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Title: Certain copula transformations: From 2D to 3D Authors:  Martynas Manstavicius - Vilnius University (Lithuania) [presenting]
Gediminas Bagdonas - Vilnius University (Lithuania)
Egle Gutauskaite - 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, that is, the class of allowable functions $f$ can be substantially enlarged. We have previously determined sufficient conditions on $f$ for $C_f(x,y)=xyf((1-x)(1-y))$ to be a bivariate copula. We will focus on the necessary conditions, implications of such a transformation to probabilistic properties, as well as possibility to extend earlier results to trivariate copulas.