@article{eprints709,
            year = {2010},
           title = {Distorted Copulas: Constructions and Tail Dependence},
          author = {Fabrizio Durante and Rachele Foschi and Peter Sarkoci},
           pages = {2288--2301},
          number = {12},
          volume = {39},
         journal = {Communications in Statistics - Theory and Methods},
             url = {http://eprints.imtlucca.it/709/},
        abstract = {Given a copula C, we examine under which conditions on an order isomorphism {\ensuremath{\psi}} of [0, 1] the distortion C {\ensuremath{\psi}}: [0, 1]2 {$\rightarrow$} [0, 1], C {\ensuremath{\psi}}(x, y) = {\ensuremath{\psi}}\{C[{\ensuremath{\psi}}?1(x), {\ensuremath{\psi}}?1(y)]\} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on {\ensuremath{\psi}} that ensures that any distortion of C by means of {\ensuremath{\psi}} 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.},
        keywords = {Copula, Distorted probability, Isomorphic transformation, Tail dependence, TP2 property}
}