Semilinear copulas

Authors:
Fabrizio Durante;Anna Kolesárová;Radko Mesiar;Carlo Sempi
Affiliations:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, A-4040 Linz, Austria;Institute of Information Engineering, Automation and Mathematics, Slovak University of Technology, SK-812 37 Bratislava, Slovakia;Department of Mathematics and Descriptive Geometry, Slovak University of Technology, SK-813 68 Bratislava, Slovakia and Institute of Information Theory and Automation, Czech Academy of Sciences, C ...;Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, I-73100 Lecce, Italy
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

A family of copulas, called semilinear, is constructed starting with some assumptions about the linearity of the copulas along some segments of the unit square. This family contains some other known families of copulas (e.g., Cuadras-Auge, Frechet) and has a nice statistical interpretation. Several construction methods are provided, especially concerning aggregation of semilinear copulas, and a special form of ordinal sum construction is introduced. Some results about related families of quasi-copulas and semicopulas are hence given.