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Title: Some transformations of bivariate independence copula Authors:  Martynas Manstavicius - Vilnius University (Lithuania) [presenting]
Gediminas Bagdonas - Vilnius University (Lithuania)
Abstract: Necessary and sufficient conditions on $f$ for the function $H_f(C)(x,y)=C(x,y)f(1-x-y+C(x,y))$, $x,y\in[0,1]$ to be a bivariate copula for \emph{any} bivariate copula $C$ are known. If, on the other hand, $C(x,y)=\Pi(x,y)=xy$ is fixed, then some of those conditions become no longer necessary, presenting an interesting problem. Sufficient conditions, which unify several known examples, will be provided, and a discussion on their necessity, as well as on several interesting properties of $C_f$ when it is indeed a copula, will be given.