椭球等高分布族中下三角分解的一些结果

Some Results Obtained from Elliptically Contoured Matrix Population Based on the Lower-triangular Matrix Decomposion

该文证明了正定阵下三角分解存在且唯一的结论,运用外微分的方法给出该分解的Jacobian,再分别得到Wishart分布、矩阵Beta分布、逆矩阵Beta分布和矩阵F分布的下三角分解的相应结果。

It calculates the Jacobian of the lower triangular decomposition of positive matrix through the methods of exterior differential, and then gets the statistical relationship among the elements within a certain triangular matrix decomposed from the Wishart matrix,Beta matrix, inverse Beta matrix or F matrix in the family of elliptically contoured distribution.