NormalFactory

(Source code, png)

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

Normal factory.

Available constructors:

NormalFactory(robust=False)

Parameters:
robustbool, optional

Flag to select robust estimators of the parameters

See also

DistributionFactory, Normal, NormalCopulaFactory

Notes

The parameters are estimated by likelihood maximization if robust=False:

\begin{eqnarray*} \displaystyle\Hat{\vect{\mu}}_n^{\strut} = \bar{\vect{x}}_n\\ \displaystyle\Hat{\mathrm{Cov}}_n = \frac{1}{n-1}\sum_{i=1}^n\left(\vect{X}_i-\Hat{\vect{\mu}}_n\right)\left(\vect{X}_i-\Hat{\vect{\mu}}_n\right)^t \end{eqnarray*}

If robust=True, the estimation is done using the empirical median q_{n, 0.5} as an estimate of \mu, the empirical inter-quartile frac{q_{n, 0.75}-q_{n, 0.25}}{a_{0.75}-a_{0.25}} as an estimate of the standard deviation, where a_{0.75} and a_{0.25} are the 75% and 25% quantiles of the standard normal distribution, and the correlation matrix R_n is estimated as the shape matrix of the underlying NormalCopula using NormalCopulaFactory.

Examples

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

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> size = 10000
>>> distribution = ot.Normal(1.0, 2.0)
>>> sample = distribution.getSample(size)
>>> factory = ot.NormalFactory()
>>> estimated = factory.build(sample)

Methods

build(*args)

Build the distribution.

buildAsNormal(*args)

Estimate the distribution as native distribution.

buildEstimator(sample)

Build the distribution and the parameter distribution.

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)

Build the distribution.

Available usages:

build(sample)

build(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:
distDistribution

The built distribution.

buildAsNormal(*args)

Estimate the distribution as native distribution.

Parameters:
sampleSample

Data

Returns:
distributionNormal

The estimated distribution

buildEstimator(sample)

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.

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.

Examples using the class

Fit a parametric distribution

Fit a parametric distribution

Get the asymptotic distribution of the estimators

Get the asymptotic distribution of the estimators

Use the Kolmogorov/Lilliefors test

Use the Kolmogorov/Lilliefors test

Estimate Sobol indices on a field to point function

Estimate Sobol indices on a field to point function