gemseo / uncertainty / distributions / scipy

# distribution module¶

Class to create a probability distribution from the SciPy library.

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

The SPDistribution of a given uncertain variable is built from mandatory arguments:

• a variable name,

• a distribution name recognized by SciPy,

• a set of parameters provided as a dictionary of keyword arguments named as the arguments of the scipy constructor of this distribution.

Warning

The distribution parameters must be provided according to the signature of the scipy classes. Access the scipy documentation.

The constructor has also optional arguments:

• a variable dimension (default: 1),

• a standard representation of these parameters (default: use parameters).

Classes:

 SPDistribution(variable, …[, dimension, …]) SciPy probability distribution.
class gemseo.uncertainty.distributions.scipy.distribution.SPDistribution(variable, interfaced_distribution, parameters, dimension=1, standard_parameters=None)[source]

SciPy probability distribution.

Create a probability distribution for an uncertain variable from its dimension and distribution names and properties.

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
• variable (str) –

• interfaced_distribution (str) –

• parameters (ParametersType) –

• dimension (int) –

• standard_parameters (Optional[StandardParametersType]) –

Return type

None

Example

>>> from gemseo.uncertainty.distributions.scipy.distribution import (
...    SPDistribution
... )
>>> distribution = SPDistribution('x', 'expon', {'loc': 3, 'scale': 1/2.})
>>> print(distribution)
expon(loc=3, scale=0.5)


Parameters: variable: The name of the random variable. interfaced_distribution: 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.

parameters: The parameters of the class

related to distribution.

dimension: The dimension of the random variable. standard_parameters: The standard representation

of the parameters of the probability distribution.

variable: The name of the random variable. interfaced_distribution: 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.

parameters: The parameters of the probability distribution. dimension: The dimension of the random variable. standard_parameters (dict, optional): The standard representation

of the parameters of the probability distribution.

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.

Attributes:

 mean The analytical mean of the random variable. range The numerical range. standard_deviation The analytical standard deviation of the random variable. support The mathematical support.
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 (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

numpy.ndarray

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 from directory_path, file_name and file_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 post-processing.

• 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 from directory_path, file_name and file_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 post-processing.

• 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.