The class of multivariate max-id copulas with $\ell_{1}$-norm symmetric exponent measure

Abstract

Members of the well-known family of bivariate Galambos copulas can be expressed in a closed form in terms of the univariate Fréchet distribution. This formula extends to any dimension and can be used to define a whole new class of tractable multivariate copulas that are generated by suitable univariate distributions. This paper gives necessary and sufficient conditions on the underlying univariate distribution which ensure that the resulting copula exists. It is also shown that these new copulas are in fact dependence structures of certain max-id distributions with $\ell_{1}$-norm symmetric exponent measure. The basic dependence properties of this new class of multivariate exchangeable copulas is investigated, and an efficient algorithm is provided for generating observations from distributions in this class.