gemseo / uncertainty / distributions

sp_dist module

Distributions based on scipy

Overview

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.

Construction

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

  • a variable name,

  • a distribution name recognized by OpenTURNS,

  • 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).

Classical distributions

This module also implements a deliberately limited selection of classical probability distributions in a user-friendly way: SPExponentialDistribution, SPNormalDistribution, SPTriangularDistribution, and SPUniformDistribution. More precisely, the argument whose nature is a dictionary of keyword parameters is replaced with several user-defined keyword arguments. In this way, the use writes SPUniformDistribution('x', -1., 3.) or SPUniformDistribution('x', lower=-1., upper=3.) instead of SPDistribution('x', 'Normal', (-1., 3.)). Furthermore, these classes inheriting from SPDistribution are documented in such a way that a newbie could easily apprehend them.

class gemseo.uncertainty.distributions.sp_dist.SPDistribution(variable, distribution, parameters, dimension=1, standard_parameters=None)[source]

Bases: gemseo.uncertainty.distributions.distribution.Distribution

The SPDistribution inherits from Distribution. It relies on the probabilistic modeling features of the scipy library.

Constructor

Parameters

  • variable (str) – variable name.

  • distribution (str) – distribution name.

  • parameters (tuple) – distribution parameters.

  • dimension (int) – variable dimension.

  • standard_parameters (dict) – standard parameters.

COMPOSED_DISTRIBUTION

alias of gemseo.uncertainty.distributions.sp_cdist.SPComposedDistribution

cdf(vector)[source]

Evaluate the cumulative density function of the random variable marginals for a given instance.

Parameters

vector (array) – instance of the random variable.

Returns

cdf values

Return type

array

get_sample(n_samples=1)[source]

Get several samples.

Parameters

n_samples (int) – number of samples.

Returns

samples

Return type

array

inverse_cdf(vector)[source]

Evaluate the inverse of the cumulative density function of the random variable marginals for a given unit vector .

Parameters

vector (array) – vector of values comprised between 0 and 1 with same dimension as the random variable.

Returns

inverse cdf values

Return type

array

property mean

Get the mean of the random variable.

Returns

mean of the random variable.

Return type

array

property standard_deviation

Get the standard deviation of the random variable.

Returns

standard deviation of the random variable.

Return type

array

class gemseo.uncertainty.distributions.sp_dist.SPExponentialDistribution(variable, rate=1.0, loc=0.0, dimension=1)[source]

Bases: gemseo.uncertainty.distributions.sp_dist.SPDistribution

Create a exponential distribution.

Constructor.

Parameters

  • variable (str) – variable name.

  • rate (float) – rate parameter.

  • loc (float) – location parameter.

  • dimension (int) – dimension.

class gemseo.uncertainty.distributions.sp_dist.SPNormalDistribution(variable, mu=0.0, sigma=1.0, dimension=1)[source]

Bases: gemseo.uncertainty.distributions.sp_dist.SPDistribution

Create a normal distribution.

Constructor.

Parameters

  • variable (str) – variable name.

  • mu (float) – mean.

  • sigma (float) – standard deviation.

  • dimension (int) – dimension.

class gemseo.uncertainty.distributions.sp_dist.SPTriangularDistribution(variable, lower=0.0, mode=0.5, upper=1.0, dimension=1)[source]

Bases: gemseo.uncertainty.distributions.sp_dist.SPDistribution

Create a triangular distribution.

Constructor.

Parameters

  • variable (str) – variable name.

  • lower (float) – lower bound.

  • mode (float) – mode.

  • upper (float) – upper bound.

  • dimension (int) – dimension.

class gemseo.uncertainty.distributions.sp_dist.SPUniformDistribution(variable, lower=0.0, upper=1.0, dimension=1)[source]

Bases: gemseo.uncertainty.distributions.sp_dist.SPDistribution

Create a uniform distribution.

Constructor.

Parameters

  • variable (str) – variable name.

  • lower (float) – lower bound.

  • upper (float) – upper bound.

  • dimension (int) – dimension.