  Liouville copulas, which were introduced in McNeil and Neslehova (2010), are
asymmetric generalizations of the ubiquitous Archimedean copula class. They are
the dependence structures of scale mixtures of Dirichlet distributions, also
called Liouville distributions. In this paper, the limiting extreme-value
copulas of Liouville copulas and of their survival counterparts are derived.
The limiting max-stable models, termed here the scaled extremal Dirichlet, are
new and encompass several existing classes of multivariate max-stable
distributions, including the logistic, negative logistic and extremal
Dirichlet. As shown herein, the stable tail dependence function and angular
density of the scaled extremal Dirichlet model have a tractable form, which in
turn leads to a simple de Haan representation. The latter is used to design
efficient algorithms for unconditional simulation based on the work of Dombry,
Engelke and Oesting (2015) and to derive tractable formulas for
maximum-likelihood inference. The scaled extremal Dirichlet model is
illustrated on river flow data of the river Isar in southern Germany.
