论文标题
表达具有异质性超几何函数的单数beta f-matrix的最大特征值
Expressing the largest eigenvalue of a singular beta F-matrix with heterogeneous hypergeometric functions
论文作者
论文摘要
在本文中，讨论了奇异随机矩阵的最大特征值的确切分布，用于多变量分析（MANOVA）。开发奇异随机矩阵特征值的分布理论的关键是使用两个矩阵参数使用异质性超几何函数。在这项研究中，我们定义了奇异的beta f -matrix，并将非键βf -matrix的分布扩展到奇异病例。我们还提供了特征值的关节密度，并在异质性高几幅功能方面提供了最大特征值的确切分布。
In this paper, the exact distribution of the largest eigenvalue of a singular random matrix for multivariate analysis of variance (MANOVA) is discussed. The key to developing the distribution theory of eigenvalues of a singular random matrix is to use heterogeneous hypergeometric functions with two matrix arguments. In this study, we define the singular beta F-matrix and extend the distributions of a nonsingular beta F -matrix to the singular case. We also give the joint density of eigenvalues and the exact distribution of the largest eigenvalue in terms of heterogeneous hypergeometric functions.
