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.
Classes:

OpenTURNS composed distribution. 
 class gemseo.uncertainty.distributions.openturns.composed.OTComposedDistribution(distributions, copula='independent_copula')[source]¶
Bases:
gemseo.uncertainty.distributions.composed.ComposedDistribution
OpenTURNS composed distribution.
 Attributes
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.
distribution (InterfacedDistributionClass) – The probability distribution of the random variable.
marginals (list(InterfacedDistributionClass)) – The marginal distributions of the components of the random variable.
dimension (int) – The number of dimensions of the random variable.
variable_name (str) – The name of the random variable.
distribution_name (str) – The name of the probability distribution.
transformation (str) – The transformation applied to the random variable, e.g. ‘sin(x)’.
parameters (tuple or dict) – The parameters of the probability distribution.
standard_parameters (dict, optional) – The standard representation of the parameters of the distribution, used for its string representation.
 Parameters
distributions (Sequence[OTDistribution]) –
copula (str) –
 Return type
None
Parameters: distributions: The distributions. copula: A name of copula. distributions: The distributions. copula: A name of copula.
Attributes:
The analytical mean of the random variable.
The numerical range.
The analytical standard deviation of the random variable.
The mathematical support.
Methods:
compute_cdf
(vector)Evaluate the cumulative density function (CDF).
compute_inverse_cdf
(vector)Evaluate the inverse of the cumulative density function (ICDF).
compute_samples
([n_samples])Sample the random variable.
plot
([index, show, save, file_path, …])Plot both probability and cumulative density functions for a given component.
plot_all
([show, save, file_path, …])Plot both probability and cumulative density functions for all components.
 AVAILABLE_COPULA_MODELS = ['independent_copula']¶
 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.
 Parameters
vector (Iterable[float]) – A realization of the random variable.
 Returns
The CDF values of the components of the random variable.
 Return type
numpy.ndarray
 compute_inverse_cdf(vector)[source]¶
Evaluate the inverse of the cumulative density function (ICDF).
 Parameters
vector (numpy.ndarray) – A vector of values comprised between 0 and 1 whose length is equal to the dimension of the random variable.
 Returns
The ICDF values of the components of the random variable.
 Return type
Iterable[float]
 compute_samples(n_samples=1)[source]¶
Sample the random variable.
 Parameters
n_samples (int) – The number of samples.
 Returns
The samples of the random variable,
The number of columns is equal to the dimension of the variable and the number of lines is equal to the number of samples.
 Return type
numpy.ndarray
 property mean¶
The analytical mean of the random variable.
 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.
save (bool) – If True, save the figure.
show (bool) – If True, display the figure.
file_path (Optional[Union[str, pathlib.Path]]) – The path of the file to save the figures. If the extension is missing, use
file_extension
. If None, create a file path fromdirectory_path
,file_name
andfile_extension
.directory_path (Optional[Union[str, pathlib.Path]]) – The path of the directory to save the figures. If None, use the current working directory.
file_name (Optional[str]) – The name of the file to save the figures. If None, use a default one generated by the postprocessing.
file_extension (Optional[str]) – A file extension, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.
 Returns
The figure.
 Return type
matplotlib.figure.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.
show (bool) – If True, display the figure.
file_path (Optional[Union[str, pathlib.Path]]) – The path of the file to save the figures. If the extension is missing, use
file_extension
. If None, create a file path fromdirectory_path
,file_name
andfile_extension
.directory_path (Optional[Union[str, pathlib.Path]]) – The path of the directory to save the figures. If None, use the current working directory.
file_name (Optional[str]) – The name of the file to save the figures. If None, use a default one generated by the postprocessing.
file_extension (Optional[str]) – A file extension, e.g. ‘png’, ‘pdf’, ‘svg’, … If None, use a default file extension.
 Returns
The figures.
 Return type
List[matplotlib.figure.Figure]
 property range¶
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.
 property standard_deviation¶
The analytical standard deviation of the random variable.
 property support¶
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.