International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 645-655

Copula and semicopula transforms

Fabrizio Durante and Carlo Sempi

Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, Lecce 73100, Italy

Received 22 April 2004

Copyright © 2005 Fabrizio Durante and Carlo Sempi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We characterize the transformation, defined for every copula C, by Ch(x,y):=h[1](C(h(x),h(y))), where x and y belong to [0,1] and h is a strictly increasing and continuous function on [0,1]. We study this transformation also in the class of quasi-copulas and semicopulas.