Name
Abstract | ||
|---|---|---|
In recent years, there has been a raise of interest in the determination of copulas with given values at some fixed points, or with given horizontal, vertical, affine, diagonal, or sub-diagonal sections and combinations thereof. Closely related to these investigations are the determination and characterization of increasing and 2-increasing functions with given margins whose domain is a subset of the unit square as well as necessary and sufficient conditions providing that the combination (patchwork) of such functions on sub-domains yields a (new) 2-increasing aggregation function on [0, 1](2), in particular a copula. In the present contribution we provide a full characterization of increasing, 2-increasing functions with prescribed margins acting on a sub-rectangle of the unit square. The characterization allows to determine easily the greatest and smallest such functions and to look at the results on copulas with given horizontal and/or vertical sections and its boundaries from a more general and unified viewpoint. We further discuss necessary and sufficient conditions for a patchwork based on triangular sub-domains. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1007/978-3-540-85027-4_42 | SOFT METHODS FOR HANDLING VARIABILITY AND IMPRECISION |
Keywords | Field | DocType |
fixed point | Affine transformation,Diagonal,Discrete mathematics,Tail dependence,Copula (linguistics),Soft computing,Fixed point,Unit square,Statistics,Moment problem,Mathematics | Conference |
Volume | ISSN | Citations |
48 | 1615-3871 | 4 |
PageRank | References | Authors |
0.57 | 8 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Fabrizio Durante | 1 | 391 | 59.28 |
| Susanne Saminger-Platz | 2 | 76 | 10.94 |
| Peter Sarkoci | 3 | 113 | 12.64 |