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补充四元数线性变换下四元数正态分布的性质 ,给出四元数非中心 χ2 分布 ,t分布 ,F分布的定义 ,导出密度函数及其性质 ,并研究四元数正态分布条件下样本均值及方差的分布 . 相似文献
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利用四元数矩阵变元的带状多项式定义及性质推导出四元数非中心Wishart分布及其特征根分布。 相似文献
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在多元统计分析中,经典样本理论向非正态样本发展时,椭球等高分布族理论被建立,八十年代初期已有学讨论了广义中心x^2分布的定义和分布问题,本导出了广义非中心x^2分布的精确表达式。 相似文献
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四元数矩阵实表示的基本性质及应用 总被引:2,自引:0,他引:2
郑福 《数学的实践与认识》2009,39(4)
在四元数实矩阵表示的基础上,给出了四元数矩阵的相同表示,利用友向量的概念,给出了这种实表示的性质,并进一步研究了四元数力学中的系列数值计算问题. 相似文献
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四元数分析是单复变函数理论在高维空间的最自然的推广,已经被应用于数学物理和工程技术中的一些问题研究中,但是其很多理论还需要建立和完善.本文讨论了四元数分析中的正则函数的某些函数论性质,推广了单复变中的解析函数相关理论. 相似文献
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Noncentral elliptical configuration density 总被引:1,自引:0,他引:1
Francisco J. Caro-Lopera Jos A. Díaz-García Graciela Gonzlez-Farías 《Journal of multivariate analysis》2010,101(1):32-43
The noncentral configuration density, derived under an elliptical model, generalizes and corrects the Gaussian configuration and some Pearson results. Partition theory is then used to obtain explicit configuration densities associated with matrix variate symmetric Kotz type distributions (including the normal distribution), matrix variate Pearson type VII distributions (including t and Cauchy distributions), the matrix variate symmetric Bessel distribution (including the Laplace distribution) and the matrix variate symmetric Jensen-logistic distribution. 相似文献
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Djalil Chafaï 《Journal of Theoretical Probability》2010,23(4):945-950
Let (X jk )j,k≥1 be an infinite array of i.i.d. complex random variables with mean 0 and variance 1. Let λ n,1,…,λ n,n be the eigenvalues of \((\frac{1}{\sqrt{n}}X_{jk})_{1\leqslant j,k\leqslant n}\). The strong circular law theorem states that, with probability one, the empirical spectral distribution \(\frac{1}{n}(\delta _{\lambda _{n,1}}+\cdots+\delta _{\lambda _{n,n}})\) converges weakly as n→∞ to the uniform law over the unit disc {z∈?,|z|≤1}. In this short paper, we provide an elementary argument that allows us to add a deterministic matrix M to (X jk )1≤ j,k ≤ n provided that Tr(MM *)=O(n 2) and rank(M)=O(n α ) with α<1. Conveniently, the argument is similar to the one used for the noncentral version of the Wigner and Marchenko–Pastur theorems. 相似文献
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Eckhard M. S. Hitzer 《Advances in Applied Clifford Algebras》2007,17(3):497-517
We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications.
Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to
the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging
non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier
transformations.
I thank my family and FTHD organizer S.L. Eriksson.
Soli Deo Gloria 相似文献
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《Journal of computational and graphical statistics》2013,22(1):208-221
This article takes up Bayesian inference in linear models with disturbances from a noncentral Student-t distribution. The distribution is useful when both long tails and asymmetry are features of the data. The distribution can be expressed as a location-scale mixture of normals with inverse weights distributed according to a chi-square distribution. The computations are performed using Gibbs sampling with data augmentation. An empirical application to Standard and Poor's stock returns indicates that posterior odds strongly favor a noncentral Student-t specification over its symmetric counterpart. 相似文献
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四元数矩阵的实表示与四元数矩阵方程 总被引:7,自引:0,他引:7
四元数矩阵与四元数矩阵方程在力学和工程问题的理论研究和实际数值计算中都起到重要的作用.该文借助四元数矩阵的实表示方法,研究了一般四元数矩阵方程AXB-CYD=E的解的问题,给出了一种求解四元数矩阵方程的算法技巧.该文还得到了四元数矩阵的Roth's定理. 相似文献
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Qi Keng LU 《数学学报(英文版)》2005,21(3):449-456
Since the quaternion ball was used to study the AdS/CFT problems tor spinor fields, it is worthwhile to study further the geometry (in sense of Klein) and analysis on it and on its extended space (in the sense of Behnke-Thullen), the quaternion projective space. 相似文献
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Noncentral quadratic forms of the skew elliptical variables 总被引:1,自引:0,他引:1
In this paper the quadratic forms in the skew elliptical variables are studied. A family of the noncentral generalized Dirichlet distributions is introduced and their distribution functions and probability density functions are obtained. The moment generating functions of the quadratic forms in the skew normal variables are obtained. Sufficient and necessary conditions for the quadratic forms in the skew normal variables to have the noncentral generalized Dirichlet distributions are obtained. This leads to the noncentral Cochran's Theorem for the skew normal distribution. 相似文献
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In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their fundamental matrices. After that we investigate commutative quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of commutative quaternion matrices and give some of their properties. 相似文献