A directory of families of infinitely extendible Archimedean copulas

This article introduces families of strict multivariate Archimedean copulas, C  , the ordering of copulas within these families, and associated boundary copulas. The new families are compared with the Clayton, Frank, and Gumbel families with regard to measures of dependence, including tail dependence, Kendall's tau, and Spearman's rho for dimensions 2, 3, and 4. A new inequality that gives maximal values of C(u,v)−uvC(u,v)−uv is conjectured.