## Class DirichletDistribution

• All Implemented Interfaces:
MultivariateProbabilityDistribution

public class DirichletDistribution
extends Object
implements MultivariateProbabilityDistribution
The Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir(a), is a family of continuous multivariate probability distributions parametrized by a vector a of positive reals. It is the multivariate generalization of the beta distribution. Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. That is, its probability density function returns the belief that the probabilities of K rival events are x_i given that each event has been observed a_{i-1} times. The R equivalent function is ddirichlet in package gtools.
Wikipedia: Probability density function
• ### Constructor Summary

Constructors
Constructor Description
DirichletDistribution​(double[] a)
Constructs an instance of Dirichlet distribution.
DirichletDistribution​(double[] a, double epsilon)
Constructs an instance of Dirichlet distribution.
• ### Method Summary

All Methods
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 Detail

• #### DirichletDistribution

public DirichletDistribution​(double[] a,
double epsilon)
Constructs an instance of Dirichlet distribution.
Parameters:
a - the parameters
epsilon - a precision parameter: when a number |x| ≤ ε, it is considered 0
• #### DirichletDistribution

public DirichletDistribution​(double[] a)
Constructs an instance of Dirichlet distribution.
Parameters:
a - the parameters
• ### 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
Wikipedia: Entropy (information theory)
• #### 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))