gemseo.uncertainty.statistics.sp_parametric_statistics module

SciPy-based parametric estimation of statistics from a dataset.

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

Bases: BaseParametricStatistics[SPDistribution, AndersonDarling, DistributionName, FittingCriterion, FittingCriterion]

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

Examples

>>> from gemseo import (
...     create_discipline,
...     create_parameter_space,
...     sample_disciplines,
... )
>>> from gemseo.uncertainty.statistics.sp_parametric_statistics import (
...     SPParametricStatistics,
... )
>>>
>>> discipline = create_discipline(
...     "AnalyticDiscipline", {"y1": "x1+2*x2", "y2": "x1-3*x2"}
... )
>>>
>>> parameter_space = create_parameter_space()
>>> parameter_space.add_random_variable(
...     "x1", "SPUniformDistribution", minimum=-1, maximum=1
... )
>>> parameter_space.add_random_variable(
...     "x2", "SPNormalDistribution", mu=0.5, sigma=2
... )
>>>
>>> dataset = sample_disciplines(
...     [discipline],
...     parameter_space,
...     ["y1"],
...     algo_name="OT_MONTE_CARLO",
...     n_samples=100,
... )
>>>
>>> statistics = SPParametricStatistics(dataset, ["norm", "uniform", "triang"])
>>> 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

alpha = 'alpha'

anglit = 'anglit'

arcsine = 'arcsine'

argus = 'argus'

beta = 'beta'

betaprime = 'betaprime'

bradford = 'bradford'

burr = 'burr'

burr12 = 'burr12'

cauchy = 'cauchy'

chi = 'chi'

chi2 = 'chi2'

cosine = 'cosine'

crystalball = 'crystalball'

dgamma = 'dgamma'

dpareto_lognorm = 'dpareto_lognorm'

dweibull = 'dweibull'

expon = 'expon'

exponnorm = 'exponnorm'

exponpow = 'exponpow'

exponweib = 'exponweib'

f = 'f'

fatiguelife = 'fatiguelife'

foldcauchy = 'foldcauchy'

foldnorm = 'foldnorm'

gamma = 'gamma'

gausshyper = 'gausshyper'

genexpon = 'genexpon'

genextreme = 'genextreme'

gengamma = 'gengamma'

genhalflogistic = 'genhalflogistic'

genhyperbolic = 'genhyperbolic'

geninvgauss = 'geninvgauss'

genlogistic = 'genlogistic'

gennorm = 'gennorm'

genpareto = 'genpareto'

gibrat = 'gibrat'

gompertz = 'gompertz'

gumbel_l = 'gumbel_l'

gumbel_r = 'gumbel_r'

halfcauchy = 'halfcauchy'

halfgennorm = 'halfgennorm'

halflogistic = 'halflogistic'

halfnorm = 'halfnorm'

hypsecant = 'hypsecant'

invgamma = 'invgamma'

invgauss = 'invgauss'

invweibull = 'invweibull'

irwinhall = 'irwinhall'

jf_skew_t = 'jf_skew_t'

johnsonsb = 'johnsonsb'

johnsonsu = 'johnsonsu'

kappa3 = 'kappa3'

kappa4 = 'kappa4'

ksone = 'ksone'

kstwo = 'kstwo'

kstwobign = 'kstwobign'

landau = 'landau'

laplace = 'laplace'

laplace_asymmetric = 'laplace_asymmetric'

levy = 'levy'

levy_l = 'levy_l'

levy_stable = 'levy_stable'

loggamma = 'loggamma'

logistic = 'logistic'

loglaplace = 'loglaplace'

lognorm = 'lognorm'

lomax = 'lomax'

maxwell = 'maxwell'

mielke = 'mielke'

moyal = 'moyal'

nakagami = 'nakagami'

ncf = 'ncf'

nct = 'nct'

ncx2 = 'ncx2'

norm = 'norm'

norminvgauss = 'norminvgauss'

pareto = 'pareto'

pearson3 = 'pearson3'

powerlaw = 'powerlaw'

powerlognorm = 'powerlognorm'

powernorm = 'powernorm'

rayleigh = 'rayleigh'

rdist = 'rdist'

recipinvgauss = 'recipinvgauss'

reciprocal = 'reciprocal'

rel_breitwigner = 'rel_breitwigner'

rice = 'rice'

rv_histogram = 'rv_histogram'

semicircular = 'semicircular'

skewcauchy = 'skewcauchy'

skewnorm = 'skewnorm'

studentized_range = 'studentized_range'

t = 't'

trapezoid = 'trapezoid'

triang = 'triang'

truncexpon = 'truncexpon'

truncnorm = 'truncnorm'

truncpareto = 'truncpareto'

truncweibull_min = 'truncweibull_min'

tukeylambda = 'tukeylambda'

uniform = 'uniform'

vonmises = 'vonmises'

weibull_max = 'weibull_max'

weibull_min = 'weibull_min'

wrapcauchy = 'wrapcauchy'

class FittingCriterion(*values)

Bases: StrEnum

ANDERSON_DARLING = 'AndersonDarling'

CRAMER_VON_MISES = 'CramerVonMises'

FILLIBEN = 'Filliben'

KOLMOGOROV_SMIRNOV = 'KolmogorovSmirnov'

SignificanceTest

alias of FittingCriterion