MultivariateTDistribution

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

MultivariateTDistribution[Σ,m]
represents the multivariate Student distribution with scale matrix Σ and degrees of freedom parameter m.

MultivariateTDistribution[μ,Σ,m]
represents the multivariate Student distribution with location μ, scale matrix Σ, and m degrees of freedom.

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  • To use MultivariateTDistribution, you first need to load the Multivariate Statistics Package using Needs["MultivariateStatistics`"].
  • The probability density for vector x in a multivariate t distribution is proportional to (1+(x-μ).Σ-1.(x-μ)/m)-(m+Length[Σ])/2.
  • The scale matrix Σ can be any realvalued symmetric positive definite matrix.
  • With specified location μ, μ can be any vector of real numbers, and Σ can be any symmetric positive definite p×p matrix with p=Length[μ].
  • The multivariate Student 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.

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基本范例  (3)基本范例  (3)

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The mean of a bivariate distribution with 10 degrees of freedom:

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The variances of each dimension:

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Probability density function:

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