On the role of ultramodularity (and Schur concavity) in the construction of binary copulas
Il prossimo Venerdì 2 ottobre, ore 14:30,
presso l'Aula di Consiglio del Dipartimento di Matematica dell'Universita' La Sapienza
Tutte le persone interessate sono invitate ad intervenire
Fabio Spizzichino
Abstract.
We discuss and stress the role of ultramodularity in special types of constructions of binary copulas.
After recalling of some known ultamodularity-based results, we focus on a the so-called D-product of a copula and its dual. We show that for each copula D which is ultramodular and Schur concave on the left upper triangle of the unit square, this D-product of an arbitrary copula and its dual is again a copula. Several examples and counterexamples are given. Finally, some of our results are generalized to the case of semicopulas and quasi-copulas.
Work in collaboration with E. P. Klement, A. Kolesarova and S. Saminger-Platz