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 nonexchangeability, and study maximally nonexchangeable random variables and copulas. In particular, we show that maximally nonexchangeable random variables are negatively correlated in the sense of Spearman's rho.
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An erratum to this article is available at http://dx.doi.org/10.1007/s00362-007-0380-9.
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Nelson, R.B. Extremes of nonexchangeability. Statistical Papers 48, 329–336 (2007). https://doi.org/10.1007/s00362-006-0336-5
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DOI: https://doi.org/10.1007/s00362-006-0336-5