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

.. only:: html

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

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

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

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py:


Create an extreme value distribution
====================================

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Abstract
--------

In this example we show how to define extreme values distributions.

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.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv
    from matplotlib import pylab as plt

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









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The generalized extreme value distribution (GEV)
------------------------------------------------

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The :class:`~openturns.GeneralizedExtremeValue` distribution is a family of continuous probability distributions
that combine the :class:`~openturns.Gumbel`, :class:`~openturns.Frechet` and :class:`~openturns.WeibullMax` distribution,
all extreme value distribution.

We define a generalized extreme value distribution with parameters :math:`\mu = 0.0`, :math:`\sigma = 1.0` and :math:`\xi = 0.0`

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.. code-block:: Python

    myDistribution = ot.GeneralizedExtremeValue(0.0, 1.0, 0.0)








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The `GeneralizedExtremeValue` class acts as a proxy class. We can get the actual distribution (Weibull, Frechet or Gumbel) with the `getActualDistribution` method :

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.. code-block:: Python

    print(myDistribution.getActualDistribution())





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

 .. code-block:: none

    Gumbel(beta = 1, gamma = 0)




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For the chosen parameters it is a Gumbel distribution with parameters
:math:`beta=1.0` and :math:`\gamma = 0.0`.

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We draw its PDF and CDF :

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.. code-block:: Python

    graphPDF = myDistribution.drawPDF()
    graphPDF.setTitle(
        r"PDF of the GEV with parameters $\mu = 0.0$, $\sigma = 1.0$ and $\xi = 0.0$ "
    )
    view = otv.View(graphPDF)

    graphCDF = myDistribution.drawCDF()
    graphCDF.setTitle(
        r"CDF of the GEV with parameters $\mu = 0.0$, $\sigma = 1.0$ and $\xi = 0.0$ "
    )
    view = otv.View(graphCDF)




.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_001.png
         :alt: PDF of the GEV with parameters $\mu = 0.0$, $\sigma = 1.0$ and $\xi = 0.0$ 
         :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_001.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_002.png
         :alt: CDF of the GEV with parameters $\mu = 0.0$, $\sigma = 1.0$ and $\xi = 0.0$ 
         :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_002.png
         :class: sphx-glr-multi-img





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The Generalized Pareto Distribution (GPD)
-----------------------------------------

In this paragraph we turn to the definition of a :class:`~openturns.GeneralizedPareto` distribution.
For instance we build a generalized Pareto distribution with parameters :math:`\sigma = 1.0`, :math:`\xi = 0.0` and :math:`u = 0.0` :


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.. code-block:: Python

    myGPD = ot.GeneralizedPareto(1.0, 0.0, 0.0)








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We draw its PDF and CDF :

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.. code-block:: Python

    graphPDF = myGPD.drawPDF()
    graphPDF.setTitle(
        r"PDF of the GPD with parameters $\sigma = 1.0$, $\xi = 0.0$ and $u = 0.0$ "
    )
    view = otv.View(graphPDF)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_003.png
   :alt: PDF of the GPD with parameters $\sigma = 1.0$, $\xi = 0.0$ and $u = 0.0$ 
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_003.png
   :class: sphx-glr-single-img





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.. code-block:: Python

    graphCDF = myGPD.drawCDF()
    graphCDF.setTitle(
        r"CDF of the GPD with parameters $\sigma = 1.0$, $\xi = 0.0$ and $u = 0.0$ "
    )
    view = otv.View(graphCDF)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_004.png
   :alt: CDF of the GPD with parameters $\sigma = 1.0$, $\xi = 0.0$ and $u = 0.0$ 
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_extreme_value_distribution_004.png
   :class: sphx-glr-single-img





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Display all figures

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.. code-block:: Python

    plt.show()








.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_create_extreme_value_distribution.py:

.. only:: html

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

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

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

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

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