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Extremes of nonexchangeability. (English) Zbl 1110.62071
Summary: For identically distributed random variables \(X\) and \(Y\) with joint distribution function \(H\), we show that the supremum of \(|H(x,y)-H(y,x)|\) is \(1/3\). Using copulas, we define a measure of non-exchangeability, and study maximally non-exchangeable random variables and copulas. In particular, we show that maximally non-exchangeable random variables are negatively correlated in the sense of Spearman’s rho.

MSC:
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H20 Measures of association (correlation, canonical correlation, etc.)
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