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OBSOLETE MULTIVARIATE STATISTICS PACKAGE SYMBOL

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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.

MORE INFORMATION

To use , you first need to load the Multivariate Statistics Package using .

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.

can be used with such functions as Mean, CDF, and RandomReal.

EXAMPLES

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Basic Examples (3)

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:

In[2]:=

Out[2]=

Needs["MultivariateStatistics`"]

The variances of each dimension:

In[2]:=

Out[2]=

Needs["MultivariateStatistics`"]

Probability density function:

In[2]:=

Out[2]=

In[3]:=

Out[3]=

Scope (3)

Generate a set of pseudorandom vectors that follow a trivariate t distribution:

Applications (1)

Equal probability contours for a bivariate t distribution:

Properties & Relations (1)

The probability density function integrates to unity:

Possible Issues (2)

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: