On the convergence of entropy for K-th extreme

2024/07/15 by Ali Saeb, Saeb, Ali
Economics, Econometrics and Finance · #60-F10 #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2407.11264

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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→∞, 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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