A measure of multivariate mutual complete dependence

The authors propose a multivariate version of Siburg and Stoimenov's measure of mutual complete dependence. This multivariate version is, however, not the distance between a copula and the product copula C-1 under the modified Sobolev norm since the set of mutual complete dependence copulas does not lie on the sphere centered at C-1. To overcome this difficulty, the authors choose another center and define measures of complete dependence based on the modified Sobolev norm and this center. The measure of multivariate mutual complete dependence is then defined as the summation of the (normalized) measures of complete dependence. (C) 2013 Elsevier Inc. All rights reserved.