We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1F_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions are considered.

翻译：我们推导了非中心均值矩阵与样本协方差矩阵之比的分布。该结果与非中心单变量Student's t中的合流项${}_1F_1$一致。此外，本文还考虑了矩阵变量分布的一些推广形式。