FisherSnedecorFactory¶

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class FisherSnedecorFactory(*args)¶

Fisher-Snedecor factory.

Available constructor:: FisherSnedecorFactory()

See also

DistributionFactory, FisherSnedecor

Notes

Several estimators to build a FisherSnedecor distribution from a scalar sample are proposed.

Maximum likelihood estimator:

The parameters are estimated by numerical maximum likelihood estimation. The starting point of the optimization algorithm is based on the moment based estimator.

The optimization sets lower bounds for the $d_1$ and $d_2$ parameters in order to ensure that $d_1>0$ and $d_2>0$ . The default values for these lower bounds are from the ResourceMap keys FisherSnedecorFactory-D1LowerBound and FisherSnedecorFactory-D2LowerBound.

Moment based estimator:

Lets denote:

$\displaystyle \overline{x}_n = \frac{1}{n} \sum_{i=1}^n x_i$ the empirical mean of the sample,
$\displaystyle s_n^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \overline{x}_n)^2$ its empirical variance,

We first compute $d_2$ :

$d_2 = \frac{2 \overline{x}_n}{\overline{x}_n-1}$

if $\overline{x}_n>1$ (otherwise, the moment based estimator fails).

Then we compute $d_1$ :

$d_1 = \frac{2 d_2^2 (d_2-2)}{(d_2-2)^2 (d_2-4)s_n^2 - 2d_2^2}$

if $s_n^2>0$ (otherwise, the moment based estimator fails).

Examples

In the following example, the parameters of a FisherSnedecor are estimated from a sample.

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> size = 10000
>>> distribution = ot.FisherSnedecor(4.5, 8.4)
>>> sample = distribution.getSample(size)
>>> factory = ot.TruncatedNormalFactory()
>>> estimated = factory.build(sample)
>>> estimated = factory.buildMethodOfMoments(sample)
>>> estimated = factory.buildMethodOfLikelihoodMaximization(sample)

Methods

`build`(*args)	Estimate the distribution using the default strategy.
`buildAsFisherSnedecor`(*args)	Estimate the distribution using the default strategy.
`buildEstimator`(*args)	Build the distribution and the parameter distribution.
`buildMethodOfLikelihoodMaximization`(sample)	Method of likelihood maximization.
`buildMethodOfMoments`(sample)	Method of moments estimator.
`getBootstrapSize`()	Accessor to the bootstrap size.
`getClassName`()	Accessor to the object's name.
`getId`()	Accessor to the object's id.
`getName`()	Accessor to the object's name.
`getShadowedId`()	Accessor to the object's shadowed id.
`getVisibility`()	Accessor to the object's visibility state.
`hasName`()	Test if the object is named.
`hasVisibleName`()	Test if the object has a distinguishable name.
`setBootstrapSize`(bootstrapSize)	Accessor to the bootstrap size.
`setName`(name)	Accessor to the object's name.
`setShadowedId`(id)	Accessor to the object's shadowed id.
`setVisibility`(visible)	Accessor to the object's visibility state.

__init__(*args)¶

build(*args)¶

Estimate the distribution using the default strategy.

Parameters

sampleSample: Data

Returns

distributionDistribution: The estimated distribution

Notes

The default strategy is using the maximum likelihood estimators.

buildAsFisherSnedecor(*args)¶

Estimate the distribution using the default strategy.

Available usages:

buildAsFisherSnedecor(sample)

buildAsFisherSnedecor(param)

Parameters

sample2-d sequence of float: Sample from which the distribution parameters are estimated.
paramCollection of PointWithDescription: A vector of parameters of the distribution.

Returns

distFisherSnedecor: The built distribution.

Notes

The default strategy is using the maximum likelihood estimators.

buildEstimator(*args)¶

Build the distribution and the parameter distribution.

Parameters

sample2-d sequence of float: Sample from which the distribution parameters are estimated.
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.

buildMethodOfLikelihoodMaximization(sample)¶

Method of likelihood maximization.

Refer to MaximumLikelihoodFactory.

Parameters

sampleSample: Data

Returns

distributionFisherSnedecor: The estimated distribution

buildMethodOfMoments(sample)¶

Method of moments estimator.

Parameters

sampleSample: Data

Returns

distributionFisherSnedecor: The estimated distribution

getBootstrapSize()¶

Accessor to the bootstrap size.

Returns

sizeinteger: Size of the bootstrap.

getClassName()¶

Accessor to the object’s name.

Returns

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

getId()¶

Accessor to the object’s id.

Returns

idint: Internal unique identifier.

getName()¶

Accessor to the object’s name.

Returns

namestr: The name of the object.

getShadowedId()¶

Accessor to the object’s shadowed id.

Returns

idint: Internal unique identifier.

getVisibility()¶

Accessor to the object’s visibility state.

Returns

visiblebool: Visibility flag.

hasName()¶

Test if the object is named.

Returns

hasNamebool: True if the name is not empty.

hasVisibleName()¶

Test if the object has a distinguishable name.

Returns

hasVisibleNamebool: True if the name is not empty and not the default one.

setBootstrapSize(bootstrapSize)¶

Accessor to the bootstrap size.

Parameters

sizeinteger: Size of the bootstrap.

setName(name)¶

Accessor to the object’s name.

Parameters

namestr: The name of the object.

setShadowedId(id)¶

Accessor to the object’s shadowed id.

Parameters

idint: Internal unique identifier.

setVisibility(visible)¶

Accessor to the object’s visibility state.

Parameters

visiblebool: Visibility flag.

OpenTURNS

An Open source initiative for the Treatment of Uncertainties, Risks'N Statistics

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