Hotelling's T-squared distribution

Summary

Hotelling's T-squared distribution is the multivariate analogue of the square of Student's $t$-distribution. It is the distribution of a squared Mahalanobis-type length $m\, x^T M^{-1} x$ of a normal vector $x$, measured with an independent Wishart matrix $M$. A rescaling of it is an F-distribution. It is the null distribution of Hotelling's $T^2$ test for the mean vector of a multivariate normal sample.