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International Summer School on Aggregation Operators

AGOP 2017: Aggregation Functions in Theory and in Practice pp 21–30Cite as

On Some Applications of Williamson’s Transform in Copula Theory

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

Abstract

We show several interesting examples of connection between distribution of a positively valued random variable and an Archimedean copula through Williamson’s transformation (and Laplace transform), especially when arranged in a sequence. Naturally, there appears a question: how can we use statistical properties of distance functions to draw statistical properties of copulas, and vice versa? This question is formulated in two open problems.

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Acknowledgement

The work on this paper was supported by grant APVV-14-0013.

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Authors and Affiliations

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

    Tomáš Bacigál

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  1. Tomáš Bacigál
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Correspondence to Tomáš Bacigál .

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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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Bacigál, T. (2018). On Some Applications of Williamson’s Transform in Copula Theory. 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_3

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  • DOI: https://doi.org/10.1007/978-3-319-59306-7_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59305-0

  • Online ISBN: 978-3-319-59306-7

  • eBook Packages: EngineeringEngineering (R0)

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