umontreal.iro.lecuyer.probdistmulti

Class MultiNormalDist

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)

Method Summary

Modifier and Type	Method and Description
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[] 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 ρij = σij/(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 σij = E[(Xi - μi)(Xj - μj)].
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 μi = E[Xi].
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.