Class MultivariateTDistribution
- java.lang.Object
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- dev.nm.stat.distribution.multivariate.MultivariateTDistribution
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- All Implemented Interfaces:
MultivariateProbabilityDistribution
public class MultivariateTDistribution extends Object implements MultivariateProbabilityDistribution
The multivariate T distribution or multivariate Student distribution, is a generalization of the one-dimensional (univariate) Student's t-distribution to higher dimensions. An equivalent function in R isdmvtfrom the packagemvtnorm.- See Also:
- Wikipedia: Multivariate t-distribution
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Constructor Summary
Constructors Constructor Description MultivariateTDistribution(int dim, int v)Constructs an instance of the standard t distribution, mean 0, variance 1.MultivariateTDistribution(int v, Vector mu, Matrix Sigma)Constructs an instance with the given mean and scale matrix.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description doublecdf(Vector x)Gets the cumulative probability F(x) = Pr(X ≤ x).Matrixcovariance()Gets the covariance matrix of this distribution.doubledensity(Vector x)The density function, which, if exists, is the derivative of F.doubleentropy()Gets the entropy of this distribution.Vectormean()Gets the mean of this distribution.Vectormode()Gets the mode of this distribution.doublemoment(Vector t)The moment generating function is the expected value of etX.
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Constructor Detail
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MultivariateTDistribution
public MultivariateTDistribution(int v, Vector mu, Matrix Sigma)Constructs an instance with the given mean and scale matrix.- Parameters:
v- the degree of freedommu- the mean, a px1 vector, where p is the dimensionSigma- the scale or dispersion matrix, a positive definite, real, pxp matrix; this is not the covariance matrix
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MultivariateTDistribution
public MultivariateTDistribution(int dim, int v)Constructs an instance of the standard t distribution, mean 0, variance 1.- Parameters:
dim- the dimensionality of the distributionv- the degree of freedom; v > 2
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Method Detail
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cdf
public double cdf(Vector x)
Description copied from interface:MultivariateProbabilityDistributionGets the cumulative probability F(x) = Pr(X ≤ x).- Specified by:
cdfin interfaceMultivariateProbabilityDistribution- Parameters:
x- x- Returns:
- F(x) = Pr(X ≤ x)
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density
public double density(Vector x)
Description copied from interface:MultivariateProbabilityDistributionThe density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.f(x) = dF(X) / dx
This may not always exist. For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.- Specified by:
densityin interfaceMultivariateProbabilityDistribution- Parameters:
x- x- Returns:
- f(x)
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mean
public Vector mean()
Description copied from interface:MultivariateProbabilityDistributionGets the mean of this distribution.- Specified by:
meanin interfaceMultivariateProbabilityDistribution- Returns:
- the mean
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mode
public Vector mode()
Description copied from interface:MultivariateProbabilityDistributionGets the mode of this distribution.- Specified by:
modein interfaceMultivariateProbabilityDistribution- Returns:
- the mean
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covariance
public Matrix covariance()
Description copied from interface:MultivariateProbabilityDistributionGets the covariance matrix of this distribution.- Specified by:
covariancein interfaceMultivariateProbabilityDistribution- Returns:
- the covariance
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entropy
public double entropy()
Description copied from interface:MultivariateProbabilityDistributionGets the entropy of this distribution.- Specified by:
entropyin interfaceMultivariateProbabilityDistribution- Returns:
- the entropy
- See Also:
- Wikipedia: Entropy (information theory)
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moment
public double moment(Vector t)
Description copied from interface:MultivariateProbabilityDistributionThe moment generating function is the expected value of etX. That is,E(etX)
This may not always exist.- Specified by:
momentin interfaceMultivariateProbabilityDistribution- Parameters:
t- t- Returns:
- E(exp(tX))
- See Also:
- Wikipedia: Moment-generating function
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