椭球等高矩阵分布关于非奇异矩阵变换的不变性  

An Invariant Property of the Elliptically Contoured Distribution about the Non-Singular Matrix Transformation

作　　者：石爱菊[1,2] 林金官[1] 

机构地区：[1]东南大学数学系,南京210096 [2]南京邮电大学理学院,南京210046

出　　处：《应用概率统计》2010年第5期449-458,共10页Chinese Journal of Applied Probability and Statistics

摘　　要：本文首先将矩阵F分布和矩阵t分布的定义推广到左球分布类,其密度函数与产生它们的左球分布或球对称分布的密度均无关.然后讨论了椭球等高分布关于非奇异矩阵变换的不变性问题,包括矩阵Beta分布、逆矩阵Beta分布、矩阵Dirichlet分布、逆矩阵Dirichlet分布、矩阵F分布和矩阵t等分布.在非奇异变换下,这些分布的密度不但与产生它们的左球分布的密度函数无关,而且与非奇异变换矩阵无关.In this paper, we first extend the definitions of matrix F and t distributions to the left spherical distribution family, prove the density functions have no relation with the one producing them and then show that discuss the elliptieally contoured distributions are invariant under nonsingular matrix transformations. These distributions include the matrix Beta, inverse Beta, Dirichlet, inverse Dirichlet, F and t etc. And finally it is shown that their distribution density functions not only have no relation with the density function generating them but also the transformation matrix.

关 键 词：椭球等高分布 矩阵t分布 矩阵F分布 矩阵Beta分布 矩阵Dirichlet分布 非奇异矩阵变换 不变性 

分 类 号：O212.4[理学—概率论与数理统计]