This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

WishartDistribution


represents a Wishart distribution with scale matrix and degrees of freedom parameter m.
  • The probability density for a symmetric positive definite matrix x in a Wishart distribution is proportional to x(m-p-1)/2-Tr[-1.x/2].
  • The scale matrix can be any symmetric positive definite matrix. The parameter m can be any number such that m>Length[].
  • For integer m, the Wishart distribution gives the distribution of covariance matrices of multinormal samples.
The mean of a Wishart distribution:
The variance:
Probability density function:
Needs["MultivariateStatistics`"]
The mean of a Wishart distribution:
In[2]:=
Click for copyable input
Out[2]=
 
Needs["MultivariateStatistics`"]
The variance:
In[2]:=
Click for copyable input
Out[2]=
 
Needs["MultivariateStatistics`"]
Probability density function:
In[2]:=
Click for copyable input
Out[2]=
Generate a set of pseudorandom matrices that follow a Wishart distribution:
is not defined when is not symmetric and positive definite:
is not defined when m<Length[]:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful: