Analysis of correlation among components of a Flexible Dirichlet Distribution

Components in random compositions can never be stochastically independent, so the traditional concept of independence has to be changed with a compositional framework (Aitchison (1986)). The aim of this paper is to analyze the feasibility of Chayes’ approximation (Chayes (1960)) in testing some forms of compositional independence between a couple of Flexible Dirichlet distribution components (Ongaro et al. (2008)). The only case of strict independence for a Flexible Dirichlet composition is possible when this kind of distribution coincides with the Dirichlet one. Some Monte Carlo simulations have been hereby provided in order to show whether the Chayes’ approximation testing “null correlation” can work or not in presence of specific parametric configurations.