java.lang.Object
- dev.nm.stat.distribution.multivariate.MultivariateNormalDistribution

All Implemented Interfaces:

MultivariateProbabilityDistribution
```
public class MultivariateNormalDistribution
extends Object
implements MultivariateProbabilityDistribution
```
The multivariate Normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) Normal distribution to higher dimensions.
An equivalent function in R is dmvnorm from the package mvtnorm.

See Also:

Wikipedia: Multivariate normal distribution

Constructor Summary

Constructors
Constructor	Description
`MultivariateNormalDistribution(int dim)`	Constructs an instance of the standard Normal distribution.
`MultivariateNormalDistribution(Vector mu, Matrix Sigma)`	Constructs an instance with the given mean and covariance matrix.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method	Description
`double`	`cdf(Vector x)`	Gets the cumulative probability F(x) = Pr(X ≤ x).
`Matrix`	`covariance()`	Gets the covariance matrix of this distribution.
`double`	`density(Vector x)`	The density function, which, if exists, is the derivative of F.
`double`	`entropy()`	Gets the entropy of this distribution.
`Vector`	`mean()`	Gets the mean of this distribution.
`Vector`	`mode()`	Gets the mode of this distribution.
`double`	`moment(Vector t)`	The moment generating function is the expected value of e^tX.

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

- Constructor Detail
  - MultivariateNormalDistribution
```
public MultivariateNormalDistribution(Vector mu,
                                      Matrix Sigma)
```
    Constructs an instance with the given mean and covariance matrix.
    
    Parameters:
    
    mu - the mean
    
    Sigma - the covariance matrix which must be positive definite
  - MultivariateNormalDistribution
```
public MultivariateNormalDistribution(int dim)
```
    Constructs an instance of the standard Normal distribution.
    
    Parameters:
    
    dim - the dimensionality of the distribution
- Method Detail
  - cdf
```
public double cdf(Vector x)
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    Gets the cumulative probability F(x) = Pr(X ≤ x).
    
    Specified by:
    
    cdf in interface MultivariateProbabilityDistribution
    
    Parameters:
    
    x - x
    
    Returns:
    
    F(x) = Pr(X ≤ x)
  - density
```
public double density(Vector x)
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    The density function, which, if exists, is the derivative of F. It describes the density of probability at each point in the sample space.
    f(x) = dF(X) / dx
    This may not always exist.
    For the discrete cases, this is the probability mass function. It gives the probability that a discrete random variable is exactly equal to some value.
    
    Specified by:
    
    density in interface MultivariateProbabilityDistribution
    
    Parameters:
    
    x - x
    
    Returns:
    
    f(x)
  - mean
```
public Vector mean()
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    Gets the mean of this distribution.
    
    Specified by:
    
    mean in interface MultivariateProbabilityDistribution
    
    Returns:
    
    the mean
  - mode
```
public Vector mode()
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    Gets the mode of this distribution.
    
    Specified by:
    
    mode in interface MultivariateProbabilityDistribution
    
    Returns:
    
    the mean
  - covariance
```
public Matrix covariance()
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    Gets the covariance matrix of this distribution.
    
    Specified by:
    
    covariance in interface MultivariateProbabilityDistribution
    
    Returns:
    
    the covariance
  - entropy
```
public double entropy()
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    Gets the entropy of this distribution.
    
    Specified by:
    
    entropy in interface MultivariateProbabilityDistribution
    
    Returns:
    
    the entropy
    
    See Also:
    
    Wikipedia: Entropy (information theory)
  - moment
```
public double moment(Vector t)
```
    Description copied from interface: MultivariateProbabilityDistribution
    
    The moment generating function is the expected value of e^tX. That is,
    E(e^tX)
    This may not always exist.
    
    Specified by:
    
    moment in interface MultivariateProbabilityDistribution
    
    Parameters:
    
    t - t
    
    Returns:
    
    E(exp(tX))
    
    See Also:
    
    Wikipedia: Moment-generating function

Class MultivariateNormalDistribution

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MultivariateNormalDistribution

MultivariateNormalDistribution

Method Detail

cdf

density

mean

mode

covariance

entropy

moment