Estimation of Dirichlet distribution parameters with bias-reducing adjusted score functions

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.