On a family of copulas constructed from the diagonal section. (English) Zbl 1098.60016

Summary: We characterize the class of copulas that can be constructed from the diagonal section by means of the functional equation \(C (x, y)+| x - y |= C (x \vee y, x \vee y)\), for all \((x, y)\) in the unit square such that \(C (x, y)>0\). Some statistical properties of this class are given.


60E05 Probability distributions: general theory
26B35 Special properties of functions of several variables, Hölder conditions, etc.
62H20 Measures of association (correlation, canonical correlation, etc.)
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