java.lang.Object
- dev.nm.stat.distribution.multivariate.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.

See Also:

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 Instance Methods Concrete 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 e^tX.

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
    
    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

Class DirichletDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

DirichletDistribution

DirichletDistribution

Method Detail

density

cdf

mean

mode

covariance

entropy

moment