  A multivariate extension of the Dickman distribution was recently introduced,
but very few properties have been studied. We discuss several properties with
an emphasis on simulation. Further, we introduce and study a multivariate
extension of the more general class of Vervaat perpetuities and derive a number
of properties and representations. Most of our results are presented in the
even more general context of so-called $\alpha$-times self-decomposable
distributions.
