Hotelling T^2 Distribution

A univariate distribution proportional to the F-distribution. If the vector  is Gaussian multivariate-distributed with zero mean and unit covariance matrix  and  is an  matrix with a Wishart distribution with unit scale matrix and  degrees of freedom , then  has the Hotelling  distribution with parameters  and , denoted . This distribution is commonly used to describe the sample Mahalanobis distance between two populations, and is implemented as HotellingTSquareDistribution[p, m] in the Wolfram Language package MultivariateStatistics` , where  is the dimensionality parameter and  is the number of degrees of freedom.

REFERENCES:

NIST/SEMATECH. "Hotelling  Squared." §6.5.4.3 in NIST/Sematech Engineering Statistics Internet Handbook. https://www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htm.