Goodness-of-fit tests for the Dirichlet distribution

We propose two new goodness-of-fit tests for the Dirichlet distribution. The first test exploits the Darroch–Ratcliff characterisation of neutrality, whereas the second quantifies the discrepancy between the empirical characteristic function and a numerical approximation to the Dirichlet characteristic function. We discuss asymptotic aspects of both tests and, through a simulation study, show that they are competitive alternatives to the very limited number of tests currently available in the literature. An application to several classical compositional datasets further illustrates the practical utility of the proposed methods.