The maximal correlation coefficient associated with the minimum

2025/12/17 by Chang, Yinshan, Chen, Qinwei
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Statistical Distribution Estimation and Applications

paper · doi:10.48550/arxiv.2512.15135

openalex publication_date 2025/12/17 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28

Abstract

For independent random variables (X_i)_{1≤ i≤ n}, we consider the maximal correlation coefficient R=R(min_{i:1≤ i≤ m}X_i,min_{j:ℓ+1≤ j≤ n}X_j). If X₁,X₂,…,X_n are identically distributed with the same continuous distribution, we find that R=(m-ℓ)/√(m(n-ℓ)). 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.

Citations

• On the maximal correlation of some stochastic processes
• On the maximal correlation coefficient for the bivariate Marshall Olkin distribution

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