for k-th largest order statistics under linear normalization. We show the necessary and sufficient conditions which convergence entropy of k-th extreme holds.