The maximal correlation coefficient associated with the minimum

Yinshan Chang; Qinwei Chen

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arXiv · 2512.15135

The maximal correlation coefficient associated with the minimum

Yinshan Chang·Qinwei Chen

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Abstract

For independent random variables $(X_i)_{1\leq i\leq n}$, we consider the maximal correlation coefficient $R=R(\min_{i:1\leq i\leq m}X_i,\min_{j:\ell+1\leq j\leq n}X_j)$. If $X_1,X_2,\ldots,X_n$ are identically distributed with the same continuous distribution, we find that $R=(m-\ell)/\sqrt{m(n-\ell)}$. For discrete distributions, we calculate the maximal correlation coefficient $R$ for Bernoulli distributions, geometric distributions, binomial distributions and Poisson distributions. Our paper answers a question in \cite[Section~6]{ChangChen}.

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Yinshan Chang, Qinwei Chen. 2025-12-17. The maximal correlation coefficient associated with the minimum. https://arxiv.org/abs/2512.15135

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