Distributions for Random Compositions

Abstract

Distribution models are descriptions of the randomness or uncertainty on a phenomenon. The most typical distribution models for compositions are the Dirichlet and the additive logistic normal (or normal on the simplex). For count compositions, the multinomial distribution and the double stochastic distribution are the reference models. The first two sections of this chapter summarize the definitions of these models, together with some other complementary probability models, as well as the available functions to work with them. The last section summarizes some properties and relations between the several distributions presented before. Tests for the various distribution models are discussed after presenting each model.