FrechetFactory

(Source code, png)

../../_images/openturns-FrechetFactory-1.png
class FrechetFactory(*args)

Frechet factory.

See also

DistributionFactory, Frechet

Notes

The parameters are estimated by likelihood maximization. The starting point is obtained from the estimation of a Gumbel distribution based on the logarithm of the shifted observations:

\begin{eqnarray*} \displaystyle\Hat{\alpha} & = & \frac{\pi}{\Hat{\sigma}_y\sqrt{6}} \\ \displaystyle\Hat{\beta} & = & \exp\left\{\bar{y}_n-\frac{\gamma\sqrt{6}}{\pi}\Hat{\sigma}_y\right\} \\ \displaystyle\Hat{\gamma} & = & x_{(1)} - \frac{|x_{(1)}|}{n+2} \end{eqnarray*}

with \gamma \simeq 0.57721 as Euler’s constant (not to be confused with the location parameter of the Frechet distribution!), x_{(1)}=\min_{i=1,\dots,n}x_i and y_i=x_i-\Hat{\gamma}.

Methods

build(*args)

Build the distribution.

buildAsFrechet(*args)

Build the Frechet distribution.

buildEstimator(*args)

Build the distribution and the parameter distribution.

getBootstrapSize()

Accessor to the bootstrap size.

getClassName()

Accessor to the object's name.

getName()

Accessor to the object's name.

hasName()

Test if the object is named.

setBootstrapSize(bootstrapSize)

Accessor to the bootstrap size.

setName(name)

Accessor to the object's name.
__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.

buildAsFrechet(*args)

Build the Frechet distribution.

Available usages:

buildAsFrechet()

buildAsFrechet(sample)

buildAsFrechet(param)

Parameters:
sample2-d sequence of float

Sample from which the distribution parameters are estimated.

paramsequence of float

The parameters of the Frechet.

Returns:
distFrechet

The estimated distribution as a Frechet.

In the first usage, the default Frechet distribution 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__).

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.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

Examples using the class

Fit an extreme value distribution

Fit an extreme value distribution