A New Method for the Construction of Bivariate Archimedean Copulas Based on the Function

We introduce and discuss a general method for constructing bivariate Archimedean copula families. The central item in our method is the function [image omitted] (t[0, 1]), where phi is the generator of the Archimedean copula. The construction of new copulas by means of has several advantages. The most important one is the straightforward relationship between the function and Kendall's and the coefficients of upper and lower tail dependence L and U, as defined in Joe (1997), which makes it possible to use these quantities as copula parameters and to control them independently of each other. Furthermore, the -method allows to construct multi-parameter families in a clear and organized way. The methodology is explained and illustrated by two- and three-parameter copula families.