此为 Mathematica 7 文档,内容基于更早版本的 Wolfram 语言
查看最新文档(版本11.1)

MultivariateTDistribution

MultivariateTDistribution[CapitalSigma, m]
represents the multivariate Student t distribution with scale matrix CapitalSigma and degrees of freedom parameter m.
MultivariateTDistribution[Mu, CapitalSigma, m]
represents the multivariate Student t distribution with location Mu, scale matrix CapitalSigma and m degrees of freedom.
  • The probability density for vector x in a multivariate t distribution is proportional to (1+(x-Mu).CapitalSigma-1.(x-Mu)/m)-(m+Length[CapitalSigma])/2.
  • The scale matrix CapitalSigma can be any real-valued symmetric positive definite matrix.
  • With specified location Mu, Mu can be any vector of real numbers, and CapitalSigma can be any symmetric positive definite p×p matrix with p=Length[Mu].
  • The multivariate Student t distribution characterizes the ratio of a multinormal to the covariance between the variates.
  • MultivariateTDistribution can be used with such functions as Mean, CDF, and RandomReal.
Needs["MultivariateStatistics`"]
The mean of a bivariate t distribution with 10 degrees of freedom:
In[2]:=
Click for copyable input
Out[2]=
 
Needs["MultivariateStatistics`"]
The variances of each dimension:
In[2]:=
Click for copyable input
Out[2]=
 
Needs["MultivariateStatistics`"]
Probability density function:
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=