一类新的多元t-型分布  

New class of multivariate t-type distributions

作　　者：温阳俊[1] 朱道元[1] 

机构地区：[1]东南大学理学院

出　　处：《东南大学学报（自然科学版）》2007年第3期543-548,共6页Journal of Southeast University：Natural Science Edition

摘　　要：为了在椭球等高分布的基础上建立样本的理论,需将随机向量的分布推广到随机矩阵的形式.运用3种不同的方法(密度生成函数方法,逆维希特分布方法,2个独立的随机矩阵构造新的随机矩阵的方法)分别提出了矩阵Kotz-型分布,矩阵逆Γ分布和矩阵t-型分布,证明了它们是一个矩阵分布密度,并着重研究了矩阵t-型分布的有关分布性质,包括其随机表示、期望、线性组合分布及二次型等.In order to found the sample theory based on the elliptically contoured distribution, the distributions of random vectors must be extended to that of random matrices. In this paper, definitions of matrix Kotz-type distribution, matrix inverse gamma distribution and matrix t-type distribution are proposed through three different methods, i.e. , density generator approach, inverse Wishart distribution approach and construction approach of the matrix t-type distribution using two independent random matrices. And it is proved that they are densities of matrix distribution. The properties about matrix t-type distribution are stressed. Stochastic representation, expectation, linear transformations and quadratic forms are derived.

关 键 词：矩阵Kotz-型分布 矩阵逆Γ分布 矩阵t-型分布 椭球等高矩阵分布 密度生成函数 

分 类 号：O212.4[理学—概率论与数理统计]