# Class MultinomialDistribution

java.lang.Object
dev.nm.stat.distribution.multivariate.MultinomialDistribution
All Implemented Interfaces:
MultivariateProbabilityDistribution

public class MultinomialDistribution extends Object implements MultivariateProbabilityDistribution
• ## Constructor Summary

Constructors
Constructor
Description
MultinomialDistribution(int n, double... p)
Constructs an instance of a Multinomial distribution.
• ## Method Summary

Modifier and Type
Method
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 etX.

### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ## Constructor Details

• ### 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 Details

• ### 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
• ### moment

public double moment(Vector t)
Description copied from interface: MultivariateProbabilityDistribution
The moment generating function is the expected value of etX. That is,
E(etX)
This may not always exist.
Specified by:
moment in interface MultivariateProbabilityDistribution
Parameters:
t - t
Returns:
E(exp(tX))