# Probability distributions¶

Warning

Some algorithms may require the installation of GEMSEO with all its features and some others may depend on plugins.

Note

All the features of the wrapped algorithm libraries may not be exposed through GEMSEO.

## OTComposedDistribution¶

Required parameters
• distributions : Sequence[OTDistribution]

The marginal distributions.

• variable : str

The name of the variable, if any; otherwise, concatenate the names of the random variables defined by distributions.

Optional parameters
• copula : ots.Distribution | None, optional

A copula distribution defining the dependency structure between random variables; if None, consider an independent copula.

By default it is set to None.

## OTDiracDistribution¶

Required parameters
• variable : str

The name of the random variable.

Optional parameters
• dimension : int, optional

The dimension of the random variable.

By default it is set to 1.

• lower_bound : float | None, optional

A lower bound to truncate the probability distribution. If None, no lower truncation.

By default it is set to None.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. $$\sin(x)$$. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the probability distribution. If None, no upper truncation.

By default it is set to None.

• variable_value : float, optional

The value of the random variable.

By default it is set to 0.0.

## OTDistribution¶

Required parameters
• interfaced_distribution : str

The name of the probability distribution, typically the name of a class wrapped from an external library, such as "Normal".

• parameters : ParametersType

The parameters of the probability distribution.

• variable : str

The name of the random variable.

Optional parameters
• dimension : int, optional

The dimension of the random variable.

By default it is set to 1.

• lower_bound : float | None, optional

A lower bound to truncate the probability distribution. If None, no lower truncation.

By default it is set to None.

• standard_parameters : StandardParametersType | None, optional

The standard representation of the parameters of the probability distribution.

By default it is set to None.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. $$\sin(x)$$. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the probability distribution. If None, no upper truncation.

By default it is set to None.

## OTExponentialDistribution¶

Required parameters
• variable : str

The name of the exponential random variable.

Optional parameters
• dimension : int, optional

The dimension of the exponential random variable.

By default it is set to 1.

• loc : float, optional

The location of the exponential random variable.

By default it is set to 0.0.

• lower_bound : float | None, optional

A lower bound to truncate the distribution. If None, no lower truncation.

By default it is set to None.

• rate : float, optional

The rate of the exponential random variable.

By default it is set to 1.0.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. ‘sin(x)’. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the distribution. If None, no upper truncation.

By default it is set to None.

## OTNormalDistribution¶

Required parameters
• variable : str

The name of the normal random variable.

Optional parameters
• dimension : int, optional

The dimension of the normal random variable.

By default it is set to 1.

• lower_bound : float | None, optional

A lower bound to truncate the distribution. If None, no lower truncation.

By default it is set to None.

• mu : float, optional

The mean of the normal random variable.

By default it is set to 0.0.

• sigma : float, optional

The standard deviation of the normal random variable.

By default it is set to 1.0.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. ‘sin(x)’. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the distribution. If None, no upper truncation.

By default it is set to None.

## OTTriangularDistribution¶

Required parameters
• variable : str

The name of the triangular random variable.

Optional parameters
• dimension : int, optional

The dimension of the triangular random variable.

By default it is set to 1.

• lower_bound : float | None, optional

A lower bound to truncate the distribution. If None, no lower truncation.

By default it is set to None.

• maximum : float, optional

The maximum of the random variable.

By default it is set to 1.0.

• minimum : float, optional

The minimum of the triangular random variable.

By default it is set to 0.0.

• mode : float, optional

The mode of the triangular random variable.

By default it is set to 0.5.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. ‘sin(x)’. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the distribution. If None, no upper truncation.

By default it is set to None.

## OTUniformDistribution¶

Required parameters
• variable : str

The name of the uniform random variable.

Optional parameters
• dimension : int, optional

The dimension of the uniform random variable.

By default it is set to 1.

• lower_bound : float | None, optional

A lower bound to truncate the distribution. If None, no lower truncation.

By default it is set to None.

• maximum : float, optional

The maximum of the uniform random variable.

By default it is set to 1.0.

• minimum : float, optional

The minimum of the uniform random variable.

By default it is set to 0.0.

• threshold : float, optional

A threshold in [0,1].

By default it is set to 0.5.

• transformation : str | None, optional

A transformation applied to the random variable, e.g. ‘sin(x)’. If None, no transformation.

By default it is set to None.

• upper_bound : float | None, optional

An upper bound to truncate the distribution. If None, no upper truncation.

By default it is set to None.

## SPComposedDistribution¶

Required parameters
• distributions : Sequence[SPDistribution]

The marginal distributions.

• variable : str

The name of the variable, if any; otherwise, concatenate the names of the random variables defined by distributions.

Optional parameters
• copula : None, optional

A copula distribution defining the dependency structure between random variables; if None, consider an independent copula.

By default it is set to None.

## SPDistribution¶

Required parameters
• interfaced_distribution : str

The name of the probability distribution, typically the name of a class wrapped from an external library, such as "norm" for SciPy.

• parameters : ParametersType

The parameters of the probability distribution.

• variable : str

The name of the random variable.

Optional parameters
• dimension : int, optional

The dimension of the random variable.

By default it is set to 1.

• standard_parameters : StandardParametersType | None, optional

The standard representation of the parameters of the probability distribution.

By default it is set to None.

## SPExponentialDistribution¶

Required parameters
• variable : str

The name of the exponential random variable.

Optional parameters
• dimension : int, optional

The dimension of the exponential random variable.

By default it is set to 1.

• loc : float, optional

The location of the exponential random variable.

By default it is set to 0.0.

• rate : float, optional

The rate of the exponential random variable.

By default it is set to 1.0.

## SPNormalDistribution¶

Required parameters
• variable : str

The name of the normal random variable.

Optional parameters
• dimension : int, optional

The dimension of the normal random variable.

By default it is set to 1.

• mu : float, optional

The mean of the normal random variable.

By default it is set to 0.0.

• sigma : float, optional

The standard deviation of the normal random variable.

By default it is set to 1.0.

## SPTriangularDistribution¶

Required parameters
• variable : str

The name of the triangular random variable.

Optional parameters
• dimension : int, optional

The dimension of the triangular random variable.

By default it is set to 1.

• maximum : float, optional

The maximum of the triangular random variable.

By default it is set to 1.0.

• minimum : float, optional

The minimum of the triangular random variable.

By default it is set to 0.0.

• mode : float, optional

The mode of the triangular random variable.

By default it is set to 0.5.

## SPUniformDistribution¶

Required parameters
• variable : str

The name of the uniform random variable.

Optional parameters
• dimension : int, optional

The dimension of the uniform random variable.

By default it is set to 1.

• maximum : float, optional

The maximum of the uniform random variable.

By default it is set to 1.0.

• minimum : float, optional

The minimum of the uniform random variable.

By default it is set to 0.0.