Matrix Variate Distributions
Matrix Variate Distributions
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DOI：
10.1198/jasa.2003.s280
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发表时间：
1999-10
影响因子：
3.7
通讯作者：
A. Rukhin
中科院分区：
文献类型：
--
作者：
A. Rukhin
初等矩阵代数变换的雅可比积分带状多项式广义Hermite多项式广义Hermite多项式矩阵问题的概念矩阵变量正态分布密度函数性质奇异矩阵变量正态分布对称矩阵变量正态分布约束矩阵变量q-广义正态分布矩阵广义正态分布引入密度函数性质逆Wishart分布非中心Wishart分布矩阵变量Gamma分布逼近矩阵变量t-分布密度函数性质逆矩阵t-分布伪装矩阵变量t-分布限制矩阵变量t-分布二次型矩阵分布非中心矩阵密度函数性质相关分布非中心矩阵Beta分布矩阵变量Dirichlet分布密度函数性质相关分布非中心矩阵变量Dirichlet分布矩阵二次型分布密度函数性质二次型密度函数级数表示非中心密度函数期望值二次型Xax‘+1/2型(Lx’+Xl‘)+C型二次型Wishart分布的正态分布Bimatix Wishart分布广义Bingham-Von分布的正态分布Bimatix Wishart分布Beta-Wishart型二次型的正态分布分布合流超几何函数类型1分布合流超几何函数类型2分布超几何函数分布广义超几何函数分布复矩阵变量分布矩阵变量球分布矩阵变量椭球分布矩阵变量椭圆轮廓分布正交不变和剩余独立矩阵分布词汇参考主题索引每章还包括引言和问题@
PRELIMINARIES Matrix Algebra Jacobians of Transformations Integration Zonal Polynomials Hypergeometric Functions of Matrix Argument LaGuerre Polynomials Generalized Hermite Polynomials Notion of Random Matrix Problems MATRIX VARIATE NORMAL DISTRIBUTION Density Function Properties Singular Matrix Variate Normal distribution Symmetic Matrix Variate Normal Distribution Restricted Matrix Variate Normal Distribution Matrix Variate Q-Generalized Normal Distribution WISHART DISTRIBUTION Introduction Density Function Properties Inverted Wishart Distribution Noncentral Wishart Distribution Matrix Variate Gamma Distribution Approximations MATRIX VARIATE t-DISTRIBUTION Density Function Properties Inverted Matrix Variate t-Distribution Disguised Matrix Variate t-Distribution Restricted Matrix Variate t-Distribution Noncentral Matrix Variate t-Distribution Distribution of Quadratic Forms MATRIX VARIATE BETA DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Beta Distribution MATRIX VARIATE DIRICHLET DISTRIBUTIONS Density Functions Properties Related Distributions Noncentral Matrix Variate Dirichlet Distributions DISTRIBUTION OF MATRIX QUADRATIC FORMS Density Function Properties Functions of Quadratic Forms Series Representation of the Density Noncentral Density Function Expected Values Wishartness and Independence of Quadratic Forms of the Type XAX' Wishartness and Independence of Quadratic Forms of the Type XAX'+1/2(LX'+XL')+C Wishartness and Independence of Quadratic Forms of the Type XAX'+L1X'+XL'2+C MISCELLANEOUS DISTRIBUTIONS Uniform Distribution on Stiefel Manifold Von Mises-Fisher Distribution Bingham Matrix Distribution Generalized Bingham-Von Mises Matrix Distribution Manifold Normal Distribution Matrix Angular Central Gaussian Distribution Bimatix Wishart Distribution Beta-Wishart Distribution Confluent Hypergeometric Function Kind 1 Distribution Confluent Hypergeometric Function Kind 2 Distribution Hypergeometric Function Distributions Generalized Hypergeometric Function Distributions Complex Matrix Variate Distributions GENERAL FAMILIES OF MATRIX VARIATE DISTRIBUTIONS Matrix Variate Liouville Distributions Matrix Variate Spherical Distributions Matrix Variate Elliptically Contoured Distributions Orthogonally Invariant and Residual Independent Matrix Distributions GLOSSARY REFERENCES SUBJECT INDEX Each chapter also includes an Introduction and Problems @