A new multivariate distribution as a basis for compositional data

A useful method for defining models for compositional data, i.e. data representing proportions, is via normalisation of a vector (basis) of positive random variables. The well known Dirichlet distribution is obtained from a basis of independent Gamma variables. Despite its many good properties, such a distribution is inadequate for modeling compositional data, as it implies a poor and always negative dependence structure. In this work a new basis is proposed which includes the Dirichlet one and allows for fairly rich dependence patterns. Its main properties are explored. The generated compositional data distribution is derived and shown, in particular, to be capable of modeling positive dependence too.