In this paper, we study the geometry induced by the Fisher-Rao metric on the parameter space of Dirichlet distributions. We show that this space is geodesically complete and has everywhere negative sectional curvature. An important consequence of this negative curvature for applications is that the Fr{\'e}chet mean of a set of Dirichlet distributions is uniquely defined in this geometry.

翻译：在本文中,我们研究了由Fisher-Rao测量法引申的Drichlet分布的参数空间的几何学。我们展示了这个空间是地理学上完整的,而且到处都有负区段曲线。 应用的这种负曲线的一个重要后果是,在这个几何中,一套Drichlet分布法的法尔舍尔法尔法尔法尔法尔法尔特法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法特法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法尔法特法尔法尔法特。