论文信息 - Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators

Extension to copulas and quasi-copulas as special 1-Lipschitz aggregation operators

Smallest and greatest 1-Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).

Anna Kolesárová | Erich-Peter Klement

[1] Christian Genest,et al. A Characterization of Quasi-copulas , 1999 .

[2] M. J. Frank. On the simultaneous associativity of F(x, y) and x+y-F(x, y). (Short Communication). , 1978 .

[3] Carles M. Cuadras,et al. Distributions With Given Marginals and Statistical Modelling , 2002 .

[4] Engin A. Sungur,et al. Diagonal copulas of archimedean class , 1996 .

[5] R. Mesiar,et al. Aggregation operators: properties, classes and construction methods , 2002 .

[6] Roger B. Nelsen,et al. The Bertino Family of Copulas , 2002 .

[7] Roger B. Nelsen,et al. Best-possible bounds on sets of bivariate distribution functions , 2004 .

[8] M. Sklar. Fonctions de repartition a n dimensions et leurs marges , 1959 .

[9] Anna Kolesárová,et al. 1-Lipschitz aggregation operators and quasi-copulas , 2003, Kybernetika.

[10] R. Nelsen. An Introduction to Copulas , 1998 .

[11] R. Mesiar,et al. On a family of copulas constructed from the diagonal section , 2006, Soft Comput..

[12] Claudi Alsina,et al. On the characterization of a class of binary operations on distribution functions , 1993 .

[13] Abe Sklar,et al. Random variables, joint distribution functions, and copulas , 1973, Kybernetika.

[14] Josef Štěpán,et al. Distributions with given marginals and moment problems , 1997 .

[15] Roger B. Nelsen,et al. Copulas Constructed from Diagonal Sections , 1997 .