MultiNormalDist (Java Libraries for Stochastic Simulation)

java.lang.Object
- umontreal.iro.lecuyer.probdistmulti.ContinuousDistributionMulti
- - umontreal.iro.lecuyer.probdistmulti.MultiNormalDist

```
public class MultiNormalDist
extends ContinuousDistributionMulti
```
Implements the abstract class ContinuousDistributionMulti for the multinormal distribution with mean vector μ and covariance matrix Σ. The probability density is

P[X = (x₁,..., x_d)] = exp(- (x - μ)^TΣ^-1(x - μ)/2)/((2π)^d |Σ|)^1/2

Constructor Summary

Constructors
Constructor and Description

MultiNormalDist(double[] mu, double[][] sigma)

Constructors
Constructor and Description
`MultiNormalDist(double[] mu, double[][] sigma)`

Method Summary

Methods
Modifier and Type	Method and Description
`double`	`density(double[] x)` Returns f (x₁, x₂,…, x_d), the probability density of X evaluated at the point x, where x = {x₁, x₂,…, x_d}.
`static double`	`density(double[] mu, double[][] sigma, double[] x)` Computes the density of the multinormal distribution with parameters μ = `mu` and Σ = `sigma`, evaluated at `x`.
`double[][]`	`getCorrelation()` Returns the correlation matrix of the distribution, defined as ρ_ij = σ_ij/(σ_iiσ_jj)^1/2.
`static double[][]`	`getCorrelation(double[] mu, double[][] sigma)` Computes the correlation matrix of the multinormal distribution with parameters μ and Σ).
`double[][]`	`getCovariance()` Returns the variance-covariance matrix of the distribution, defined as σ_ij = E[(X_i - μ_i)(X_j - μ_j)].
`static double[][]`	`getCovariance(double[] mu, double[][] sigma)` Computes the covariance matrix of the multinormal distribution with parameters μ and Σ.
`int`	`getDimension()` Returns the dimension d of the distribution.
`static double[]`	`getMaximumLikelihoodEstimateMu(double[][] x, int n, int d)` Deprecated.
`static double[][]`	`getMaximumLikelihoodEstimateSigma(double[][] x, int n, int d)` Deprecated.
`double[]`	`getMean()` Returns the mean vector of the distribution, defined as μ_i = E[X_i].
`static double[]`	`getMean(double[] mu, double[][] sigma)` Returns the mean E[X] = μ of the multinormal distribution with parameters μ and Σ.
`static double[]`	`getMLEMu(double[][] x, int n, int d)` Estimates the parameters μ of the multinormal distribution using the maximum likelihood method.
`static double[][]`	`getMLESigma(double[][] x, int n, int d)` Estimates the parameters Σ of the multinormal distribution using the maximum likelihood method.
`double[]`	`getMu()` Returns the parameter μ of this object.
`double`	`getMu(int i)` Returns the i-th component of the parameter μ of this object.
`double[][]`	`getSigma()` Returns the parameter Σ of this object.
`void`	`setParams(double[] mu, double[][] sigma)` Sets the parameters μ and Σ of this object.

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

- Constructor Detail
  - MultiNormalDist
```
public MultiNormalDist(double[] mu,
               double[][] sigma)
```
- Method Detail
  - density
```
public double density(double[] x)
```
    Description copied from class: ContinuousDistributionMulti
    
    Returns f (x₁, x₂,…, x_d), the probability density of X evaluated at the point x, where x = {x₁, x₂,…, x_d}. The convention is that x[i - 1] = x_i.
    
    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 μ_i = E[X_i].
    
    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
    σ_ij = E[(X_i - μ_i)(X_j - μ_j)].
    
    Specified by:
    
    getCovariance in class ContinuousDistributionMulti
  - getCorrelation
```
public double[][] getCorrelation()
```
    Description copied from class: ContinuousDistributionMulti
    
    Returns the correlation matrix of the distribution, defined as ρ_ij = σ_ij/(σ_iiσ_jj)^1/2.
    
    Specified by:
    
    getCorrelation in class ContinuousDistributionMulti
  - density
```
public static double density(double[] mu,
             double[][] sigma,
             double[] x)
```
    Computes the density of the multinormal distribution with parameters μ = mu and Σ = sigma, evaluated at x.
  - getDimension
```
public int getDimension()
```
    Returns the dimension d of the distribution.
    
    Overrides:
    
    getDimension in class ContinuousDistributionMulti
  - getMean
```
public static double[] getMean(double[] mu,
               double[][] sigma)
```
    Returns the mean E[X] = μ of the multinormal distribution with parameters μ and Σ.
  - getCovariance
```
public static double[][] getCovariance(double[] mu,
                       double[][] sigma)
```
    Computes the covariance matrix of the multinormal distribution with parameters μ and Σ.
  - getCorrelation
```
public static double[][] getCorrelation(double[] mu,
                        double[][] sigma)
```
    Computes the correlation matrix of the multinormal distribution with parameters μ and Σ).
  - getMaximumLikelihoodEstimateMu
```
@Deprecated
public static double[] getMaximumLikelihoodEstimateMu(double[][] x,
                                                 int n,
                                                 int d)
```
    Deprecated.
    
    It is now called getMLEMu.
  - getMLEMu
```
public static double[] getMLEMu(double[][] x,
                int n,
                int d)
```
    Estimates the parameters μ of the multinormal 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 used to evaluate parameters
    n - the number of observations used to evaluate parameters
    d - the dimension of each observation
    
    Returns:
    returns the parameters [μ₁,...,μ_d]
  - getMaximumLikelihoodEstimateSigma
```
@Deprecated
public static double[][] getMaximumLikelihoodEstimateSigma(double[][] x,
                                                      int n,
                                                      int d)
```
    Deprecated.
    
    It is now called getMLESigma.
  - getMLESigma
```
public static double[][] getMLESigma(double[][] x,
                     int n,
                     int d)
```
    Estimates the parameters Σ of the multinormal 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 used to evaluate parameters
    n - the number of observations used to evaluate parameters
    d - the dimension of each observation
    
    Returns:
    returns the covariance matrix Σ
  - getMu
```
public double[] getMu()
```
    Returns the parameter μ of this object.
  - getMu
```
public double getMu(int i)
```
    Returns the i-th component of the parameter μ of this object.
  - getSigma
```
public double[][] getSigma()
```
    Returns the parameter Σ of this object.
  - setParams
```
public void setParams(double[] mu,
             double[][] sigma)
```
    Sets the parameters μ and Σ of this object.

Class MultiNormalDist

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MultiNormalDist

Method Detail

density

getMean

getCovariance

getCorrelation

density

getDimension

getMean

getCovariance

getCorrelation

getMaximumLikelihoodEstimateMu

getMLEMu

getMaximumLikelihoodEstimateSigma

getMLESigma

getMu

getMu

getSigma

setParams