probability distribution
Hotelling T2 distribution
Hotelling T squared distribution is a probability distribution used in multivariate hypothesis testing, which is a univariate distribution proportional to the F-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's t-distribution.
In particular, the distribution arises in multivariate statistics in undertaking tests of the differences between the (multivariate) means of different populations, where tests for univariate problems would make use of a t-test.
The distribution is named for Harold Hotelling, who developed it[1] as a generalization of Student's t-distribution.
This distribution is commonly used to describe the sample Mahalanobis distance between two populations.