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Symmetry and dependence properties within a semiparametric family of bivariate copulas. (English) Zbl 1019.62046

Summary: We study a semiparametric family of bivariate copulas. The family is generated by a univariate function, determining the symmetry (radial symmetry, joint symmetry) and dependence properties (quadrant dependence, total positivity, \(\dots)\) of the copulas. We provide bounds on different measures of association (such as Kendall’s Tau, Spearman’s Rho) for this family and several choices of generating functions for which these bounds can be reached.

MSC:

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