  The Dirichlet distribution, also known as multivariate beta, is the most used
to analyse frequencies or proportions data. Maximum likelihood is widespread
for estimation of Dirichlet's parameters. However, for small sample sizes, the
maximum likelihood estimator may shows a significant bias. In this paper,
Dirchlet's parameters estimation is obtained through modified score functions
aiming at mean and median bias reduction of the maximum likelihood estimator,
respectively. A simulation study and an application compare the adjusted score
approaches with maximum likelihood.
