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Geometry of generators of triangular norms and copulas

Author

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  • Houšková Kamila

    (Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, CZ-166 27 Prague, Czech Republic)

  • Navara Mirko

    (Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University in Prague, CZ-166 27 Prague, Czech Republic)

Abstract

We study the relations between the shapes of strict triangular norms and their generators. The generators are not unique; to avoid this ambiguity, we introduce the class of balanced generators. We find conditions for their existence and a procedure of their computation. We formulate their influence on local properties of the corresponding triangular norms, in particular at the extremes of their domain. Many strict triangular norms are also copulas; thus, our results can also be applied to bivariate extreme value distributions described by some families of copulas.

Suggested Citation

  • Houšková Kamila & Navara Mirko, 2024. "Geometry of generators of triangular norms and copulas," Dependence Modeling, De Gruyter, vol. 12(1), pages 1-16.
    • Handle: RePEc:vrs:demode:v:12:y:2024:i:1:p:16:n:1001
    DOI: 10.1515/demo-2024-0004
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    References listed on IDEAS

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    1. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
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