HistogramFactory¶
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class
HistogramFactory
(*args)¶ Histogram factory.
 Available constructor:
HistogramFactory()
See also
Notes
The range is .
See the computeBandwidth method for the bandwidth selection.
Examples
Create an histogram:
>>> import openturns as ot >>> sample = ot.Normal().getSample(50) >>> histogram = ot.HistogramFactory().build(sample)
Create an histogram from a number of bins:
>>> import openturns as ot >>> sample = ot.Normal().getSample(50) >>> binNumber = 10 >>> histogram = ot.HistogramFactory().build(sample, binNumber)
Create an histogram from a bandwidth:
>>> import openturns as ot >>> sample = ot.Normal().getSample(50) >>> bandwidth = 0.5 >>> histogram = ot.HistogramFactory().build(sample, bandwidth)
Create an histogram from a first value and widths:
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> sample = ot.Normal().getSample(50) >>> first = 4 >>> width = ot.Point(7, 1.) >>> histogram = ot.HistogramFactory().build(sample, first, width)
Compute bandwidth with default robust estimator:
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> sample = ot.Normal().getSample(50) >>> factory = ot.HistogramFactory() >>> factory.computeBandwidth(sample) 0.8207...
Compute bandwidth with optimal estimator:
>>> import openturns as ot >>> ot.RandomGenerator.SetSeed(0) >>> sample = ot.Normal().getSample(50) >>> factory = ot.HistogramFactory() >>> factory.computeBandwidth(sample, False) 0.9175...
Methods
build
(*args)Build the distribution.
buildAsHistogram
(*args)Estimate the distribution as native distribution.
buildEstimator
(*args)Build the distribution and the parameter distribution.
computeBandwidth
(sample[, useQuantile])Compute the bandwidth.
Accessor to the bootstrap size.
Accessor to the object’s name.
getId
()Accessor to the object’s id.
getName
()Accessor to the object’s name.
Accessor to the object’s shadowed id.
Accessor to the object’s visibility state.
hasName
()Test if the object is named.
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)¶ Initialize self. See help(type(self)) for accurate signature.

build
(*args)¶ Build the distribution.
Available usages:
build(sample)
build(param)
 Parameters
 sample2d sequence of float
Sample from which the distribution parameters are estimated.
 paramCollection of
PointWithDescription
A vector of parameters of the distribution.
 Returns
 dist
Distribution
The built distribution.
 dist

buildAsHistogram
(*args)¶ Estimate the distribution as native distribution.
If the sample is constant, the range of the histogram would be zero. In this case, the range is set to be a factor of the DistributionDefaultCDFEpsilon key of the
ResourceMap
.Available usages:
build(sample)
build(sample, binNumber)
build(sample, bandwidth)
build(sample, first, width)

buildEstimator
(*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.

computeBandwidth
(sample, useQuantile=True)¶ Compute the bandwidth.
The bandwidth of the histogram is based on the asymptotic mean integrated squared error (AMISE).
When useQuantile is True (the default), the bandwidth is based on the quantiles of the sample. For any , let be the empirical quantile at level of the sample. Let and be the first and last quartiles of the sample:
and let be the interquartiles range:
In this case, the bandwidth is the robust estimator of the AMISEoptimal bandwith, known as Freedman and Diaconis rule [freedman1981]:
where is the quantile function of the gaussian standard distribution. The expression is the normalized interquartile range and is equal to the standard deviation of the gaussian distribution. The normalized interquartile range is a robust estimator of the scale of the distribution (see [wand1994], page 60).
When useQuantile is False, the bandwidth is the AMISEoptimal one, known as Scott’s rule:
where is the unbiaised variance of the data. This estimator is optimal for the gaussian distribution (see [scott1992]). In this case, the AMISE is .
If the bandwidth is computed as zero (for example, if the sample is constant), then the DistributionDefaultQuantileEpsilon key of the
ResourceMap
is used instead. Parameters
 sample
Sample
Data
 sample
 Returns
 bandwidthfloat
The estimated bandwidth
 useQuantilebool, optional (default=`True`)
If True, then use the robust bandwidth estimator based on Freedman and Diaconis rule. Otherwise, use the optimal bandwidth estimator based on Scott’s rule.

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.