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 deviation 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 certain heterogeneous hypergeometric functions. Exact computation of the distribution of the largest eigenvalue is conducted here for a real case.

中文翻译：

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具有两个矩阵参数和奇异 beta-Wishart 矩阵的最大特征值的精确分布的异构超几何函数

本文讨论了具有两个矩阵参数的异构超几何函数的某些性质。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 beta-Wishart 矩阵的特征值的某些分布的偏差时非常有用。特征值的联合密度函数和最大特征值的分布可以用某些异构超几何函数来表示。此处针对实际情况对最大特征值的分布进行了精确计算。