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Generalized Farlie-Gumbel-Morgenstern Copulas

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

Abstract

The Farlie-Gumbel-Morgenstern copulas are related to the independence copula \(\varPi \) and can be seen as perturbations of \(\varPi \). Based on quadratic constructions of copulas, we provide a new look at them. Starting from any 2-dimensional copula and an appropriate real function, we introduce new parametric families of copulas which in the case of the independence copula \(\varPi \) coincide with the Farlie-Gumbel-Morgenstern family. Using the proposed approach, we also obtain as a particular case a subclass of the Fréchet family of copulas containing all three basic copulas \(W, \varPi \) and M, i.e. a comprehensive family of copulas. Finally, based on an iterative approach, we introduce copula families \(\left( C_r\right) _{r\in [-\infty ,\infty ]}\) complete w.r.t. dependence parameters, resulting in the case of the independence copula and parameters \(r\in [-1,1]\) in the Farlie-Gumbel-Morgenstern family.

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Acknowledgments

The first two authors kindly acknowledge the support of the project of Science and Technology Assistance Agency under the contract No. APVV–14–0013. The work of A. Kolesárová was also supported by the grant VEGA 1/0891/17. The second and third author also acknowledge the support of the “Technologie-Transfer-Förderung" of the Upper Austrian Government (Wi-2014-200710/13-Kx/Kai).

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Authors and Affiliations

  1. Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37, Bratislava, Slovakia

    Anna Kolesárová

  2. Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 810 05, Bratislava, Slovakia

    Radko Mesiar

  3. Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040, Linz, Austria

    Susanne Saminger-Platz

Authors
  1. Anna Kolesárová
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  2. Radko Mesiar
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  3. Susanne Saminger-Platz
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Corresponding author

Correspondence to Radko Mesiar .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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Kolesárová, A., Mesiar, R., Saminger-Platz, S. (2018). Generalized Farlie-Gumbel-Morgenstern Copulas. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_21

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91472-5

  • Online ISBN: 978-3-319-91473-2

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