In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence conditions for these functions. The joint density of eigenvalues and the distribution function of the largest eigenvalue for a singular elliptical Wishart matrix are represented by these functions. Numerical computations for the distribution of the largest eigenvalue were conducted under the matrix-variate $t$ and Kotz-type models.

翻译：在本研究中,我们从一个奇异的Wishart矩阵的精华值的精确分布中得出一个奇异 Wishart 矩阵的精华值的精确分布。我们用两个矩阵参数界定了通用的多元超几何函数,并为这些函数提供了趋同条件。这些函数代表了该值的共同密度和一个奇异的日新星矩阵的最大精华值的分布功能。在矩阵-变量美元和Kotz型模型下对最大的精华值的分布进行了数值计算。