The maximal correlation coefficient associated with the minimum
Abstract
For independent random variables (Xi)1≤ i≤ n, we consider the maximal correlation coefficient R=R(i:1≤ i≤ mXi,j:+1≤ j≤ nXj). If X1,X2,…,Xn are identically distributed with the same continuous distribution, we find that R=(m-)/m(n-). 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 [Section~6]ChangChen.
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