The simplex is the geometrical locus of D-dimensional positive data with constant sum, called compositions. A possible distribution for compositions is the Dirichlet. In Dirichlet models, there are no scale parameters and the D shapes are assumed dependent on auxiliary variables. This peculiar feature makes Dirichlet models difficult to apply and to interpret. Here, we propose a generalization of the Dirichlet, called the simplicial generalized Beta (SGB) distribution. It includes an overall shape parameter, a scale composition and the D Dirichlet shapes. The SGB is flexible enough to accommodate many practical situations. SGB regression models are applied to data from the United Kingdom Time Use Survey. The R-package SGB makes the methods accessible to users.

单纯形是具有恒定总和的D维正数据的几何轨迹，称为合成。成分的可能分布是Dirichlet。在Dirichlet模型中，没有比例尺参数，并且D形状取决于辅助变量。这种独特的功能使Dirichlet模型难以应用和解释。在这里，我们提出Dirichlet的广义化，称为简单广义Beta（SGB）分布。它包括总体形状参数，比例组成和DDirichlet形状。SGB足够灵活，可以适应许多实际情况。SGB回归模型应用于来自英国时间使用情况调查的数据。R包SGB使用户可以访问这些方法。