[1]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.[doi:10.3969/j.issn.1001-0505.2007.03.038]
 Wen Yangjun,Zhu Daoyuan.New class of multivariate t-type distributions[J].Journal of Southeast University (Natural Science Edition),2007,37(3):543-548.[doi:10.3969/j.issn.1001-0505.2007.03.038]
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一类新的多元t-型分布()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
37
期数:
2007年第3期
页码:
543-548
栏目:
数学、物理学、力学
出版日期:
2007-05-20

文章信息/Info

Title:
New class of multivariate t-type distributions
作者:
温阳俊12 朱道元1
1 东南大学理学院, 南京 210096; 2 南京农业大学数学系, 南京 210095
Author(s):
Wen Yangjun12 Zhu Daoyuan1
1 School of Sciences, Southeast University, Nanjing 210096, China
2 Department of Mathmatics, Nanjing Agricultural University, Nanjing 210095, China
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
Keywords:
matrix Kotz-type distribution matrix inverse gamma distribution matrix t-type distribution elliptically contoured matrix distribution density generator
分类号:
O212.4
DOI:
10.3969/j.issn.1001-0505.2007.03.038
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.
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.

参考文献/References:

[1] Nadarajah S.Sampling distributions associated with the multivariate t distribution[J]. Statistica Neerlandica,2005,59(2):214-234.
[2] 朱道元,吴诚鸥,秦伟良.多元统计分析与软件SAS[M].南京:东南大学出版社,1999:174,175,197.
[3] Butler R J,McDonald J B,Nelson R D,et al.Robust and partially adaptive estimation of regression models[J]. Rev Econom Statist, 1990,72:321-327.
[4] Arslan O.Family of multivariate generalized t distributions[J].J Multivar Anal,2004,89(2):329-337.
[5] Arslan O.A new class of multivariate distribution:scale mixture of Kotz-type distributions[J]. Statist Prob Lett,2005,75(11):18-28.
[6] Johnson N L,Kotz S,Balakrishnan N.Continuous univariate distributions[M].New York:Wiley,1995:401-401.
[7] 方开泰,张尧庭.广义多元分析[M].北京:科学出版社,1993:122-145.

备注/Memo

备注/Memo:
作者简介: 温阳俊(1978—),女,硕士生; 朱道元(联系人),男,教授,zhudy@seu.edu.cn.
更新日期/Last Update: 2007-05-20