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Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Normal and Related Distributions > MultivariateTDistribution >
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MultivariateTDistribution

MultivariateTDistribution
represents the multivariate Student distribution with scale matrix and degrees of freedom parameter .
MultivariateTDistribution
represents the multivariate Student distribution with location , scale matrix , and degrees of freedom.
MORE INFORMATION
  • The probability density for vector in a multivariate distribution is proportional to , where is the length of .
  • The multivariate Student distribution characterizes the ratio of a multinormal to the covariance between the variates.
  • MultivariateTDistribution allows to be any × symmetric positive definite matrix, any vector of real numbers where p=Length[], and any positive real number.
EXAMPLESCLOSE ALL
Basic Examples   (4)
Probability density function:
Cumulative distribution function:
Mean and variance:
Covariance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Covariance:
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Scope   (8)
Generate a set of pseudorandom vectors that follow a bivariate distribution:
Visualize the sample using a histogram:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Goodness-of-fit test:
Skewness:
Skewness is always 0 when defined:
Kurtosis:
Kurtosis depends only on the degrees of freedom:
As number of degrees of freedom approaches , the kurtosis approaches kurtosis of MultinormalDistribution:
Correlation for bivariate distribution:
Different mixed moments for a standard bivariate distribution:
Mixed central moments:
Mixed factorial moments:
Mixed cumulants:
Hazard function:
The marginals follow StudentTDistribution:
Applications   (2)
Show a distribution function and its histogram in the same plot:
Compare the PDF to its histogram version:
Compare the CDF to its histogram version:
A multivariate Student distribution is used to define a copula distribution:
Probability density function:
Mean and variance:
Generate random numbers:
Properties & Relations   (5)
Equal probability contours for a bivariate distribution:
Multivariate Student distribution is closed under affine transformations:
Relationships to other distributions:
Multinormal distribution is the limit of MultivariateTDistribution as goes to :
The default location is 0:
Possible Issues   (2)
MultivariateTDistribution is not defined when is not a symmetric positive definite matrix:
MultivariateTDistribution is not defined when is not positive:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
Neat Examples   (1)
PDFs for different correlations:
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