On a generalization of Archimedean copula family

•We introduce a new family of multivariate copula functions defined by two generators.•The copula family is a generalization of Archimedean copula family.•We extend the bivariate copula in Durante et al. (2007a) to multivariate case.•The probabilistic structure of the copula function is given.•Multivariate tail dependence and uniqueness are discussed.

This paper introduces a new family of multivariate copula functions defined by two generators, which is a multi-dimensional extension of the bivariate copula presented in Durante et al. (2007a). The copula family is also a generalization of Archimedean copula family to allow for tail dependence. The probabilistic structure of the copula function is given. Some properties of the copula function are discussed, such as multivariate tail dependence and uniqueness.