Multivariate Archimedean copulas, d-monotone functions and ℓ1-norm symmetric distributions

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional ℓ1-norm... View More