.. 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

        :ref:`Go to the end <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 9-13

.. code-block:: Python

    import openturns as ot

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 14-15

Create the data.

.. GENERATED FROM PYTHON SOURCE LINES 17-20

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 21-26

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 28-31

.. code-block:: Python

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





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

 .. code-block:: none

    Conclusion= True P-value= 0.9861140480396968




.. GENERATED FROM PYTHON SOURCE LINES 32-33

Test succeeded ?

.. GENERATED FROM PYTHON SOURCE LINES 35-37

.. code-block:: Python

    result.getBinaryQualityMeasure()





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

 .. code-block:: none


    True



.. GENERATED FROM PYTHON SOURCE LINES 38-39

P-Value associated to the risk

.. GENERATED FROM PYTHON SOURCE LINES 41-43

.. code-block:: Python

    result.getPValue()





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

 .. code-block:: none


    0.9861140480396968



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Threshold associated to the test.

.. GENERATED FROM PYTHON SOURCE LINES 47-49

.. code-block:: Python

    result.getThreshold()





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

 .. code-block:: none


    0.01



.. GENERATED FROM PYTHON SOURCE LINES 50-51

Observed value of the statistic.

.. GENERATED FROM PYTHON SOURCE LINES 53-55

.. code-block:: Python

    result.getStatistic()





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

 .. code-block:: none


    0.06127263683768702



.. GENERATED FROM PYTHON SOURCE LINES 56-61

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 63-65

.. code-block:: Python

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








.. GENERATED FROM PYTHON SOURCE LINES 66-68

.. code-block:: Python

    distributionFactory = ot.NormalFactory()








.. GENERATED FROM PYTHON SOURCE LINES 69-72

.. code-block:: Python

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





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

 .. code-block:: none

    Conclusion= True P-value= 0.983




.. GENERATED FROM PYTHON SOURCE LINES 73-75

.. code-block:: Python

    dist






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    Normal
    <ul>
      <li>name=Normal</li>
      <li>dimension=1</li>
      <li>weight=1</li>
      <li>range=]-inf (-7.33957), (7.29505) +inf[</li>
      <li>description=[X0]</li>
      <li>isParallel=true</li>
      <li>isCopula=false</li>
    </ul>

    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 76-77

Test succeeded ?

.. GENERATED FROM PYTHON SOURCE LINES 79-81

.. code-block:: Python

    result.getBinaryQualityMeasure()





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

    result.getPValue()





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

 .. code-block:: none


    0.983



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Threshold associated to the test.

.. GENERATED FROM PYTHON SOURCE LINES 91-93

.. code-block:: Python

    result.getThreshold()





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

 .. code-block:: none


    0.01



.. GENERATED FROM PYTHON SOURCE LINES 94-95

Observed value of the statistic.

.. GENERATED FROM PYTHON SOURCE LINES 97-99

.. code-block:: Python

    result.getStatistic()





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

 .. code-block:: none


    0.05110645729712043



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Reset default settings

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.. code-block:: Python

    ot.ResourceMap.Reload()








.. _sphx_glr_download_auto_data_analysis_statistical_tests_plot_kolmogorov_test.py:

.. only:: html

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

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

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

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

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