Probability distributions#

Warning

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

Warning

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

OTBetaDistribution#

Module: gemseo.uncertainty.distributions.openturns.beta

Optional settings

  • alpha : float, optional

    The first shape parameter of the beta random variable.

    By default it is set to 2.0.

  • beta : float, optional

    The second shape parameter of the beta random variable.

    By default it is set to 2.0.

  • 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.

  • maximum : float, optional

    The maximum of the beta random variable.

    By default it is set to 1.0.

  • minimum : float, optional

    The minimum of the beta random variable.

    By default it is set to 0.0.

  • threshold : float, optional

    A threshold in [0,1] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTDiracDistribution#

Module: gemseo.uncertainty.distributions.openturns.dirac

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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#

Module: gemseo.uncertainty.distributions.openturns.distribution

Optional settings

  • 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, optional

    The parameters of the probability distribution used for string representation only (use parameters for computation). If empty, 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 {}.

  • threshold : float, optional

    A threshold in [0,1] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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#

Module: gemseo.uncertainty.distributions.openturns.exponential

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTJointDistribution#

Module: gemseo.uncertainty.distributions.openturns.joint

Required settings

  • distributions : Sequence[OTDistribution]

    The marginal distributions.

Optional settings

  • copula : 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.

OTLogNormalDistribution#

Module: gemseo.uncertainty.distributions.openturns.log_normal

Optional settings

  • location : float, optional

    The location of the log-normal 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.

  • mu : float, optional

    Either the mean of the log-normal random variable or that of its logarithm when set_log is True.

    By default it is set to 1.0.

  • set_log : bool, optional

    Whether mu and sigma apply to the logarithm of the log-normal random variable. Otherwise, mu and sigma apply to the log-normal random variable directly.

    By default it is set to False.

  • sigma : float, optional

    Either the standard deviation of the log-normal random variable or that of its logarithm when set_log is True.

    By default it is set to 1.0.

  • threshold : float, optional

    A threshold in [0,1] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTNormalDistribution#

Module: gemseo.uncertainty.distributions.openturns.normal

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTTriangularDistribution#

Module: gemseo.uncertainty.distributions.openturns.triangular

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTUniformDistribution#

Module: gemseo.uncertainty.distributions.openturns.uniform

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

OTWeibullDistribution#

Module: gemseo.uncertainty.distributions.openturns.weibull

Optional settings

  • 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] (see OpenTURNS documentation).

    By default it is set to 0.5.

  • transformation : str

    A transformation applied to the random variable, e.g. \(\sin(x)\). If empty, no transformation.

    By default it is set to .

  • 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.

SPBetaDistribution#

Module: gemseo.uncertainty.distributions.scipy.beta

Optional settings

  • alpha : float, optional

    The first shape parameter of the beta random variable.

    By default it is set to 2.0.

  • beta : float, optional

    The second shape parameter of the beta random variable.

    By default it is set to 2.0.

  • maximum : float, optional

    The maximum of the beta random variable.

    By default it is set to 1.0.

  • minimum : float, optional

    The minimum of the beta random variable.

    By default it is set to 0.0.

SPDistribution#

Module: gemseo.uncertainty.distributions.scipy.distribution

Optional settings

  • 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 : StrKeyMapping | tuple[Any, ...], optional

    The parameters of the probability distribution.

    By default it is set to {}.

  • standard_parameters : StandardParametersType, optional

    The parameters of the probability distribution used for string representation only (use parameters for computation). If empty, use parameters instead. For instance, let us consider the interfaced SciPy distribution "uniform". Then, the string representation of SPDistribution("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("uniform", parameters) is "uniform(loc=1, scale=2)".

    By default it is set to {}.

SPExponentialDistribution#

Module: gemseo.uncertainty.distributions.scipy.exponential

Optional settings

  • 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.

SPJointDistribution#

Module: gemseo.uncertainty.distributions.scipy.joint

Required settings

  • distributions : Sequence[SPDistribution]

    The marginal distributions.

Optional settings

  • 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.

SPLogNormalDistribution#

Module: gemseo.uncertainty.distributions.scipy.log_normal

Optional settings

  • location : float, optional

    The location of the log-normal random variable.

    By default it is set to 0.0.

  • mu : float, optional

    Either the mean of the log-normal random variable or that of its logarithm when set_log is True.

    By default it is set to 1.0.

  • set_log : bool, optional

    Whether mu and sigma apply to the logarithm of the log-normal random variable. Otherwise, mu and sigma apply to the log-normal random variable directly.

    By default it is set to False.

  • sigma : float, optional

    Either the standard deviation of the log-normal random variable or that of its logarithm when set_log is True.

    By default it is set to 1.0.

SPNormalDistribution#

Module: gemseo.uncertainty.distributions.scipy.normal

Optional settings

  • 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

Optional settings

  • 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

Optional settings

  • 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.

SPWeibullDistribution#

Module: gemseo.uncertainty.distributions.scipy.weibull

Optional settings

  • 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.