SSJ
V. 2.6.

## umontreal.iro.lecuyer.probdistmulti Class DirichletDist

```java.lang.Object
umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti
umontreal.iro.lecuyer.probdistmulti.DirichletDist
```

`public class DirichletDistextends ContinuousDistributionMulti`

Implements the abstract class `ContinuousDistributionMulti` for the Dirichlet distribution with parameters (α1,...,αd), αi > 0. The probability density is

f (x1,…, xd) = Γ(α0)∏i=1dxiαi-1/(∏i=1dΓ(αi))

where xi >=  0, i=1dxi = 1, α0 = ∑i=1dαi, and Γ is the Gamma function.

Constructor Summary
`DirichletDist(double[] alpha)`

Method Summary
` double` `density(double[] x)`
Returns f (x1, x2,…, xd), the probability density of X evaluated at the point x, where x = {x1, x2,…, xd}.
`static double` ```density(double[] alpha, double[] x)```
Computes the density of the Dirichlet distribution with parameters (α1, ..., αd).
` double[]` `getAlpha()`
Returns the parameters (α1, ..., αd) of this object.
` double` `getAlpha(int i)`
Returns the ith component of the alpha vector.
` double[][]` `getCorrelation()`
Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.
`static double[][]` `getCorrelation(double[] alpha)`
Computes the correlation matrix of the Dirichlet distribution with parameters (α1, ..., αd).
` double[][]` `getCovariance()`
Returns the variance-covariance matrix of the distribution, defined as
σij = E[(Xi - μi)(Xj - μj)].
`static double[][]` `getCovariance(double[] alpha)`
Computes the covariance matrix of the Dirichlet distribution with parameters (α1, ..., αd).
` double[]` `getMean()`
Returns the mean vector of the distribution, defined as μi = E[Xi].
`static double[]` `getMean(double[] alpha)`
Computes the mean E[X] = αi/α0 of the Dirichlet distribution with parameters (α1, ..., αd), where α0 = ∑i=1dαi.
`static double[]` ```getMLE(double[][] x, int n, int d)```
Estimates the parameters [ hat(α_1),…, hat(α_d)] of the Dirichlet distribution using the maximum likelihood method.
` void` `setParams(double[] alpha)`
Sets the parameters (α1, ..., αd) of this object.

Methods inherited from class umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti
`getDimension`

Methods inherited from class java.lang.Object
`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Constructor Detail

### DirichletDist

`public DirichletDist(double[] alpha)`
Method Detail

### density

`public double density(double[] x)`
Description copied from class: `ContinuousDistributionMulti`
Returns f (x1, x2,…, xd), the probability density of X evaluated at the point x, where x = {x1, x2,…, xd}. The convention is that x[i - 1] = xi.

Specified by:
`density` in class `ContinuousDistributionMulti`
Parameters:
`x` - value at which the density is evaluated
Returns:
density function evaluated at x

### getMean

`public double[] getMean()`
Description copied from class: `ContinuousDistributionMulti`
Returns the mean vector of the distribution, defined as μi = E[Xi].

Specified by:
`getMean` in class `ContinuousDistributionMulti`

### getCovariance

`public double[][] getCovariance()`
Description copied from class: `ContinuousDistributionMulti`
Returns the variance-covariance matrix of the distribution, defined as
σij = E[(Xi - μi)(Xj - μj)].

Specified by:
`getCovariance` in class `ContinuousDistributionMulti`

### getCorrelation

`public double[][] getCorrelation()`
Description copied from class: `ContinuousDistributionMulti`
Returns the correlation matrix of the distribution, defined as ρij = σij/(σ_iiσ_jj)1/2.

Specified by:
`getCorrelation` in class `ContinuousDistributionMulti`

### density

```public static double density(double[] alpha,
double[] x)```
Computes the density of the Dirichlet distribution with parameters (α1, ..., αd).

### getCovariance

`public static double[][] getCovariance(double[] alpha)`
Computes the covariance matrix of the Dirichlet distribution with parameters (α1, ..., αd).

### getCorrelation

`public static double[][] getCorrelation(double[] alpha)`
Computes the correlation matrix of the Dirichlet distribution with parameters (α1, ..., αd).

### getMLE

```public static double[] getMLE(double[][] x,
int n,
int d)```
Estimates the parameters [ hat(α_1),…, hat(α_d)] of the Dirichlet distribution using the maximum likelihood method. It uses the n observations of d components in table x[i][j], i = 0, 1,…, n - 1 and j = 0, 1,…, d - 1.

Parameters:
`x` - the list of observations to use to evaluate parameters
`n` - the number of observations to use to evaluate parameters
`d` - the dimension of each vector
Returns:
returns the parameter [ hat(α_1),…, hat(α_d)]

### getMean

`public static double[] getMean(double[] alpha)`
Computes the mean E[X] = αi/α0 of the Dirichlet distribution with parameters (α1, ..., αd), where α0 = ∑i=1dαi.

### getAlpha

`public double[] getAlpha()`
Returns the parameters (α1, ..., αd) of this object.

### getAlpha

`public double getAlpha(int i)`
Returns the ith component of the alpha vector.

### setParams

`public void setParams(double[] alpha)`
Sets the parameters (α1, ..., αd) of this object.

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.