  The class of Archimax copulas is generalized to hierarchical Archimax copulas
in two ways. First, a hierarchical construction of $d$-norm generators is
introduced to construct hierarchical stable tail dependence functions which
induce a hierarchical structure on Archimax copulas. Second, by itself or
additionally, hierarchical frailties are introduced to extend Archimax copulas
to hierarchical Archimax copulas in a similar way as nested Archimedean copulas
extend Archimedean copulas. Possible extensions to nested Archimax copulas are
discussed. Additionally, a general formula for the density and its evaluation
of Archimax copulas is introduced.
