矩阵正态变量二次型的分布

矩阵正态变量二次型的分布 THE DISTRIBUTION OF A QUADRATIC FORM OF NORMAL RANDOM MATRIX 黄秦 Huang Qin 1 first-author 株洲电子研究所 株洲电子研究所 < 正 > §1.引言本文引入正态变量阵的概念,利用特征函数来导出正态变量阵的二次型的分布。设X是n×p的矩阵,X中的元素用x ij 表示,{x ij :i=1,2,…,n,j=1,2,…,p}是相互独立的标准正态变量(即Ex ij =0,V ar (x ij )=1的正态变量),于是X的特征函数考虑随机变量阵Y=AXB’+M的特征函数,于是 In this paper, We get two main results: （1） If Q=Y’AY+B’Y+Y’B+C, where A, B, C are constant matrices and Y is a normal distributed random matrix, Then the expression of the characteristic function of Q is where and （2） The aecessary and sufficient conditions for that Q is distributed by wishart distribution are obtained. 1982-03-01 2021-04-01 3