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

中文翻译：

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广义异构超几何函数和椭圆Wishart矩阵的最大特征值分布

在本文中，我们推导了椭圆模型下奇异 Wishart 矩阵的特征值的精确分布。我们定义了具有两个矩阵参数的广义异构超几何函数，并提供了这些函数的收敛条件。用这些函数表示奇异椭圆Wishart矩阵的特征值的联合密度和最大特征值的分布函数。最大特征值分布的数值计算是在矩阵变量t和 Kotz 类型模型下进行的。