Geometry of generators of triangular norms and copulas

Houšková Kamila () and Navara Mirko ()
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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

Dependence Modeling, 2024, vol. 12, issue 1, 16

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.

Keywords: multiplicative generator; additive generator; balanced generator; Frank copula; Ali-Mikhail-Haq copula; extreme value distribution (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:demode:v:12:y:2024:i:1:p:16:n:1001

DOI: 10.1515/demo-2024-0004

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