Implements the abstract class ContinuousDistributionMulti for the multinormal distribution with mean vector \(\boldsymbol{\mu}\) and covariance matrix \(\boldsymbol{\Sigma}\). More...
Public Member Functions | |
| MultiNormalDist (double[] mu, double[][] sigma) | |
| double | density (double[] x) |
| double [] | getMean () |
| double [][] | getCovariance () |
| double [][] | getCorrelation () |
| int | getDimension () |
| Returns the dimension \(d\) of the distribution. | |
| double [] | getMu () |
| Returns the parameter \(\boldsymbol{\mu}\) of this object. | |
| double | getMu (int i) |
| Returns the \(i\)-th component of the parameter \(\boldsymbol{\mu}\) of this object. | |
| double [][] | getSigma () |
| Returns the parameter \(\boldsymbol{\Sigma}\) of this object. | |
| void | setParams (double[] mu, double[][] sigma) |
| Sets the parameters \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}\) of this object. | |
 Public Member Functions inherited from ContinuousDistributionMulti | |
| abstract double | density (double[] x) |
| Returns \(f(x_1, x_2, …, x_d)\), the probability density of \(X\) evaluated at the point \(x\), where \(x = \{x_1, x_2, …, x_d\}\). More... | |
| int | getDimension () |
| Returns the dimension \(d\) of the distribution. | |
| abstract double [] | getMean () |
| Returns the mean vector of the distribution, defined as \(\mu_i = E[X_i]\). | |
| abstract double [][] | getCovariance () |
| Returns the variance-covariance matrix of the distribution, defined as \(\sigma_{ij} = E[(X_i - \mu_i)(X_j - \mu_j)]\). | |
| abstract double [][] | getCorrelation () |
| Returns the correlation matrix of the distribution, defined as \(\rho_{ij} = \sigma_{ij}/\sqrt{\sigma_{ii}\sigma_{jj}}\). | |
Static Public Member Functions | |
| static double | density (double[] mu, double[][] sigma, double[] x) |
Computes the density ( fMultinormal ) of the multinormal distribution with parameters \(\boldsymbol{\mu}=\) mu and \(\boldsymbol{\Sigma}=\) sigma, evaluated at x. | |
| static double [] | getMean (double[] mu, double[][] sigma) |
| Returns the mean \(E[\mathbf{X}] = \boldsymbol{\mu}\) of the multinormal distribution with parameters \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}\). | |
| static double [][] | getCovariance (double[] mu, double[][] sigma) |
| Computes the covariance matrix of the multinormal distribution with parameters \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}\). | |
| static double [][] | getCorrelation (double[] mu, double[][] sigma) |
| Computes the correlation matrix of the multinormal distribution with parameters \(\boldsymbol{\mu}\) and \(\boldsymbol{\Sigma}\)). | |
| static double [] | getMLEMu (double[][] x, int n, int d) |
| Estimates the parameters \(\boldsymbol{\mu}\) of the multinormal distribution using the maximum likelihood method. More... | |
| static double [][] | getMLESigma (double[][] x, int n, int d) |
| Estimates the parameters \(\boldsymbol{\Sigma}\) of the multinormal distribution using the maximum likelihood method. More... | |
Protected Attributes | |
| int | dim |
| double [] | mu |
| DoubleMatrix2D | sigma |
| DoubleMatrix2D | invSigma |
| Protected Attributes inherited from ContinuousDistributionMulti | |
| int | dimension |
Static Protected Attributes | |
| static Algebra | algebra = new Algebra() |
Detailed Description
Implements the abstract class ContinuousDistributionMulti for the multinormal distribution with mean vector \(\boldsymbol{\mu}\) and covariance matrix \(\boldsymbol{\Sigma}\).
\[ f(\mathbf{x}) = \frac{1}{\sqrt{(2\pi)^d \det\boldsymbol{\Sigma}}} \exp\left(-\frac{1}{2}(\mathbf{x}- \boldsymbol{\mu})^T \boldsymbol{\Sigma}^{-1} (\mathbf{x}- \boldsymbol{\mu})\right) \tag{fMultinormal} \]
where \(\mathbf{x}= (x_1,…,x_d)\).
Member Function Documentation
◆ getMLEMu()
|
static |
Estimates the parameters \(\boldsymbol{\mu}\) 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 [ \(\boldsymbol{\mu}_1\),…, \(\boldsymbol{\mu}_d\)]
◆ getMLESigma()
|
static |
Estimates the parameters \(\boldsymbol{\Sigma}\) 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 \(\boldsymbol{\Sigma}\)
The documentation for this class was generated from the following file:
- MultiNormalDist.java
