Hotelling T^2 Distribution
A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is an m×p matrix with a Wishart distribution with unit scale matrix and m degrees of freedom W_p(I,m), then md^(T)M^(-1)d has the Hotelling T^2 distribution with parameters p and m, denoted T^2(p,m). 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 p is the dimensionality parameter and m is the number of degrees of freedom.
See also
F-distribution, Hotelling's T2 Test, Wishart DistributionExplore with Wolfram|Alpha
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References
NIST/SEMATECH. "Hotelling T Squared." §6.5.4.3 in NIST/Sematech Engineering Statistics Internet Handbook. http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc543.htm.Referenced on Wolfram|Alpha
Hotelling T^2 DistributionCite this as:
Weisstein, Eric W. "Hotelling T^2 Distribution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HotellingT-SquaredDistribution.html