| 一类新的多元t-型分布 |
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| 引用本文： | 温阳俊,朱道元.一类新的多元t-型分布[J].东南大学学报(自然科学版),2007,37(3):543-548. |
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| 作者姓名： | 温阳俊 朱道元 |
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| 作者单位： | 东南大学理学院,南京,210096;南京农业大学数学系,南京,210095;东南大学理学院,南京,210096 |
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| 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.
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| 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 |
| 文章编号： | 1001-0505（2007）03-0543-06 |
| 修稿时间： | 2006-09-19 |
New class of multivariate t-type distributions |
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| Wen Yangjun,Zhu Daoyuan.New class of multivariate t-type distributions[J].Journal of Southeast University(Natural Science Edition),2007,37(3):543-548. |
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| Authors: | Wen Yangjun Zhu Daoyuan |
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| Institution: | 1. School of Sciences, Southeast University, Nanjing 210096, China;2Department of Mathmatics, Nanjing Agricultural University, Nanjing 210095, China |
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| Abstract: | 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. |
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| Keywords: | matrix Kotz-type distribution matrix inverse gamma distribution matrix t-type distribution elliptically contoured matrix distribution density generator |
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