FarlieGumbelMorgensternCopulaFactory

class FarlieGumbelMorgensternCopulaFactory(*args)

Farlie Gumbel Morgenstern Copula factory.

Methods

build(*args)

Build the distribution.

buildAsFarlieGumbelMorgensternCopula(*args)

Estimate the copula as native copula.

buildEstimator(*args)

Build the distribution and the parameter distribution.

getBootstrapSize()

Accessor to the bootstrap size.

getClassName()

Accessor to the object's name.

getKnownParameterIndices()

Accessor to the known parameters indices.

getKnownParameterValues()

Accessor to the known parameters values.

getName()

Accessor to the object's name.

hasName()

Test if the object is named.

setBootstrapSize(bootstrapSize)

Accessor to the bootstrap size.

setKnownParameter(values, positions)

Accessor to the known parameters.

setName(name)

Accessor to the object's name.

See also

DistributionFactory, FarlieGumbelMorgensternCopula

Notes

We note \Hat{\tau}_n the Kendall-\tau of the sample and \Hat{\rho}_n its Spearman correlation coefficient.

We use the following estimators:

\Hat{\theta}_n = \displaystyle \frac{9}{2}\Hat{\tau}_n^{\strut}`

if |\Hat{\theta}_n|<1.

Otherwise

\Hat{\theta}_n = \displaystyle 3\Hat{\rho}_n^{\strut}`

if |\Hat{\theta}_n|<1.

Otherwise, the estimation is not possible.

__init__(*args)
build(*args)

Build the distribution.

Available usages:

build()

build(sample)

build(param)

Parameters:
sample2-d sequence of float

Data.

paramsequence of float

The parameters of the distribution.

Returns:
distDistribution

The estimated distribution.

In the first usage, the default native distribution is built.

buildAsFarlieGumbelMorgensternCopula(*args)

Estimate the copula as native copula.

Available usages:

buildAsFarlieGumbelMorgensternCopula()

buildAsFarlieGumbelMorgensternCopula(sample)

buildAsFarlieGumbelMorgensternCopula(param)

Parameters:
sample2-d sequence of float

Data of dimension 2.

paramsequence of float

The parameter \theta.

Returns:
copulaFarlieGumbelMorgensternCopula

The estimated copula as a FarlieGumbelMorgenstern copula.

In the first usage, the default FarlieGumbelMorgenstern copula is built.

buildEstimator(*args)

Build the distribution and the parameter distribution.

Parameters:
sample2-d sequence of float

Data.

parametersDistributionParameters

Optional, the parametrization.

Returns:
resDistDistributionFactoryResult

The results.

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.

getBootstrapSize()

Accessor to the bootstrap size.

Returns:
sizeint

Size of the bootstrap.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

The object class name (object.__class__.__name__).

getKnownParameterIndices()

Accessor to the known parameters indices.

Returns:
indicesIndices

Indices of the known parameters.

getKnownParameterValues()

Accessor to the known parameters values.

Returns:
valuesPoint

Values of known parameters.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

hasName()

Test if the object is named.

Returns:
hasNamebool

True if the name is not empty.

setBootstrapSize(bootstrapSize)

Accessor to the bootstrap size.

Parameters:
sizeint

The size of the bootstrap.

setKnownParameter(values, positions)

Accessor to the known parameters.

Parameters:
valuessequence of float

Values of known parameters.

positionssequence of int

Indices of known parameters.

Examples

When a subset of the parameter vector is known, the other parameters only have to be estimated from data.

In the following example, we consider a sample and want to fit a Beta distribution. We assume that the a and b parameters are known beforehand. In this case, we set the third parameter (at index 2) to -1 and the fourth parameter (at index 3) to 1.

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> distribution = ot.Beta(2.3, 2.2, -1.0, 1.0)
>>> sample = distribution.getSample(10)
>>> factory = ot.BetaFactory()
>>> # set (a,b) out of (r, t, a, b)
>>> factory.setKnownParameter([-1.0, 1.0], [2, 3])
>>> inf_distribution = factory.build(sample)
setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.