Moment-type estimators for the Dirichlet and the multivariate gamma distributions

This study presents new closed-form estimators for the Dirichlet and the multivariate gamma distribution families, whose maximum likelihood estimator cannot be explicitly derived. The methodology builds upon the score-adjusted estimators for the beta and gamma distributions, extending their applicability to the Dirichlet and multivariate gamma distributions. Expressions for the asymptotic variance–covariance matrices are provided, demonstrating the superior performance of score-adjusted estimators over the traditional moment ones. Leveraging well-established connections between the Dirichlet and multivariate gamma distributions, a novel class of estimators for the latter is introduced, referred to as “Dirichlet-based moment-type estimators”. The general asymptotic variance–covariance matrix form for this estimator class is derived. To facilitate the application of these innovative estimators, an R package called joker is developed and made publicly available.