Susanne Saminger-Platz: On perturbing copulas: some techniques and dependence properties

V četrtek, 23. 5. 2024, ob 14:15 bo v predavalnici 3.06 v okviru seminarja VeSFiM potekalo predavanje Susanne Saminger-Platz (Johannes Kepler University Linz) z naslovom On perturbing copulas: some techniques and dependence properties.

Povzetek: The relevance of copulas in dependence modeling originates from the fact that, due to Sklar's theorem, for (continuous) multivariate distributions the modeling of its univariate marginals and the dependence structure can be separated, where the latter can be represented by a copula. A copula may be seen as a multivariate distribution function with all univariate margins being uniformly distributed on [0,1]. Hence, if C is a copula, then it is the distribution function of a vector of dependent U(0,1) random variables; in case of independence, the corresponding copula being the product. In literature one may find quite some different classes and families of copulas either deduced, e.g., from multivariate distributions or following different construction approaches like, e.g., Archimedean copulas or some patchwork and gluing techniques; as such also examplifying the many views one can have on this class of functions, its analytical, probabilistic, measure-theoretic, or also algebraic properties, as well as different fields of applications, like, e.g., in finance and hydrology. In this talk we elaborate on a few techniques for constructing copulas. We will then focus on bivariate copulas. The Fréchet-Hoeffding bounds W(x,y)=max{x+y-1,0} and M(x,y)=min{x,y} allowing, as extremal cases, to model the counter- or comonotone behaviour of a pair of continuous random variables. We are interested in perturbing and modifying basic copulas by some parametrized transformations and study under which conditions we obtain again copulas and how their dependence behaviour changes by means of the transformations. This talk will report on joint work with E.P.Klement, A.Kolesarova, R.Mesiar, A.Seliga.

Predavanje bo potekalo v živo, bo pa omogočen tudi prenos prek interneta. Povezava na videokonferenčni sistem ZOOM: https://uni-lj-si.zoom.us/j/95492285750 ID: 954 9228 5750

Vljudno vabljeni!