BernsteinCopulaFactory¶

class
BernsteinCopulaFactory
(*args)¶ BernsteinCopula copula factory.
This class allows to estimate a copula in a nonparametric way as an
EmpiricalBernsteinCopula
.See also
Methods
ComputeAMISEBinNumber
(sample)Compute the optimal AMISE number of bins.
ComputeLogLikelihoodBinNumber
(\*args)Compute the optimal loglikelihood number of bins by crossvalidation.
Compute the optimal penalized Csiszar divergence number of bins.
build
(self, \*args)Build the nonparametric Bernstein copula estimator based on the empirical copula.
buildAsEmpiricalBernsteinCopula
(self, \*args)Build the nonparametric Bernstein copula estimator based on the empirical copula.
buildEstimator
(self, \*args)Build the distribution and the parameter distribution.
getBootstrapSize
(self)Accessor to the bootstrap size.
getClassName
(self)Accessor to the object’s name.
getId
(self)Accessor to the object’s id.
getName
(self)Accessor to the object’s name.
getShadowedId
(self)Accessor to the object’s shadowed id.
getVisibility
(self)Accessor to the object’s visibility state.
hasName
(self)Test if the object is named.
hasVisibleName
(self)Test if the object has a distinguishable name.
setBootstrapSize
(self, bootstrapSize)Accessor to the bootstrap size.
setName
(self, name)Accessor to the object’s name.
setShadowedId
(self, id)Accessor to the object’s shadowed id.
setVisibility
(self, visible)Accessor to the object’s visibility state.
BuildCrossValidationSamples

__init__
(self, *args)¶ Initialize self. See help(type(self)) for accurate signature.

static
ComputeAMISEBinNumber
(sample)¶ Compute the optimal AMISE number of bins.
 Parameters
 sample2d sequence of float, of dimension 1
The sample from which the optimal AMISE bin number is computed.
Notes
The number of bins is computed by minimizing the asymptotic mean integrated squared error (AMISE), leading to
where is the largest integer less than or equal to , the sample size and the sample dimension.

static
ComputeLogLikelihoodBinNumber
(*args)¶ Compute the optimal loglikelihood number of bins by crossvalidation.
 Parameters
 sample2d sequence of float, of dimension 1
The sample of size from which the optimal loglikelihood bin number is computed.
 kFractionint,
The fraction of the sample used for the validation.
Notes
Let be the given sample. If , the bin number is given by:
where is the density function of the
EmpiricalBernsteinCopula
associated to the sample and the bin number .If , the bin number is given by:
where and

static
ComputePenalizedCsiszarDivergenceBinNumber
(*args)¶ Compute the optimal penalized Csiszar divergence number of bins.
 Parameters
 sample2d sequence of float, of dimension 1
The sample of size from which the optimal AMISE bin number is computed.
 f
Function
The function defining the Csiszar divergence of interest.
 alphafloat,
The penalization factor.
Notes
Let be the given sample. The bin number is given by:
where is the density function of the
EmpiricalBernsteinCopula
associated to the sample and the bin number , a Monte Carlo estimate of the Csiszar divergence, the exact Spearman correlation of the empirical Bernstein copula and the empirical Spearman correlation of the sample .The parameter is controlled by the ‘BernsteinCopulaFactorySamplingSize’ key in
ResourceMap
.

build
(self, *args)¶ Build the nonparametric Bernstein copula estimator based on the empirical copula.
Available usages:
build()
build(sample)
build(sample, method, objective)
build(sample, m)
 Parameters
 sample2d sequence of float, of dimension d
The sample of size from which the copula is estimated.
 methodstr
The name of thebin number selection method. Possible choices are AMISE, LogLikelihood and PenalizedCsiszarDivergence. Default is LogLikelihood, given by the ‘BernsteinCopulaFactoryBinNumberSelection’ entry of
ResourceMap
. mint
The number of subintervals in which all the edges of the unit cube are regularly partitioned.
 Returns
 copula
Distribution
The estimated copula as a generic distribution.
 copula

buildAsEmpiricalBernsteinCopula
(self, *args)¶ Build the nonparametric Bernstein copula estimator based on the empirical copula.
Available usages:
buildAsEmpiricalBernsteinCopula()
buildAsEmpiricalBernsteinCopula(sample)
buildAsEmpiricalBernsteinCopula(sample, method, objective)
buildAsEmpiricalBernsteinCopula(sample, m)
 Parameters
 sample2d sequence of float, of dimension d
The sample of size from which the copula is estimated.
 methodstr
The name of thebin number selection method. Possible choices are AMISE, LogLikelihood and PenalizedCsiszarDivergence. Default is LogLikelihood, given by the ‘BernsteinCopulaFactoryBinNumberSelection’ entry of
ResourceMap
. mint
The number of subintervals in which all the edges of the unit cube are regularly partitioned.
 Returns
 copula
EmpiricalBernsteinCopula
The estimated copula as an empirical Bernstein copula.
 copula

buildEstimator
(self, *args)¶ Build the distribution and the parameter distribution.
 Parameters
 sample2d sequence of float
Sample from which the distribution parameters are estimated.
 parameters
DistributionParameters
Optional, the parametrization.
 Returns
 resDist
DistributionFactoryResult
The results.
 resDist
Notes
According to the way the native parameters of the distribution are estimated, the parameters distribution differs:
Moments method: the asymptotic parameters distribution is normal and estimated by Bootstrap on the initial data;
Maximum likelihood method with a regular model: the asymptotic parameters distribution is normal and its covariance matrix is the inverse Fisher information matrix;
Other methods: the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting (see
KernelSmoothing
).
If another set of parameters is specified, the native parameters distribution is first estimated and the new distribution is determined from it:
if the native parameters distribution is normal and the transformation regular at the estimated parameters values: the asymptotic parameters distribution is normal and its covariance matrix determined from the inverse Fisher information matrix of the native parameters and the transformation;
in the other cases, the asymptotic parameters distribution is estimated by Bootstrap on the initial data and kernel fitting.
Examples
Create a sample from a Beta distribution:
>>> import openturns as ot >>> sample = ot.Beta().getSample(10) >>> ot.ResourceMap.SetAsUnsignedInteger('DistributionFactoryDefaultBootstrapSize', 100)
Fit a Beta distribution in the native parameters and create a
DistributionFactory
:>>> fittedRes = ot.BetaFactory().buildEstimator(sample)
Fit a Beta distribution in the alternative parametrization :
>>> fittedRes2 = ot.BetaFactory().buildEstimator(sample, ot.BetaMuSigma())

getBootstrapSize
(self)¶ Accessor to the bootstrap size.
 Returns
 sizeinteger
Size of the bootstrap.

getClassName
(self)¶ Accessor to the object’s name.
 Returns
 class_namestr
The object class name (object.__class__.__name__).

getId
(self)¶ Accessor to the object’s id.
 Returns
 idint
Internal unique identifier.

getName
(self)¶ Accessor to the object’s name.
 Returns
 namestr
The name of the object.

getShadowedId
(self)¶ Accessor to the object’s shadowed id.
 Returns
 idint
Internal unique identifier.

getVisibility
(self)¶ Accessor to the object’s visibility state.
 Returns
 visiblebool
Visibility flag.

hasName
(self)¶ Test if the object is named.
 Returns
 hasNamebool
True if the name is not empty.

hasVisibleName
(self)¶ Test if the object has a distinguishable name.
 Returns
 hasVisibleNamebool
True if the name is not empty and not the default one.

setBootstrapSize
(self, bootstrapSize)¶ Accessor to the bootstrap size.
 Parameters
 sizeinteger
Size of the bootstrap.

setName
(self, name)¶ Accessor to the object’s name.
 Parameters
 namestr
The name of the object.

setShadowedId
(self, id)¶ Accessor to the object’s shadowed id.
 Parameters
 idint
Internal unique identifier.

setVisibility
(self, visible)¶ Accessor to the object’s visibility state.
 Parameters
 visiblebool
Visibility flag.
