Hotelling's T-squared distribution

Hotelling's T-squared distribution is a distribution that arises in multivariate statistics.

F(d, d) is equivalent to the scaled Hotelling's T-squared distribution .

Hotelling is known to statisticians because of Hotelling's T-squared distribution and its use in statistical hypothesis testing and confidence regions.

Additionally, Hotelling's T-squared distribution is a univariate distribution, generalising Student's t-distribution, that is used in multivariate hypothesis testing.

It is a multivariate generalization of the univariate F-distribution, and generalizes the F-distribution in the same way that the Hotelling's T-squared distribution generalizes Student's t-distribution.

In statistics Hotelling's T-squared distribution is important because it arises as the distribution of a set of statistics which are natural generalisations of the statistics underlying Student's t-distribution.