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.

翻译：dirichlet 分布(又称多变贝塔)是用来分析频率或比例数据的最常用方法。在估计 Dirichlet 参数时,最大可能性是普遍的。然而,对于小样本大小,最大可能性估计值可能显示重大偏差。在本文件中,Dirchlet 的参数估计是通过修改分数函数获得的,分别旨在分别减少最大概率估计值的平均和中位偏差。模拟研究和应用将调整得分方法与最大可能性进行比较。