A new mixture model for composition and size

The flexible Dirichlet distribution proposed in Ongaro and Migliorati (JMA, 2013) allows to preserve many mathematical and compositional properties of the Dirichlet without inheriting its lack of flexibility in modeling the various independence concepts appropriate for compositional data (simplicial independences). The present paper introduces a new model on the simplex which generalizes the flexible Dirichlet and which, in particular, addresses the issue of modeling the dependence between the size of the basis and the composition.