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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_data_analysis_statistical_tests_plot_test_normality.py>`
        to download the full example code

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

.. _sphx_glr_auto_data_analysis_statistical_tests_plot_test_normality.py:


Test Normality
==============

.. GENERATED FROM PYTHON SOURCE LINES 8-12

Normal fitting test using the Henry line
----------------------------------------

In this paragraph we perform a visual goodness-of-fit test for a univariate normal distribution using the Henry line test, which is the QQ plot adapted for Gaussian distributions.

.. GENERATED FROM PYTHON SOURCE LINES 14-19

.. code-block:: default

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 20-21

We first create the data :

.. GENERATED FROM PYTHON SOURCE LINES 21-24

.. code-block:: default

    distribution = ot.Normal(2.0, 0.5)
    sample1 = distribution.getSample(100)








.. GENERATED FROM PYTHON SOURCE LINES 25-26

We draw the Henry line plot and expect a good fitting :

.. GENERATED FROM PYTHON SOURCE LINES 26-29

.. code-block:: default

    graph = ot.VisualTest.DrawHenryLine(sample1)
    view = viewer.View(graph)




.. image-sg:: /auto_data_analysis/statistical_tests/images/sphx_glr_plot_test_normality_001.png
   :alt: Henry plot
   :srcset: /auto_data_analysis/statistical_tests/images/sphx_glr_plot_test_normality_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 30-31

For comparison sake e draw the Henry line plot for a Beta distribution. The result is expected to be bad.

.. GENERATED FROM PYTHON SOURCE LINES 31-36

.. code-block:: default

    sample2 = ot.Beta(0.7, 0.9, 0.0, 2.0).getSample(100)
    graph = ot.VisualTest.DrawHenryLine(sample2)
    view = viewer.View(graph)





.. image-sg:: /auto_data_analysis/statistical_tests/images/sphx_glr_plot_test_normality_002.png
   :alt: Henry plot
   :srcset: /auto_data_analysis/statistical_tests/images/sphx_glr_plot_test_normality_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 37-45

Normality tests
---------------

We use two tests to check whether a sample follows a normal distribution :

 - the Anderson-Darling test
 - the Cramer-Von Mises test


.. GENERATED FROM PYTHON SOURCE LINES 47-49

We first generate two samples, one from a standard unit gaussian and another from a Gumbel
distribution with parameters :math:`\beta = 1` and :math:`\gamma = 0`.

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: default

    sample1 = ot.Normal().getSample(200)
    sample2 = ot.Gumbel().getSample(200)








.. GENERATED FROM PYTHON SOURCE LINES 53-56

We test the normality of the sample. We can display the result of the test as a yes/no answer with
the `getBinaryQualityMeasure`. We can retrieve the p-value and the threshold with the `getPValue`
and `getThreshold` methods.

.. GENERATED FROM PYTHON SOURCE LINES 58-63

.. code-block:: default

    test_result = ot.NormalityTest.AndersonDarlingNormal(sample1)
    print('Component is normal?', test_result.getBinaryQualityMeasure(),
          'p-value=%.6g' % test_result.getPValue(),
          'threshold=%.6g' % test_result.getThreshold())





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

 Out:

 .. code-block:: none

    Component is normal? False p-value=0.021519 threshold=0.05




.. GENERATED FROM PYTHON SOURCE LINES 64-69

.. code-block:: default

    test_result = ot.NormalityTest.AndersonDarlingNormal(sample2)
    print('Component is normal?', test_result.getBinaryQualityMeasure(),
          'p-value=%.6g' % test_result.getPValue(),
          'threshold=%.6g' % test_result.getThreshold())





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

 Out:

 .. code-block:: none

    Component is normal? False p-value=1.45169e-10 threshold=0.05




.. GENERATED FROM PYTHON SOURCE LINES 70-75

.. code-block:: default

    test_result = ot.NormalityTest.CramerVonMisesNormal(sample1)
    print('Component is normal?', test_result.getBinaryQualityMeasure(),
          'p-value=%.6g' % test_result.getPValue(),
          'threshold=%.6g' % test_result.getThreshold())





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

 Out:

 .. code-block:: none

    Component is normal? False p-value=0.0438816 threshold=0.05




.. GENERATED FROM PYTHON SOURCE LINES 76-80

.. code-block:: default

    test_result = ot.NormalityTest.CramerVonMisesNormal(sample2)
    print('Component is normal?', test_result.getBinaryQualityMeasure(),
          'p-value=%.6g' % test_result.getPValue(),
          'threshold=%.6g' % test_result.getThreshold())




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

 Out:

 .. code-block:: none

    Component is normal? False p-value=4.33705e-08 threshold=0.05





.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.151 seconds)


.. _sphx_glr_download_auto_data_analysis_statistical_tests_plot_test_normality.py:


.. only :: html

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



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

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



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

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


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_