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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.)
##### Keywords:
copula; non-exchangeable random variables; Spearman’s rho
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##### References:
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