.. 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_kolmogorov_test.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_kolmogorov_test.py>`
        to download the full example code

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

.. _sphx_glr_auto_data_analysis_statistical_tests_plot_kolmogorov_test.py:


Use the Kolmogorov/Lilliefors test
==================================

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In this example we are going to perform a Kolmogorov or a Lilliefors goodness-of-fit test for a 1-d continuous distribution.

.. GENERATED FROM PYTHON SOURCE LINES 9-12

.. code-block:: default

    import openturns as ot
    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 13-14

Create the data.

.. GENERATED FROM PYTHON SOURCE LINES 16-19

.. code-block:: default

    distribution = ot.Normal()
    sample = distribution.getSample(50)








.. GENERATED FROM PYTHON SOURCE LINES 20-24

Case 1 : the distribution parameters are known.
-----------------------------------------------

In the case where the parameters of the distribution are known, we must use the `Kolmogorov` static method and the distribution to be tested.

.. GENERATED FROM PYTHON SOURCE LINES 26-30

.. code-block:: default

    result = ot.FittingTest.Kolmogorov(sample, distribution, 0.01)
    print('Conclusion=', result.getBinaryQualityMeasure(),
          'P-value=', result.getPValue())





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

 Out:

 .. code-block:: none

    Conclusion= True P-value= 0.9861140480396968




.. GENERATED FROM PYTHON SOURCE LINES 31-32

Test succeeded ?

.. GENERATED FROM PYTHON SOURCE LINES 34-36

.. code-block:: default

    result.getBinaryQualityMeasure()





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

 Out:

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 37-38

P-Value associated to the risk

.. GENERATED FROM PYTHON SOURCE LINES 40-42

.. code-block:: default

    result.getPValue()





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

 Out:

 .. code-block:: none


    0.9861140480396968



.. GENERATED FROM PYTHON SOURCE LINES 43-44

Threshold associated to the test.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: default

    result.getThreshold()





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

 Out:

 .. code-block:: none


    0.01



.. GENERATED FROM PYTHON SOURCE LINES 49-50

Observed value of the statistic.

.. GENERATED FROM PYTHON SOURCE LINES 52-54

.. code-block:: default

    result.getStatistic()





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

 Out:

 .. code-block:: none


    0.06127263683768702



.. GENERATED FROM PYTHON SOURCE LINES 55-59

Case 2 : the distribution parameters are estimated from the sample.
-------------------------------------------------------------------

In the case where the parameters of the distribution are estimated from the sample, we must use the `Lilliefors` static method and the distribution factory to be tested.

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: default

    ot.ResourceMap.SetAsUnsignedInteger(
        "FittingTest-LillieforsMaximumSamplingSize", 1000)








.. GENERATED FROM PYTHON SOURCE LINES 65-67

.. code-block:: default

    distributionFactory = ot.NormalFactory()








.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: default

    dist, result = ot.FittingTest.Lilliefors(sample, distributionFactory, 0.01)
    print('Conclusion=', result.getBinaryQualityMeasure(),
          'P-value=', result.getPValue())





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

 Out:

 .. code-block:: none

    Conclusion= True P-value= 0.983




.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: default

    dist






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <p>Normal(mu = -0.0222592, sigma = 0.956433)</p>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 76-77

Test succeeded ?

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: default

    result.getBinaryQualityMeasure()





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

 Out:

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 82-83

P-Value associated to the risk

.. GENERATED FROM PYTHON SOURCE LINES 85-87

.. code-block:: default

    result.getPValue()





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

 Out:

 .. code-block:: none


    0.983



.. GENERATED FROM PYTHON SOURCE LINES 88-89

Threshold associated to the test.

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: default

    result.getThreshold()





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

 Out:

 .. code-block:: none


    0.01



.. GENERATED FROM PYTHON SOURCE LINES 94-95

Observed value of the statistic.

.. GENERATED FROM PYTHON SOURCE LINES 97-98

.. code-block:: default

    result.getStatistic()




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

 Out:

 .. code-block:: none


    0.05110645729712043




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

   **Total running time of the script:** ( 0 minutes  0.028 seconds)


.. _sphx_glr_download_auto_data_analysis_statistical_tests_plot_kolmogorov_test.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_kolmogorov_test.py <plot_kolmogorov_test.py>`



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

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


.. only:: html

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

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