Probability distribution algorithms

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

Module: gemseo.uncertainty.distributions.openturns.composed

Required parameters

• distributions : Sequence[OTDistribution]

  The distributions.

• variable : str

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

Optional parameters

• copula : CopulaModel | str, optional

  A copula model.

  By default it is set to independent_copula.

OTDiracDistribution

Module: gemseo.uncertainty.distributions.openturns.dirac

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 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 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

Module: gemseo.uncertainty.distributions.openturns.distribution

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’ for OpenTURNS or ‘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.

• lower_bound : float | None, optional

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

  By default it is set to None.

OTExponentialDistribution

Module: gemseo.uncertainty.distributions.openturns.exponential

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

Module: gemseo.uncertainty.distributions.openturns.normal

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

Module: gemseo.uncertainty.distributions.openturns.triangular

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

Module: gemseo.uncertainty.distributions.openturns.uniform

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

Module: gemseo.uncertainty.distributions.scipy.composed

Required parameters

• distributions : Sequence[SPDistribution]

  The distributions.

• variable : str

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

Optional parameters

• copula : CopulaModel | str, optional

  A copula model.

  By default it is set to independent_copula.

SPDistribution

Module: gemseo.uncertainty.distributions.scipy.distribution

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’ for OpenTURNS or ‘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. standard_parameters (dict, optional): The standard representation of the parameters of the probability distribution.

  By default it is set to 1.

• standard_parameters : StandardParametersType | None, optional

  By default it is set to None.

SPExponentialDistribution

Module: gemseo.uncertainty.distributions.scipy.exponential

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

Module: gemseo.uncertainty.distributions.scipy.normal

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

Module: gemseo.uncertainty.distributions.scipy.triangular

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

Module: gemseo.uncertainty.distributions.scipy.uniform

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.