Theory of Probability &Its Applications, Volume 66, Issue 3, Page 391-407, January 2021.
The paper is concerned with the problem of construction of characterizing statistics for some types of distributions within certain classes. A characterizing statistic for multivariate normal distribution is constructed with the use of the theory of random matrices. Properties and characteristics of spherically symmetric distributions are studied. Examples of statistics that can be used for characterization of symmetric distributions are given. Applications of characterizing statistics to the theory of hypothesis testing are given. The problem of discrimination between the uniform and normal types of multivariate distributions within the group of spherically symmetric distributions from small samples is studied on the basis of the results obtained. A lower estimate is obtained for the number of observations that can serve as a basis for discrimination between these distributions.

中文翻译：

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表征统计及其应用

概率论及其应用，第 66 卷，第 3 期，第 391-407 页，2021 年 1 月。
该论文涉及为某些类中的某些类型的分布构建特征统计量的问题。使用随机矩阵理论构建了多元正态分布的特征统计量。研究了球对称分布的性质和特征。给出了可用于表征对称分布的统计示例。给出了特征统计在假设检验理论中的应用。在获得的结果的基础上，研究了小样本球对称分布组内均匀和正态多元分布的区分问题。