dev.nm.stat.distribution.multivariate

Class MultinomialDistribution

java.lang.Object

dev.nm.stat.distribution.multivariate.MultinomialDistribution

All Implemented Interfaces:

MultivariateProbabilityDistribution

public class MultinomialDistribution
extends Object
implements MultivariateProbabilityDistribution

See Also:

Wikipedia: Multinomial distribution

Constructor Summary

Constructors

Constructor and Description
MultinomialDistribution(int n, double... p) Constructs an instance of a Multinomial 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 \(e^{tX}\).

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

MultinomialDistribution

public MultinomialDistribution(int n,
                               double... p)

Constructs an instance of a Multinomial distribution.

Parameters:

n - the number of trials

p - the event probabilities; the sum of them equals 1

Method Detail

density

public double density(Vector x)

Description copied from interface: MultivariateProbabilityDistribution

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.

Specified by:

density in interface MultivariateProbabilityDistribution

Parameters:

x - x

Returns:

f(x)

cdf

public double cdf(Vector x)

Description copied from interface: MultivariateProbabilityDistribution

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

Specified by:

cdf in interface MultivariateProbabilityDistribution

Parameters:

x - x

Returns:

F(x) = Pr(X ≤ x)

mean

public Vector mean()

Description copied from interface: MultivariateProbabilityDistribution

Gets the mean of this distribution.

Specified by:

mean in interface MultivariateProbabilityDistribution

Returns:

the mean

mode

public Vector mode()

Description copied from interface: MultivariateProbabilityDistribution

Gets the mode of this distribution.

Specified by:

mode in interface MultivariateProbabilityDistribution

Returns:

the mean

covariance

public Matrix covariance()

Description copied from interface: MultivariateProbabilityDistribution

Gets the covariance matrix of this distribution.

Specified by:

covariance in interface MultivariateProbabilityDistribution

Returns:

the covariance

entropy

public double entropy()

Description copied from interface: MultivariateProbabilityDistribution

Gets the entropy of this distribution.

Specified by:

entropy in interface MultivariateProbabilityDistribution

Returns:

the entropy

See Also:

Wikipedia: Entropy (information theory)

moment

public double moment(Vector t)

Description copied from interface: MultivariateProbabilityDistribution

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

Specified by:

moment in interface MultivariateProbabilityDistribution

Parameters:

t - t

Returns:

E(exp(tX))

See Also:

Wikipedia: Moment-generating function