.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/statistics/nonparametric/plot_01_kolmogorov_smirnov.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_statistics_nonparametric_plot_01_kolmogorov_smirnov.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_statistics_nonparametric_plot_01_kolmogorov_smirnov.py:


The Kolmogorov-Smirnov test
================================

Draws a sample from a Student t distribution with 3 degrees of freedom
and compares its empirical CDF with the standard normal CDF. The KS
statistic is the largest vertical gap between the two curves.

.. GENERATED FROM PYTHON SOURCE LINES 11-17

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import stats

    from mathematicskit.statistics import kolmogorov_smirnov_test








.. GENERATED FROM PYTHON SOURCE LINES 18-20

One sample against a model
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 20-38

.. code-block:: Python


    rng = np.random.default_rng(0)
    data = np.sort(rng.standard_t(df=3, size=800))
    result = kolmogorov_smirnov_test(data, "norm")
    print(f"vs. N(0,1):  D = {result.statistic:.4f}, p = {result.p_value:.4f}")
    print(f"vs. t(3):    p = {kolmogorov_smirnov_test(data, stats.t(df=3).cdf).p_value:.4f}")

    ecdf = np.arange(1, data.size + 1) / data.size
    fig, ax = plt.subplots()
    ax.step(data, ecdf, where="post", label="empirical CDF")
    ax.plot(data, stats.norm.cdf(data), label="normal CDF")
    model = stats.norm.cdf(data)
    above, below = ecdf - model, model - (ecdf - 1 / data.size)
    k = int(np.argmax(np.maximum(above, below)))
    top = ecdf[k] if above[k] >= below[k] else ecdf[k] - 1 / data.size
    ax.vlines(data[k], model[k], top, color="C3", lw=3, label=f"D = {result.statistic:.3f}")
    ax.legend()




.. image-sg:: /api/gallery/statistics/nonparametric/images/sphx_glr_plot_01_kolmogorov_smirnov_001.png
   :alt: plot 01 kolmogorov smirnov
   :srcset: /api/gallery/statistics/nonparametric/images/sphx_glr_plot_01_kolmogorov_smirnov_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    vs. N(0,1):  D = 0.0539, p = 0.0184
    vs. t(3):    p = 0.6969

    <matplotlib.legend.Legend object at 0x11d82f8c0>



.. GENERATED FROM PYTHON SOURCE LINES 39-41

Two samples
-----------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 41-45

.. code-block:: Python


    other = rng.normal(size=300)
    two = kolmogorov_smirnov_test(data, other)
    print(f"two-sample:  D = {two.statistic:.4f}, p = {two.p_value:.4f}")




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

 .. code-block:: none

    two-sample:  D = 0.0708, p = 0.2139





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

   **Total running time of the script:** (0 minutes 0.025 seconds)


.. _sphx_glr_download_api_gallery_statistics_nonparametric_plot_01_kolmogorov_smirnov.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_kolmogorov_smirnov.ipynb <plot_01_kolmogorov_smirnov.ipynb>`

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

      :download:`Download Python source code: plot_01_kolmogorov_smirnov.py <plot_01_kolmogorov_smirnov.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_kolmogorov_smirnov.zip <plot_01_kolmogorov_smirnov.zip>`


.. only:: html

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

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