On non-central distribution of the matrix ratio

Abstract

We derive the distribution of the ratio of a non-central mean matrix and a sample covariance matrix. This aligns with the confluent term ${}_1{F}_1$ in the non-central uni-variate Student's $t$. Some extensions of matrix-variate distributions are considered.

arXiv commentThis is the second of the series of articles: arXiv:2601.21304; arXiv:2410.14490; arXiv:2505.00470