---
name: "mlpack_distribution_GaussianDistribution"
section: "3"
platform: "linux"
package: "mlpack-doc"
version: "1.0.10-1"
release: "Debian 8 (Jessie)"
platforms: ["linux"]
url: "https://new.carta.tech/mlpack_distribution_GaussianDistribution"
---

# mlpack\_distribution\_GaussianDistribution(3)

A single multivariate Gaussian distribution.

## NAME

mlpack::distribution::GaussianDistribution -

A single multivariate Gaussian distribution.

## SYNOPSIS

### Public Member Functions

**GaussianDistribution** ()\
 *Default constructor, which creates a Gaussian with zero dimension.*  **GaussianDistribution** (const size\_t dimension)\
 *Create a Gaussian distribution with zero mean and identity covariance with the given dimensionality.*  **GaussianDistribution** (const arma::vec &**mean**, const arma::mat &**covariance**)\
 *Create a Gaussian distribution with the given mean and covariance.*  const arma::mat & **Covariance** () const \
 *Return the covariance matrix.*  arma::mat & **Covariance** ()\
 *Return a modifiable copy of the covariance.*  size\_t **Dimensionality** () const \
 *Return the dimensionality of this distribution.*  void **Estimate** (const arma::mat &observations)\
 *Estimate the Gaussian distribution directly from the given observations.*  void **Estimate** (const arma::mat &observations, const arma::vec &probabilities)\
 *Estimate the Gaussian distribution from the given observations, taking into account the probability of each observation actually being from this distribution.*  const arma::vec & **Mean** () const \
 *Return the mean.*  arma::vec & **Mean** ()\
 *Return a modifiable copy of the mean.*  double **Probability** (const arma::vec &observation) const \
 *Return the probability of the given observation.*  arma::vec **Random** () const \
 *Return a randomly generated observation according to the probability distribution defined by this object.*  std::string **ToString** () const \
 *Returns a string representation of this object.*

### Private Attributes

arma::mat **covariance**\
 *Covariance of the distribution.*  arma::vec **mean**\
 *Mean of the distribution.*

## Detailed Description

A single multivariate Gaussian distribution.

Definition at line 35 of file gaussian\_distribution.hpp.

## Constructor & Destructor Documentation

### mlpack::distribution::GaussianDistribution::GaussianDistribution ()` [inline]`

Default constructor, which creates a Gaussian with zero dimension.

Definition at line 47 of file gaussian\_distribution.hpp.

### mlpack::distribution::GaussianDistribution::GaussianDistribution (const size\_tdimension)` [inline]`

Create a Gaussian distribution with zero mean and identity covariance with the given dimensionality.

Definition at line 53 of file gaussian\_distribution.hpp.

### mlpack::distribution::GaussianDistribution::GaussianDistribution (const arma::vec &mean, const arma::mat &covariance)` [inline]`

Create a Gaussian distribution with the given mean and covariance.

Definition at line 61 of file gaussian\_distribution.hpp.

## Member Function Documentation

### const arma::mat& mlpack::distribution::GaussianDistribution::Covariance () const` [inline]`

Return the covariance matrix.

Definition at line 104 of file gaussian\_distribution.hpp.

References covariance.

### arma::mat& mlpack::distribution::GaussianDistribution::Covariance ()` [inline]`

Return a modifiable copy of the covariance.

Definition at line 106 of file gaussian\_distribution.hpp.

References covariance.

### size\_t mlpack::distribution::GaussianDistribution::Dimensionality () const` [inline]`

Return the dimensionality of this distribution.

Definition at line 65 of file gaussian\_distribution.hpp.

References mean.

### void mlpack::distribution::GaussianDistribution::Estimate (const arma::mat &observations)

Estimate the Gaussian distribution directly from the given observations.

**Parameters:**

*observations* List of observations.

### void mlpack::distribution::GaussianDistribution::Estimate (const arma::mat &observations, const arma::vec &probabilities)

Estimate the Gaussian distribution from the given observations, taking into account the probability of each observation actually being from this distribution.

### const arma::vec& mlpack::distribution::GaussianDistribution::Mean () const` [inline]`

Return the mean.

Definition at line 99 of file gaussian\_distribution.hpp.

References mean.

### arma::vec& mlpack::distribution::GaussianDistribution::Mean ()` [inline]`

Return a modifiable copy of the mean.

Definition at line 101 of file gaussian\_distribution.hpp.

References mean.

### double mlpack::distribution::GaussianDistribution::Probability (const arma::vec &observation) const` [inline]`

Return the probability of the given observation.

Definition at line 70 of file gaussian\_distribution.hpp.

References covariance, mean, and mlpack::gmm::phi().

### arma::vec mlpack::distribution::GaussianDistribution::Random () const

Return a randomly generated observation according to the probability distribution defined by this object.

**Returns:**

Random observation from this Gaussian distribution.

### std::string mlpack::distribution::GaussianDistribution::ToString () const

Returns a string representation of this object.

## Member Data Documentation

### arma::mat mlpack::distribution::GaussianDistribution::covariance` [private]`

Covariance of the distribution.

Definition at line 41 of file gaussian\_distribution.hpp.

Referenced by Covariance(), and Probability().

### arma::vec mlpack::distribution::GaussianDistribution::mean` [private]`

Mean of the distribution.

Definition at line 39 of file gaussian\_distribution.hpp.

Referenced by Dimensionality(), Mean(), and Probability().

## Author

Generated automatically by Doxygen for MLPACK from the source code.