# IterativeMoments¶

class IterativeMoments(*args)

Iterative moments.

Parameters:
orderint

Maximum order of the moments wanted

dimensionint

Dimension of the input data

Notes

This class iteratively computes the central moments of an iteratively increasing dataset without storing any data in memory.

Examples

In the following example, we iteratively compute the sample statistics of a sample. This is based on a sample with size equal to 2000. In the for loop, each realization of the distribution is used to update the statistics up to the 4th order moments.

>>> import openturns as ot
>>> distNormal = ot.Normal()
>>> order = 4
>>> dim = 1
>>> iterMoments = ot.IterativeMoments(order, dim)
>>> size = 2000
>>> meanEvolution = ot.Sample()
>>> for i in range(size):
...     point = distNormal.getRealization()
...     iterMoments.increment(point)
>>> print('Mean:     ', iterMoments.getMean())
Mean:      [-0.00726852]
>>> print('Variance: ', iterMoments.getVariance())
Variance:  [0.99156]
>>> print('Skewness: ', iterMoments.getSkewness())
Skewness:  [0.0577277]
>>> print('Kurtosis: ', iterMoments.getKurtosis())
Kurtosis:  [3.11128]

The statistics can also be updated with a single sample.

>>> distNormal = ot.Normal()
>>> dim = 1
>>> order = 1
>>> iterMoments = ot.IterativeMoments(order, dim)
>>> size = 2000
>>> sample = distNormal.getSample(size)
>>> iterMoments.increment(sample)
>>> print('Mean: ', iterMoments.getMean())
Mean:  [-0.017342]

Methods

 Returns the central moments Accessor to the object's name. Returns the coefficient of variation Get the dimension of the algorithm getId() Accessor to the object's id. Get the current iteration of the algorithm Returns the current value of the unbiased estimator of the kurtosis getMean() Returns the values of the mean getName() Accessor to the object's name. getOrder() Returns the maximum order prescribed Accessor to the object's shadowed id. Returns the current value of the unbiased estimator of the skewness Returns the standard deviation Returns the standard error of the mean Returns the current value of the unbiased estimator of the variance Accessor to the object's visibility state. hasName() Test if the object is named. Test if the object has a distinguishable name. increment(*args) Increment the internal data. 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)
getCentralMoments()

Returns the central moments

Returns:
centralMomentsSample

Current value of the central moments.

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getCoefficientOfVariation()

Returns the coefficient of variation

Returns:
coefficientOfvariationPoint

Current value of the coefficients of variation.

getDimension()

Get the dimension of the algorithm

Returns:
dimensionint

Dimension of the algorithm

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getIterationNumber()

Get the current iteration of the algorithm

Returns:
iterationint

Current iteration of the algorithm

getKurtosis()

Returns the current value of the unbiased estimator of the kurtosis

Returns:
kurtosisPoint

Current values of the iterative kurtosis.

getMean()

Returns the values of the mean

Returns:
meanPoint

Current value of the mean.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getOrder()

Returns the maximum order prescribed

Returns:
orderint

Prescribed order of the iterative object.

Accessor to the object’s shadowed id.

Returns:
idint

Internal unique identifier.

getSkewness()

Returns the current value of the unbiased estimator of the skewness

Returns:
skewnessPoint

Current values of the skewness.

getStandardDeviation()

Returns the standard deviation

Returns:
standardDeviationPoint

Current value of the standard deviation.

getStandardErrorOfTheMean()

Returns the standard error of the mean

Returns:
errorPoint

Current value of the standard error of the mean.

getVariance()

Returns the current value of the unbiased estimator of the variance

Returns:
variancePoint

Current values of the variance.

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.

increment(*args)

Increment the internal data.

Parameters:
datasequence of float or 2-d sequence of float

New input point or sample.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

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¶

Estimate moments iteratively

Estimate moments iteratively