MultivariateGaussianDistribution

java.lang.Object
- smile.stat.distribution.MultivariateGaussianDistribution

All Implemented Interfaces:

java.io.Serializable, MultivariateDistribution, MultivariateExponentialFamily
```
public class MultivariateGaussianDistribution
extends java.lang.Object
implements MultivariateDistribution, MultivariateExponentialFamily
```
Multivariate Gaussian distribution.

See Also:

GaussianDistribution, Serialized Form

Field Summary

Fields
Modifier and Type Field and Description

boolean diagonal
True if the covariance matrix is diagonal.

double[] mu
The mean vector.

Matrix sigma
The covariance matrix.

Fields
Modifier and Type	Field and Description
`boolean`	`diagonal` True if the covariance matrix is diagonal.
`double[]`	`mu` The mean vector.
`Matrix`	`sigma` The covariance matrix.

Constructor Summary

Constructors
Constructor and Description
`MultivariateGaussianDistribution(double[] mean, double variance)` Constructor.
`MultivariateGaussianDistribution(double[] mean, double[] variance)` Constructor.
`MultivariateGaussianDistribution(double[] mean, Matrix cov)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double`	`cdf(double[] x)` Algorithm from Alan Genz (1992) Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, pp.
`Matrix`	`cov()` The covariance matrix of distribution.
`double`	`entropy()` Shannon entropy of the distribution.
`static MultivariateGaussianDistribution`	`fit(double[][] data)` Estimates the mean and diagonal covariance by MLE.
`static MultivariateGaussianDistribution`	`fit(double[][] data, boolean diagonal)` Estimates the mean and covariance by MLE.
`int`	`length()` The number of parameters of the distribution.
`double`	`logp(double[] x)` The density at x in log scale, which may prevents the underflow problem.
`MultivariateMixture.Component`	`M(double[][] data, double[] posteriori)` The M step in the EM algorithm, which depends the specific distribution.
`double[]`	`mean()` The mean vector of distribution.
`double`	`p(double[] x)` The probability density function for continuous distribution or probability mass function for discrete distribution at x.
`double[]`	`rand()` Generate a random multivariate Gaussian sample.
`double[][]`	`rand(int n)` Generates a set of random numbers following this distribution.
`double`	`scatter()` Returns the scatter of distribution, which is defined as \|Σ\|.
`java.lang.String`	`toString()`

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

Methods inherited from interface smile.stat.distribution.MultivariateDistribution
likelihood, logLikelihood

- Field Detail
  - mu
```
public final double[] mu
```
    The mean vector.
  - sigma
```
public final Matrix sigma
```
    The covariance matrix.
  - diagonal
```
public final boolean diagonal
```
    True if the covariance matrix is diagonal.
- Constructor Detail
  - MultivariateGaussianDistribution
```
public MultivariateGaussianDistribution(double[] mean,
                                        double variance)
```
    Constructor. The distribution will have a diagonal covariance matrix of the same variance.
    
    Parameters:
    
    mean - mean vector.
    
    variance - variance.
  - MultivariateGaussianDistribution
```
public MultivariateGaussianDistribution(double[] mean,
                                        double[] variance)
```
    Constructor. The distribution will have a diagonal covariance matrix. Each element has different variance.
    
    Parameters:
    
    mean - mean vector.
    
    variance - variance vector.
  - MultivariateGaussianDistribution
```
public MultivariateGaussianDistribution(double[] mean,
                                        Matrix cov)
```
    Constructor.
    
    Parameters:
    
    mean - mean vector.
    
    cov - covariance matrix.
- Method Detail
  - fit
```
public static MultivariateGaussianDistribution fit(double[][] data)
```
    Estimates the mean and diagonal covariance by MLE.
    
    Parameters:
    
    data - the training data.
  - fit
```
public static MultivariateGaussianDistribution fit(double[][] data,
                                                   boolean diagonal)
```
    Estimates the mean and covariance by MLE.
    
    Parameters:
    
    data - the training data.
    
    diagonal - true if covariance matrix is diagonal.
  - length
```
public int length()
```
    Description copied from interface: MultivariateDistribution
    
    The number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
    
    Specified by:
    
    length in interface MultivariateDistribution
  - entropy
```
public double entropy()
```
    Description copied from interface: MultivariateDistribution
    
    Shannon entropy of the distribution.
    
    Specified by:
    
    entropy in interface MultivariateDistribution
  - mean
```
public double[] mean()
```
    Description copied from interface: MultivariateDistribution
    
    The mean vector of distribution.
    
    Specified by:
    
    mean in interface MultivariateDistribution
  - cov
```
public Matrix cov()
```
    Description copied from interface: MultivariateDistribution
    
    The covariance matrix of distribution.
    
    Specified by:
    
    cov in interface MultivariateDistribution
  - scatter
```
public double scatter()
```
    Returns the scatter of distribution, which is defined as |Σ|.
  - logp
```
public double logp(double[] x)
```
    Description copied from interface: MultivariateDistribution
    
    The density at x in log scale, which may prevents the underflow problem.
    
    Specified by:
    
    logp in interface MultivariateDistribution
  - p
```
public double p(double[] x)
```
    Description copied from interface: MultivariateDistribution
    
    The probability density function for continuous distribution or probability mass function for discrete distribution at x.
    
    Specified by:
    
    p in interface MultivariateDistribution
  - cdf
```
public double cdf(double[] x)
```
    Algorithm from Alan Genz (1992) Numerical Computation of Multivariate Normal Probabilities, Journal of Computational and Graphical Statistics, pp. 141-149. The difference between returned value and the true value of the CDF is less than 0.001 in 99.9% time. The maximum number of iterations is set to 10000.
    
    Specified by:
    
    cdf in interface MultivariateDistribution
  - rand
```
public double[] rand()
```
    Generate a random multivariate Gaussian sample.
  - rand
```
public double[][] rand(int n)
```
    Generates a set of random numbers following this distribution.
  - M
```
public MultivariateMixture.Component M(double[][] data,
                                       double[] posteriori)
```
    Description copied from interface: MultivariateExponentialFamily
    
    The M step in the EM algorithm, which depends the specific distribution.
    
    Specified by:
    
    M in interface MultivariateExponentialFamily
    
    Parameters:
    
    data - the input data for estimation
    
    posteriori - the posteriori probability.
    
    Returns:
    
    the (unnormalized) weight of this distribution in the mixture.
  - toString
```
public java.lang.String toString()
```
    Overrides:
    
    toString in class java.lang.Object

Class MultivariateGaussianDistribution

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface smile.stat.distribution.MultivariateDistribution

Field Detail

mu

sigma

diagonal

Constructor Detail

MultivariateGaussianDistribution

MultivariateGaussianDistribution

MultivariateGaussianDistribution

Method Detail

fit

fit

length

entropy

mean

cov

scatter

logp

p

cdf

rand

rand

M

toString