.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/distributions/plot_mixture_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_mixture_distribution.py>`
        to download the full example code

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

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_mixture_distribution.py:


Create a mixture of PDFs
========================

.. GENERATED FROM PYTHON SOURCE LINES 6-14

In this example we are going to build a distribution whose PDF is defined by a linear combination of probability density functions:

.. math::
   f(x) =  \sum_{i=1}^N \alpha_i p_i(x), \quad \alpha_i \geq 0, \quad \sum_i \alpha_i = 1

The weigths are automatically normalized.

It is also possible to create a mixture of copulas.

.. GENERATED FROM PYTHON SOURCE LINES 16-22

.. code-block:: Python

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

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








.. GENERATED FROM PYTHON SOURCE LINES 23-24

create a collection of distribution and the associated weights

.. GENERATED FROM PYTHON SOURCE LINES 24-31

.. code-block:: Python

    distributions = [
        ot.Triangular(1.0, 2.0, 4.0),
        ot.Normal(-1.0, 1.0),
        ot.Uniform(5.0, 6.0),
    ]
    weights = [0.4, 1.0, 0.2]








.. GENERATED FROM PYTHON SOURCE LINES 32-33

create the mixture

.. GENERATED FROM PYTHON SOURCE LINES 33-36

.. code-block:: Python

    distribution = ot.Mixture(distributions, weights)
    print(distribution)





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

 .. code-block:: none

    Mixture((w = 0.25, d = Triangular(a = 1, m = 2, b = 4)), (w = 0.625, d = Normal(mu = -1, sigma = 1)), (w = 0.125, d = Uniform(a = 5, b = 6)))




.. GENERATED FROM PYTHON SOURCE LINES 37-38

draw PDF

.. GENERATED FROM PYTHON SOURCE LINES 38-41

.. code-block:: Python

    graph = distribution.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_mixture_distribution_001.png
   :alt: plot mixture distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_mixture_distribution_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 42-43

define a list of copulas and the associated weights

.. GENERATED FROM PYTHON SOURCE LINES 43-46

.. code-block:: Python

    copulas = [ot.GumbelCopula(4.5), ot.ClaytonCopula(2.3)]
    weights = [0.2, 0.8]








.. GENERATED FROM PYTHON SOURCE LINES 47-48

create a mixture of copulas

.. GENERATED FROM PYTHON SOURCE LINES 48-51

.. code-block:: Python

    distribution = ot.Mixture(copulas, weights)
    print(distribution)





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

 .. code-block:: none

    Mixture((w = 0.2, d = GumbelCopula(theta = 4.5)), (w = 0.8, d = ClaytonCopula(theta = 2.3)))




.. GENERATED FROM PYTHON SOURCE LINES 52-53

draw PDF

.. GENERATED FROM PYTHON SOURCE LINES 53-56

.. code-block:: Python

    graph = distribution.drawPDF()
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_mixture_distribution_002.png
   :alt: [X0,X1] iso-PDF
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_mixture_distribution_002.png
   :class: sphx-glr-single-img






.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_mixture_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_mixture_distribution.ipynb <plot_mixture_distribution.ipynb>`

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

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