Shadow Dirichlet for Restricted Probability Modeling

Although the Dirichlet distribution is widely used, the independence structure of its components limits its accuracy as a model. The proposed shadow Dirichlet distribution manipulates the support in order to model probability mass functions (pmfs) with dependencies or constraints that often arise in real world problems, such as regularized pmfs, monotonic pmfs, and pmfs with bounded variation. We describe some properties of this new class of distributions, provide maximum entropy constructions, give an expectation-maximization method for estimating the mean parameter, and illustrate with real data.