Copulas differ not so much in the degree of association they provide, but rather in which part of the distributions the association is strongest. Often needed for property and casualty applications are copulas that emphasize correlation among large losses, i.e., in the right tails of the distributions. Several copulas that do this are discussed.
To describe aspects of the copulas, univariate functions of copulas are introduced, for example, tail concentration functions. These descriptive functions can be thought of as an intermediate step between correlation coefficients, such as Kendall, Spearman, Gini, etc., which are zero-dimensional measures of association, and the multi-dimensional copulas function itself.
The descriptive functions can be used to select copulas having desired characteristics, such as tail concentration, and they can also be used in the fitting process to judge how well the fitted copulas match those aspects of the data.
