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.
Hotelling T^2 Distribution
See also
F-distribution, Hotelling's T2 Test, Wishart DistributionExplore with Wolfram|Alpha
References
NIST/SEMATECH. "Hotelling
Squared." §6.5.4.3 in NIST/Sematech Engineering
Statistics Internet Handbook. http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htm.
Cite this as:
Weisstein, Eric W. "Hotelling T^2 Distribution." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HotellingT-SquaredDistribution.html