On the convergence of entropy for K-th extreme

Ali Saeb

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arXiv · 2407.11264

On the convergence of entropy for K-th extreme

Ali Saeb

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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.

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Ali Saeb. 2024-07-15. On the convergence of entropy for K-th extreme. https://arxiv.org/abs/2407.11264

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