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Transformations of Copulas and Quasi-Copulas

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Soft Methodology and Random Information Systems

Part of the book series: Advances in Soft Computing ((AINSC,volume 26))

Abstract

Transformations of aggregation operators preserving the class of copulas and quasi-copulas, respectively, are shown to be concave automorphisms of the unit interval. Attractors of copulas are discussed, special attention being paid to power transformations and the relationship between the corresponding attractors and the so-called maximum attractor (quasi-)copulas. The class of quasi-copulas stable under power transformations is characterized, and it is conjectured that it coincides with the class of all maximum attractor quasi-copulas. Also, examples of copulas not belonging to the maximum domain of attraction of any copula are provided.

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Author information

Authors and Affiliations

  1. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria

    Erich Peter Klement

  2. Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  3. Institute of the Theory of Information and Automation, Czech Academy of Sciences, Prague, Czech Republic

    Endre Pap

  4. Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia and Montenegro

    Endre Pap

Authors
  1. Erich Peter Klement
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  2. Radko Mesiar
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  3. Endre Pap
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© 2004 Springer-Verlag Berlin Heidelberg

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Klement, E.P., Mesiar, R., Pap, E. (2004). Transformations of Copulas and Quasi-Copulas. In: Soft Methodology and Random Information Systems. Advances in Soft Computing, vol 26. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44465-7_21

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  • DOI: https://doi.org/10.1007/978-3-540-44465-7_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22264-4

  • Online ISBN: 978-3-540-44465-7

  • eBook Packages: Springer Book Archive

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