gemseo / uncertainty / distributions / scipy

# composed module¶

Class to create a joint probability distribution from the SciPy library.

The SPComposedDistribution class is a concrete class inheriting from ComposedDistribution which is an abstract one. SP stands for scipy which is the library it relies on.

This class inherits from SPDistribution. It builds a composed probability distribution related to given random variables from a list of SPDistribution objects implementing the probability distributions of these variables based on the SciPy 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.scipy.composed.SPComposedDistribution(distributions, copula=CopulaModel.independent_copula, variable='')[source]

Scipy composed distribution.

Parameters:
• distributions (Sequence[SPDistribution]) – 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: BaseEnum

A copula model.

independent_copula = None
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:

ndarray

compute_inverse_cdf(vector)[source]

Evaluate the inverse of the cumulative density function (ICDF).

Parameters:

vector (Iterable[float]) – 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:

ndarray

compute_samples(n_samples=1)

Sample the random variable.

Parameters:

n_samples (int) –

The number of samples.

By default it is set to 1.

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:

ndarray

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. If None, create a file path from directory_path, file_name and file_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', … If None, 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. If None, create a file path from directory_path, file_name and file_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', … If None, 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.

INDEPENDENT_COPULA: Final[str] = 'independent_copula'

The name of the independent copula.

dimension: int

The number of dimensions of the random variable.

distribution: type

The probability distribution of the random variable.

distribution_name: str

The name of the probability distribution.

marginals: list[type]

The marginal distributions of the components of the random variable.

math_lower_bound: ndarray

The mathematical lower bound of the random variable.

math_upper_bound: ndarray

The mathematical upper bound of the random variable.

property mean: ndarray

The analytical mean 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.

parameters: tuple[Any] | dict[str, Any]

The parameters of the probability distribution.

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.

property standard_deviation: ndarray

The analytical standard deviation of the random variable.

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.

transformation: str

The transformation applied to the random variable, e.g. ‘sin(x)’.

variable_name: str

The name of the random variable.