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A look at copulas in a curved mirror

In: Copulas and Dependence Models with Applications

Author

Listed:
  • Bernard De Baets

    (Ghent University, KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics)

  • Hans De Meyer

    (Ghent University, Department of Applied Mathematics, Computer Science and Statistics)

Abstract

We extend the seminal work of Roger Nelsen on symmetry-related properties and the degree of asymmetry of copulas, by reattributing the role the diagonal plays as axis of symmetry to a continuous strictly increasing curve in the unit square. First, we make explicit the geometrical notion of symmetry of a function on the unit square with respect to a curve. Next, we provide a measure for quantifying to what extent a quasi-copula or copula can be regarded asymmetric with respect to a given curve. Finally, we derive a lower and upper bound on the degree of asymmetry a quasi-copula can possess with respect to a given curve and show that each bound is sharp within the class of copulas.

Suggested Citation

  • Bernard De Baets & Hans De Meyer, 2017. "A look at copulas in a curved mirror," Springer Books, in: Manuel Úbeda Flores & Enrique de Amo Artero & Fabrizio Durante & Juan Fernández Sánchez (ed.), Copulas and Dependence Models with Applications, chapter 0, pages 33-47, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-64221-5_3
    DOI: 10.1007/978-3-319-64221-5_3
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