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, useparameters
instead. For instance, let us consider the interfaced OpenTURNS distribution"Dirac"
. Then, the string representation ofOTDistribution("x", "Dirac", (1,), 1, {"loc": 1})
is"Dirac(loc=1)"
while the string representation ofOTDistribution("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
isTrue
.By default it is set to 1.0.
set_log : bool, optional
Whether
mu
andsigma
apply to the logarithm of the log-normal random variable. Otherwise,mu
andsigma
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
isTrue
.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, 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, useparameters
instead. For instance, let us consider the interfaced SciPy distribution"uniform"
. Then, the string representation ofSPDistribution("uniform", parameters, 1, {"min": 1, "max": 3})
withparameters={"loc": 1, "scale": 2}
is"uniform(max=3, min=1)"
while the string representation ofSPDistribution("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
isTrue
.By default it is set to 1.0.
set_log : bool, optional
Whether
mu
andsigma
apply to the logarithm of the log-normal random variable. Otherwise,mu
andsigma
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
isTrue
.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.