gemseo.uncertainty.statistics.ot_parametric_statistics module

OpenTURNS-based parametric estimation of statistics from a dataset.

class OTParametricStatistics(dataset, distributions, variable_names=(), fitting_criterion=None, level=0.05, selection_criterion=SelectionCriterion.BEST, name='')

Bases: BaseParametricStatistics[OTDistribution, BIC, DistributionName, FittingCriterion, SignificanceTest]

A toolbox to compute statistics using OpenTURNS probability distribution-fitting.

Examples

>>> from gemseo import (
...     create_discipline,
...     create_parameter_space,
...     sample_disciplines,
... )
>>> from gemseo.uncertainty.statistics.parametric_statistics import (
...     OTParametricStatistics,
... )
>>>
>>> discipline = create_discipline(
...     "AnalyticDiscipline", {"y1": "x1+2*x2", "y2": "x1-3*x2"}
... )
>>> parameter_space = create_parameter_space()
>>> parameter_space.add_random_variable(
...     "x1", "OTUniformDistribution", minimum=-1, maximum=1
... )
>>> parameter_space.add_random_variable(
...     "x2", "OTNormalDistribution", mu=0.5, sigma=2
... )
>>>
>>> dataset = sample_disciplines(
...     [discipline],
...     parameter_space,
...     ["y1"],
...     algo_name="OT_MONTE_CARLO",
...     n_samples=100,
... )
>>>
>>> statistics = OTParametricStatistics(
...     dataset, ["Normal", "Uniform", "Triangular"]
... )
>>> fitting_matrix = statistics.get_fitting_matrix()
>>> mean = statistics.compute_mean()

Parameters:

• dataset (Dataset) -- A dataset.

• distributions (Sequence[_DistributionNameT]) -- The names of the probability distributions.

• variable_names (Iterable[str]) --

  The names of the variables for which to compute statistics. If empty, consider all the variables of the dataset.

  By default it is set to ().

• fitting_criterion (_FittingCriterionT | None) -- The name of the fitting criterion to measure the goodness-of-fit of the probability distributions. If empty, use the default one. Use get_criteria() to get the available criteria.

• level (float) --

  A test level, i.e. the risk of committing a Type 1 error, that is an incorrect rejection of a true null hypothesis, for criteria based on test hypothesis.

  By default it is set to 0.05.

• selection_criterion (SelectionCriterion) --

  The name of the criterion to select a distribution among distributions.

  By default it is set to "best".

• name (str) --

  A name for the toolbox computing statistics. If empty, concatenate the names of the dataset and the name of the class.

  By default it is set to "".

class DistributionName(*values)

Bases: StrEnum

Arcsine = 'Arcsine'

Beta = 'Beta'

Burr = 'Burr'

Chi = 'Chi'

ChiSquare = 'ChiSquare'

Dirichlet = 'Dirichlet'

Exponential = 'Exponential'

FisherSnedecor = 'FisherSnedecor'

Frechet = 'Frechet'

Gamma = 'Gamma'

GeneralizedPareto = 'GeneralizedPareto'

Gumbel = 'Gumbel'

Histogram = 'Histogram'

InverseNormal = 'InverseNormal'

Laplace = 'Laplace'

LogNormal = 'LogNormal'

LogUniform = 'LogUniform'

Logistic = 'Logistic'

MeixnerDistribution = 'MeixnerDistribution'

Normal = 'Normal'

Pareto = 'Pareto'

Rayleigh = 'Rayleigh'

Rice = 'Rice'

Student = 'Student'

Trapezoidal = 'Trapezoidal'

Triangular = 'Triangular'

TruncatedNormal = 'TruncatedNormal'

Uniform = 'Uniform'

VonMises = 'VonMises'

WeibullMax = 'WeibullMax'

WeibullMin = 'WeibullMin'

class FittingCriterion(*values)

Bases: StrEnum

BIC = 'BIC'

ChiSquared = 'ChiSquared'

Kolmogorov = 'Kolmogorov'

class SignificanceTest(*values)

Bases: StrEnum

ChiSquared = 'ChiSquared'

Kolmogorov = 'Kolmogorov'