composed module¶
Class to create a joint probability distribution from the OpenTURNS library.
The OTComposedDistribution
class is a concrete class
inheriting from ComposedDistribution
which is an abstract one.
OT stands for OpenTURNS
which is the library it relies on.
This class inherits from OTDistribution
.
It builds a composed probability distribution
related to given random variables from a list of OTDistribution
objects
implementing the probability distributions of these variables
based on the OpenTURNS library and from a copula name.
Note
A copula is a mathematical function used to define the dependence between random variables from their cumulative density functions. See more.
- class gemseo.uncertainty.distributions.openturns.composed.OTComposedDistribution(distributions, copula=CopulaModel.independent_copula, variable='')[source]¶
Bases:
ComposedDistribution
OpenTURNS composed distribution.
- Parameters:
distributions (Sequence[OTDistribution]) – The distributions.
copula (CopulaModel | str) –
A copula model.
By default it is set to independent_copula.
variable (str) –
The name of the variable, if any; otherwise, concatenate the names of the random variables defined by
distributions
.By default it is set to “”.
- class CopulaModel(value)[source]¶
Bases:
CallableEnum
A copula model.
- independent_copula(*args, **kwargs) = <class 'openturns.model_copula.IndependentCopula'>¶
- compute_cdf(vector)[source]¶
Evaluate the cumulative density function (CDF).
Evaluate the CDF of the components of the random variable for a given realization of this random variable.
- compute_inverse_cdf(vector)[source]¶
Evaluate the inverse of the cumulative density function (ICDF).
- plot(index=0, show=True, save=False, file_path=None, directory_path=None, file_name=None, file_extension=None)¶
Plot both probability and cumulative density functions for a given component.
- Parameters:
index (int) –
The index of a component of the random variable.
By default it is set to 0.
save (bool) –
If True, save the figure.
By default it is set to False.
show (bool) –
If True, display the figure.
By default it is set to True.
file_path (str | Path | None) – The path of the file to save the figures. If the extension is missing, use
file_extension
. IfNone
, create a file path fromdirectory_path
,file_name
andfile_extension
.directory_path (str | Path | None) – The path of the directory to save the figures. If
None
, use the current working directory.file_name (str | None) – The name of the file to save the figures. If
None
, use a default one generated by the post-processing.file_extension (str | None) – A file extension, e.g.
'png'
,'pdf'
,'svg'
, … IfNone
, use a default file extension.
- Returns:
The figure.
- Return type:
Figure
- plot_all(show=True, save=False, file_path=None, directory_path=None, file_name=None, file_extension=None)¶
Plot both probability and cumulative density functions for all components.
- Parameters:
save (bool) –
If True, save the figure.
By default it is set to False.
show (bool) –
If True, display the figure.
By default it is set to True.
file_path (str | Path | None) – The path of the file to save the figures. If the extension is missing, use
file_extension
. IfNone
, create a file path fromdirectory_path
,file_name
andfile_extension
.directory_path (str | Path | None) – The path of the directory to save the figures. If
None
, use the current working directory.file_name (str | None) – The name of the file to save the figures. If
None
, use a default one generated by the post-processing.file_extension (str | None) – A file extension, e.g.
'png'
,'pdf'
,'svg'
, … IfNone
, use a default file extension.
- Returns:
The figures.
- Return type:
list[Figure]
- AVAILABLE_COPULA_MODELS: ClassVar[list[str]] = ['independent_copula']¶
The names of the models defining copulas.
- math_lower_bound: ndarray¶
The mathematical lower bound of the random variable.
- math_upper_bound: ndarray¶
The mathematical upper bound of the random variable.
- num_lower_bound: ndarray¶
The numerical lower bound of the random variable.
- num_upper_bound: ndarray¶
The numerical upper bound of the random variable.
- property range: list[numpy.ndarray]¶
The numerical range.
The numerical range is the interval defined by the lower and upper bounds numerically reachable by the random variable.
Here, the numerical range of the random variable is defined by one array for each component of the random variable, whose first element is the lower bound of this component while the second one is its upper bound.
- standard_parameters: dict[str, str] | None¶
The standard representation of the parameters of the distribution, used for its string representation.
- property support: list[numpy.ndarray]¶
The mathematical support.
The mathematical support is the interval defined by the theoretical lower and upper bounds of the random variable.
Here, the mathematical range of the random variable is defined by one array for each component of the random variable, whose first element is the lower bound of this component while the second one is its upper bound.