dev.nm.stat.distribution.multivariate

Interface MultivariateProbabilityDistribution

All Known Subinterfaces:

BivariateEVD, BivariateProbabilityDistribution

All Known Implementing Classes:

AbstractBivariateEVD, AbstractBivariateProbabilityDistribution, BivariateEVDAsymmetricLogistic, BivariateEVDAsymmetricMixed, BivariateEVDAsymmetricNegativeLogistic, BivariateEVDBilogistic, BivariateEVDColesTawn, BivariateEVDHuslerReiss, BivariateEVDLogistic, BivariateEVDNegativeBilogistic, BivariateEVDNegativeLogistic, DirichletDistribution, MultinomialDistribution, MultivariateNormalDistribution, MultivariateTDistribution

public interface MultivariateProbabilityDistribution

A multivariate or joint probability distribution for X, Y, ... is a probability distribution that gives the probability that each of X, Y, ... falls in any particular range or discrete set of values specified for that variable.

See Also:

Wikipedia: Joint probability distribution

Method Summary

Modifier and Type	Method and Description
double	cdf(Vector x) Gets the cumulative probability F(x) = Pr(X ≤ x).
Matrix	covariance() Gets the covariance matrix of this distribution.
double	density(Vector x) The density function, which, if exists, is the derivative of F.
double	entropy() Gets the entropy of this distribution.
Vector	mean() Gets the mean of this distribution.
Vector	mode() Gets the mode of this distribution.
double	moment(Vector t) The moment generating function is the expected value of \(e^{tX}\).

Method Detail

cdf

double cdf(Vector x)

Gets the cumulative probability F(x) = Pr(X ≤ x).

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

density

double density(Vector x)

The 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.

Parameters:

x - x

Returns:

f(x)

mean

Vector mean()

Gets the mean of this distribution.

Returns:

the mean

mode

Vector mode()

Gets the mode of this distribution.

Returns:

the mean

covariance

Matrix covariance()

Gets the covariance matrix of this distribution.

Returns:

the covariance

entropy

double entropy()

Gets the entropy of this distribution.

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

moment

double moment(Vector t)

The moment generating function is the expected value of \(e^{tX}\). That is, \[ E(e^{tX}) \] This may not always exist.

Parameters:

t - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function