ABSTRACT
A random distribution is a random variable taking values in a space of probability measures. We consider here distributional data as outcomes of a function of a random distribution so that interval data and histogram data are particular cases of distributional data. We are interested in the probability distribution of such data in the form of mixture models, that is convex combinations of well-known distributions such as Dirichlet Distributions, Dirichlet Process and Dependent Dirichlet Process. EM algorithm for estimating a mixture of Dirichlet Distributions is fully detailed while npEM algorithm and MCM-based algorithms can be used in the other cases.
