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Families of Perturbation Copulas Generalizing the FGM Family and Their Relations to Dependence Measures

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Aggregation Functions in Theory and in Practice (AGOP 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 581))

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Abstract

In this paper we provide an extension of special parametric class of perturbations of an arbitrary copula (given in [3]) that represent a partial generalization of the FGM family of copulas for parameters from the unit interval. However the FGM family is defined for parameters from the interval \([-1,1]\). We present a construction of perturbations of an arbitrary copula also for parameters from the interval \([-1,0]\) so that together with the former family of perturbations of copulas we get a generalization of the FGM family for the whole interval \([-1,1]\). We also investigated the influence of the parameters of the introduced class of perturbations of copulas on several measures of dependence (Spearman’s rho, Blomqvist’s beta, Gini’s gamma, Kendall’s tau).

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References

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Acknowledgement

This work was supported by Slovak Research and Development Agency under contracts No. APVV–14–0013 and by VEGA 1/0420/15.

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Authors and Affiliations

  1. Faculty of Management, Comenius University, Odbojárov 10, P.O. BOX 95, 820 05, Bratislava, Slovakia

    Jozef Komorník

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

    Magdaléna Komorníková & Jana Kalická

Authors
  1. Jozef Komorník
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  2. Magdaléna Komorníková
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  3. Jana Kalická
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Corresponding author

Correspondence to Magdaléna Komorníková .

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Editors and Affiliations

  1. School of Informatics, University of Skövde, Skövde, Sweden

    Vicenç Torra

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

    Radko Mesiar

  3. KERMIT Research Unit Knowledge-based Systems, Ghent University, Ghent, Belgium

    Bernard De Baets

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Komorník, J., Komorníková, M., Kalická, J. (2018). Families of Perturbation Copulas Generalizing the FGM Family and Their Relations to Dependence Measures. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_6

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

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