As of Version 8, HotellingTSquareDistribution is part of the built-in Wolfram Language kernel.


represents Hotelling's distribution with dimensionality parameter p and degrees of freedom parameter m.


  • To use HotellingTSquareDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
  • HotellingTSquareDistribution is a univariate distribution derived from the multivariate normal distribution.
  • The probability density for value x in Hotelling's distribution is proportional to x-1+p/2(1+x/m)-(m+1)/2 for x>0.
  • The parameters p and m can be any positive real numbers such that m>p-1.
  • HotellingTSquareDistribution can be used with such functions as Mean, CDF, and RandomReal.


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Basic Examples  (3)

The mean of a Hotelling distribution:

The variance:

Probability density function:

Scope  (3)

Generate a set of pseudorandom numbers that follow a Hotelling distribution:

Properties & Relations  (1)

The probability density function integrates to unity:

Hotelling variables are related to F-ratio variables by a multiplicative constant:

Possible Issues  (2)

HotellingTSquareDistribution is not defined when m<p:

HotellingTSquareDistribution is not defined when p is less than 0:

Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: