# 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¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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 : str, optional

The name of the random variable.

By default it is set to x.

• variable_value : float, optional

The value of the random variable.

By default it is set to 0.0.

## OTDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

By default it is set to 1.

• interfaced_distribution : str, optional

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

By default it is set to Uniform.

• 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.

• parameters : tuple[Any], optional

The parameters of the probability distribution.

By default it is set to ().

• standard_parameters : StandardParametersType | None, optional

The parameters of the probability distribution used for string representation only (use parameters for computation). If None, use parameters instead. For instance, let us consider the interfaced OpenTURNS distribution "Dirac". Then, the string representation of OTDistribution("x", "Dirac", (1,), 1, {"loc": 1}) is "Dirac(loc=1)" while the string representation of OTDistribution("x", "Dirac", (1,)) is "Dirac(1)".

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 : str, optional

The name of the random variable.

By default it is set to x.

## OTExponentialDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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 probability 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 probability distribution. If None, no upper truncation.

By default it is set to None.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## OTNormalDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• 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 probability distribution. If None, no upper truncation.

By default it is set to None.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## OTTriangularDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• 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 probability distribution. If None, no upper truncation.

By default it is set to None.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## OTUniformDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• 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 probability distribution. If None, no upper truncation.

By default it is set to None.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## 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¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

By default it is set to 1.

• interfaced_distribution : str, optional

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

By default it is set to uniform.

• parameters : Mapping[str, Any], optional

The parameters of the probability distribution.

By default it is set to {}.

• standard_parameters : StandardParametersType | None, optional

The parameters of the probability distribution used for string representation only (use parameters for computation). If None, use parameters instead. For instance, let us consider the interfaced SciPy distribution "uniform". Then, the string representation of SPDistribution("x", "uniform", parameters, 1, {"min": 1, "max": 3}) with parameters={"loc": 1, "scale": 2} is "uniform(max=3, min=1)" while the string representation of SPDistribution("x", "uniform", parameters) is "uniform(loc=1, scale=2)".

By default it is set to None.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## SPExponentialDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## SPNormalDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## SPTriangularDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• variable : str, optional

The name of the random variable.

By default it is set to x.

## SPUniformDistribution¶

Optional parameters
• dimension : int, optional

The dimension of the random variable. If greater than 1, the probability distribution is applied to all components of the random variable under the hypothesis that these components are stochastically independent. To be removed in a future version; use a ComposedDistribution instead.

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.

• variable : str, optional

The name of the random variable.

By default it is set to x.