  We construct a new distribution for the simplex using the Kumaraswamy
distribution and an ordered stick-breaking process. We explore and develop the
theoretical properties of this new distribution and prove that it exhibits
symmetry under the same conditions as the well-known Dirichlet. Like the
Dirichlet, the new distribution is adept at capturing sparsity but, unlike the
Dirichlet, has an exact and closed form reparameterization--making it well
suited for deep variational Bayesian modeling. We demonstrate the
distribution's utility in a variety of semi-supervised auto-encoding tasks. In
all cases, the resulting models achieve competitive performance commensurate
with their simplicity, use of explicit probability models, and abstinence from
adversarial training.
