# Package rst.stochastics¶

The use of the term stochastic to mean based on the theory of probability.

Wikipedia article containing the definition above
http://en.wikipedia.org/wiki/Stochastic

## Messages¶

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### Message MixtureOfGaussian1D¶

class `rst.stochastics.``MixtureOfGaussian1D`

Constraint: `sum(.components.weight) = 1`

Weighted mixture of one-dimensional Gaussian distributions.

Code author: Xavier Alameda-Pineda <xavier.alameda-pineda@inrialpes.fr>

Code author: Johannes Wienke <jwienke@techfak.uni-bielefeld.de>

`components`

Components of the mixture.

An empty set of components is not allowed. The order of elements is not significant.

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```message MixtureOfGaussian1D {

/**
* A mixture component distribution with its associated weight.
*/
message GaussianComponent1D {

/**
* The Gaussian distribution associated with this component.
*/
required Gaussian1D gaussian = 1;

/**
* Weight of this component.
*/
// @constraint(0 <= value <= 1)
required float weight = 2;

/**
* Deprecated implementation detail - do not use.
*/
required float probability_state = 3;
}

/**
* Components of the mixture.
*
* An empty set of components is not allowed.
* The order of elements is not significant.
*/
repeated GaussianComponent1D components = 1;

}
```

### Message GaussianComponent1D¶

class `rst.stochastics.MixtureOfGaussian1D.``GaussianComponent1D`

A mixture component distribution with its associated weight.

`gaussian`

The Gaussian distribution associated with this component.

`weight`
Type: `FLOAT32`

Constraint: `0 <= value <= 1`

Weight of this component.

`probability_state`
Type: `FLOAT32`

Deprecated implementation detail - do not use.

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```    message GaussianComponent1D {

/**
* The Gaussian distribution associated with this component.
*/
required Gaussian1D gaussian = 1;

/**
* Weight of this component.
*/
// @constraint(0 <= value <= 1)
required float weight = 2;

/**
* Deprecated implementation detail - do not use.
*/
required float probability_state = 3;
}
```

### Message Gaussian1D¶

class `rst.stochastics.``Gaussian1D`

Describes a one-dimensional Gaussian distribution.

Code author: Xavier Alameda-Pineda <xavier.alameda-pineda@inrialpes.fr>

Code author: Johannes Wienke <jwienke@techfak.uni-bielefeld.de>

`mean`
Type: `FLOAT32`

Mean of the distribution.

`variance`
Type: `FLOAT32`

Constraint: `value >= 0`

Variance of the distribution.

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```message Gaussian1D {

/**
* Mean of the distribution.
*/
required float mean = 1;

/**
* Variance of the distribution.
*/
// @constraint(value >= 0)
required float variance = 2;

}
```