Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix
Heterogeneous hypergeometric functions with two matrix arguments and the exact distribution of the largest eigenvalue of a singular beta-Wishart matrix
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DOI：
10.1016/j.jmva.2020.104714
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发表时间：
2019-12
期刊：
影响因子：
--
通讯作者：
Koki Shimizu;Hiroki Hashiguchi
中科院分区：
文献类型：
--
作者：
Koki Shimizu;Hiroki Hashiguchi
本文讨论了具有两个矩阵变元的非齐次超几何函数的若干性质。这些函数是新定义的，但已经出现在统计文献中，在处理奇异β-Wishart矩阵的特征值的某些分布的推导时是有用的。本征值的联合密度函数和最大本征值的分布可以用异质超几何函数表示。对真实的和复杂的情况进行了最大特征值分布的精确计算。
This paper discusses certain properties of heterogeneous hypergeometric functions with two matrix arguments. These functions are newly defined but have already appeared in statistical literature and are useful when dealing with the derivation of certain distributions for the eigenvalues of singular beta-Wishart matrices. The joint density function of the eigenvalues and the distribution of the largest eigenvalue can be expressed in terms of heterogeneous hypergeometric functions. Exact computation of the distribution of the largest eigenvalue is conducted for real and complex cases.