Probability distributions

Warning

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

Note

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

OTComposedDistribution

Module: gemseo.uncertainty.distributions.openturns.composed

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

Module: gemseo.uncertainty.distributions.openturns.dirac

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

Module: gemseo.uncertainty.distributions.openturns.distribution

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

Module: gemseo.uncertainty.distributions.openturns.exponential

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

Module: gemseo.uncertainty.distributions.openturns.normal

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

Module: gemseo.uncertainty.distributions.openturns.triangular

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

Module: gemseo.uncertainty.distributions.openturns.uniform

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.

OTWeibullDistribution

Module: gemseo.uncertainty.distributions.openturns.weibull

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.

• location : float, optional

  The location parameter \(\gamma\) of the Weibull distribution.

  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.

• scale : float, optional

  The scale parameter of the Weibull distribution.

  By default it is set to 1.0.

• shape : float, optional

  The shape parameter of the Weibull distribution.

  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.

• use_weibull_min : bool, optional

  Whether to use the Weibull minimum extreme value distribution (the support of the random variable is \([\gamma,+\infty[\)) or the Weibull maximum extreme value distribution (the support of the random variable is \(]-\infty[,\gamma]\)).

  By default it is set to True.

• variable : str, optional

  The name of the random variable.

  By default it is set to x.

SPComposedDistribution

Module: gemseo.uncertainty.distributions.scipy.composed

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

Module: gemseo.uncertainty.distributions.scipy.distribution

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

Module: gemseo.uncertainty.distributions.scipy.exponential

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

Module: gemseo.uncertainty.distributions.scipy.normal

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

Module: gemseo.uncertainty.distributions.scipy.triangular

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

Module: gemseo.uncertainty.distributions.scipy.uniform

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.

SPWeibullDistribution

Module: gemseo.uncertainty.distributions.scipy.weibull

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.

• location : float, optional

  The location parameter of the Weibull distribution.

  By default it is set to 0.0.

• scale : float, optional

  The scale parameter of the Weibull distribution.

  By default it is set to 1.0.

• shape : float, optional

  The shape parameter of the Weibull distribution.

  By default it is set to 1.0.

• use_weibull_min : bool, optional

  Whether to use the Weibull minimum extreme value distribution (the support of the random variable is \([\gamma,+\infty[\)) or the Weibull maximum extreme value distribution (the support of the random variable is \(]-\infty[,\gamma]\)).

  By default it is set to True.

• variable : str, optional

  The name of the random variable.

  By default it is set to x.