Multivariate Statistics Package >

MultivariateTDistribution

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

represents the multivariate Student t distribution with scale matrix and degrees of freedom parameter m.

represents the multivariate Student t distribution with location , scale matrix and m degrees of freedom.
  • The probability density for vector x in a multivariate t distribution is proportional to (1+(x-).-1.(x-)/m)-(m+Length[])/2.
  • The scale matrix can be any real-valued symmetric positive definite matrix.
  • With specified location , can be any vector of real numbers, and can be any symmetric positive definite p×p matrix with p=Length[].
  • The multivariate Student t distribution characterizes the ratio of a multinormal to the covariance between the variates.
The mean of a bivariate t distribution with 10 degrees of freedom:
The variances of each dimension:
Probability density function:
Needs["MultivariateStatistics`"]
The mean of a bivariate t distribution with 10 degrees of freedom:
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Needs["MultivariateStatistics`"]
The variances of each dimension:
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Needs["MultivariateStatistics`"]
Probability density function:
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Generate a set of pseudorandom vectors that follow a trivariate t distribution:
Equal probability contours for a bivariate t distribution:
The probability density function integrates to unity:
is not defined when is not a symmetric positive definite matrix:
is not defined when m is not positive:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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