.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_data_analysis_statistical_hypothesis_testing_plot_kolmogorov_test.py>`     to download the full example code
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_auto_data_analysis_statistical_hypothesis_testing_plot_kolmogorov_test.py:


Test distribution fitting using Kolmogorov/Lilliefors
=====================================================

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


.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    ot.Log.Show(ot.Log.NONE)








Create the data.


.. code-block:: default

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








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.


.. 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




Test succeeded ?


.. code-block:: default

    result.getBinaryQualityMeasure()





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

 Out:

 .. code-block:: none


    True



P-Value associated to the risk


.. code-block:: default

    result.getPValue()





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

 Out:

 .. code-block:: none


    0.9861140480396968



Threshold associated to the test.


.. code-block:: default

    result.getThreshold()





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

 Out:

 .. code-block:: none


    0.01



Observed value of the statistic.


.. code-block:: default

    result.getStatistic()





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

 Out:

 .. code-block:: none


    0.06127263683768702



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.


.. code-block:: default

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









.. code-block:: default

    distributionFactory = ot.NormalFactory()









.. 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





.. code-block:: default

    dist






.. raw:: html

    <p>Normal(mu = -0.0222592, sigma = 0.956433)</p>
    <br />
    <br />

Test succeeded ?


.. code-block:: default

    result.getBinaryQualityMeasure()





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

 Out:

 .. code-block:: none


    True



P-Value associated to the risk


.. code-block:: default

    result.getPValue()





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

 Out:

 .. code-block:: none


    0.983



Threshold associated to the test.


.. code-block:: default

    result.getThreshold()





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

 Out:

 .. code-block:: none


    0.01



Observed value of the statistic.


.. 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  0.029 seconds)


.. _sphx_glr_download_auto_data_analysis_statistical_hypothesis_testing_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>`_