.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_numerical_methods/iterative_statistics/plot_iterative_moments.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py:


Estimate moments iteratively
============================

.. GENERATED FROM PYTHON SOURCE LINES 7-12

In this example, we use the :class:`~openturns.IterativeMoments` class
to compute iterative statistics.
This class stores central moments up to a prescribed order iteratively.
Then several statistics based on the moments are available depending on the
chosen order.

.. GENERATED FROM PYTHON SOURCE LINES 14-17

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv








.. GENERATED FROM PYTHON SOURCE LINES 18-19

We first create a one-dimensional Gaussian random variable to generate data.

.. GENERATED FROM PYTHON SOURCE LINES 19-22

.. code-block:: Python

    dim = 1
    distNormal = ot.Normal(dim)








.. GENERATED FROM PYTHON SOURCE LINES 23-26

Then we use the central moments up to order 4 with the
:class:`~openturns.IterativeMoments` class by giving the order (here 4)
and the dimension (here 1):

.. GENERATED FROM PYTHON SOURCE LINES 28-32

.. code-block:: Python

    order = 4
    iterMoments = ot.IterativeMoments(order, dim)









.. GENERATED FROM PYTHON SOURCE LINES 33-41

We can now perform the simulations.
The :class:`~openturns.IterativeMoments` object stores the central
moments iteratively.
We first increment the object with one :class:`~openturns.Point` at a time.
At any given step the current mean is obtained thanks to
the :meth:`~openturns.IterativeMoments.getMean` method and the
current number of iterations is given by
the :meth:`~openturns.IterativeMoments.getIterationNumber` method.

.. GENERATED FROM PYTHON SOURCE LINES 41-48

.. code-block:: Python

    size = 2000
    meanEvolution = ot.Sample()
    for i in range(size):
        point = distNormal.getRealization()
        iterMoments.increment(point)
        meanEvolution.add(iterMoments.getMean())








.. GENERATED FROM PYTHON SOURCE LINES 49-50

We display the evolution of the mean.

.. GENERATED FROM PYTHON SOURCE LINES 50-57

.. code-block:: Python

    iterationSample = ot.Sample.BuildFromPoint(range(1, size + 1))
    curve = ot.Curve(iterationSample, meanEvolution)
    graph = ot.Graph("Evolution of the mean", "iteration nb", "mean", True)
    graph.add(curve)
    graph.setLogScale(ot.GraphImplementation.LOGX)
    view = otv.View(graph)




.. image-sg:: /auto_numerical_methods/iterative_statistics/images/sphx_glr_plot_iterative_moments_001.png
   :alt: Evolution of the mean
   :srcset: /auto_numerical_methods/iterative_statistics/images/sphx_glr_plot_iterative_moments_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 58-59

We can also increment with a :class:`~openturns.Sample`.

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: Python

    sample = distNormal.getSample(size)
    iterMoments.increment(sample)








.. GENERATED FROM PYTHON SOURCE LINES 65-66

We print the total number of iterations and the mean.

.. GENERATED FROM PYTHON SOURCE LINES 66-69

.. code-block:: Python

    print("Total number of iteration: ", iterMoments.getIterationNumber())
    print("Mean: ", iterMoments.getMean())





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Total number of iteration:  4000
    Mean:  [-0.046355]




.. GENERATED FROM PYTHON SOURCE LINES 70-74

For the order of the `iterMoments` object is 4, we also have access to
other statistics such as the variance (order 2), the skewness (order 3)
or the kurtosis (order 4). For instance, a specified order of 3 would leave
only the variance and the skewness available.

.. GENERATED FROM PYTHON SOURCE LINES 74-79

.. code-block:: Python

    print("Variance: ", iterMoments.getVariance())
    print("Skewness: ", iterMoments.getSkewness())
    print("Kurtosis: ", iterMoments.getKurtosis())

    otv.View.ShowAll()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Variance:  [1.02285]
    Skewness:  [-0.000638883]
    Kurtosis:  [2.95484]





.. _sphx_glr_download_auto_numerical_methods_iterative_statistics_plot_iterative_moments.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_iterative_moments.ipynb <plot_iterative_moments.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_iterative_moments.py <plot_iterative_moments.py>`