%0 Journal Article
%A Durante, Fabrizio
%A Foschi, Rachele
%A Sarkoci, Peter
%D 2010
%F eprints:709
%J Communications in Statistics - Theory and Methods
%K Copula, Distorted probability, Isomorphic transformation, Tail dependence, TP2 property
%N 12
%P 2288-2301
%T Distorted Copulas: Constructions and Tail Dependence
%U http://eprints.imtlucca.it/709/
%V 39
%X Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C ψ: [0, 1]2 → [0, 1], C ψ(x, y) = ψ{C[ψ−1(x), ψ−1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails.