矩阵F分布与矩阵T分布在左球分布类中的推广  

The Extension of the Matrix F and T Distributions to the Left Spherical Family

作　　者：石爱菊[1] 

机构地区：[1]南京邮电大学数理学院,江苏南京210003

出　　处：《南京邮电大学学报（自然科学版）》2008年第5期64-67,共4页Journal of Nanjing University of Posts and Telecommunications：Natural Science Edition

基　　金：南京邮电大学校科研基金(NY207092)资助项目

摘　　要：利用任意非负Borel函数的数学期望与随机向量的密度函数的关系,通过随机矩阵的变换,证明了左球分布定义的矩阵F和矩阵T仍然服从矩阵F分布和矩阵T分布,从而将矩阵F分布和矩阵T分布推广到左球分布类。这一结果扩大了椭球等高分布的应用范围。Let A be a random matrix defined by left spherical family. In this paper, by using the relation between the expectation of non - negative random Borel function and density function, we prove that the F and T distributions of the matrix A are invariant under linear transformations. Consequently, we extend the F and T distributions of a random matrix to the left spherical family, which provides other applications of elliptically contoured distribution of random matrices.

关 键 词：椭球等高分布 矩阵T分布 矩阵F分布 变换 

分 类 号：O212.4[理学—概率论与数理统计]