论文标题
单纯形上的Schlömilch积分和概率分布
Schlömilch integrals and probability distributions on the simplex
论文作者
论文摘要
回顾了Schlömilch的积分，即单纯派对Dirichlet积分的概括以及相关的概率分布。提出了一个统一差异分布的几个概括的分布，其中包括缩放的dirichlet分布和某些dirichlet混合物分布。可以发现时刻和对数的协方差。分布的归一化促进了单纯形成表示的定义，该定义是分数度的完全均匀对称多项式。
The Schlömilch integral, a generalization of the Dirichlet integral on the simplex, and related probability distributions are reviewed. A distribution that unifies several generalizations of the Dirichlet distribution is presented, with special cases including the scaled Dirichlet distribution and certain Dirichlet mixture distributions. Moments and log-ratio covariances are found, where tractable. The normalization of the distribution motivates a definition, in terms of a simplex integral representation, of complete homogeneous symmetric polynomials of fractional degree.
