.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_distributions_plot_random_mixture_distribution_discrete.py:


Create a discrete random mixture
================================

In this example we are going to build the distribution of the value of the sum of 20 dice rolls.

.. math:: 
   Y = \sum_{i=1}^{20} X_i

where :math:`X_i \sim U(1,2,3,4,5,6)`



.. code-block:: default

    from __future__ import print_function
    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt
    ot.Log.Show(ot.Log.NONE)








create the distribution associated to the dice roll


.. code-block:: default

    X = ot.UserDefined([[i] for i in range(1,7)])








Roll the dice a few times


.. code-block:: default

    X.getSample(10)






.. raw:: html

    <TABLE><TR><TD></TD><TH>v0</TH></TR>
    <TR><TH>0</TH><TD>1</TD></TR>
    <TR><TH>1</TH><TD>3</TD></TR>
    <TR><TH>2</TH><TD>6</TD></TR>
    <TR><TH>3</TH><TD>1</TD></TR>
    <TR><TH>4</TH><TD>6</TD></TR>
    <TR><TH>5</TH><TD>3</TD></TR>
    <TR><TH>6</TH><TD>2</TD></TR>
    <TR><TH>7</TH><TD>2</TD></TR>
    <TR><TH>8</TH><TD>4</TD></TR>
    <TR><TH>9</TH><TD>2</TD></TR>
    </TABLE>
    <br />
    <br />


.. code-block:: default

    N = 20








Create the collection of identically distributed Xi


.. code-block:: default

    coll = [X] * N








Create the weights


.. code-block:: default

    weight = [1.0] * N








create the affine combination


.. code-block:: default

    distribution = ot.RandomMixture(coll, weight)








probability to exceed a sum of 100 after 20 dice rolls


.. code-block:: default

    distribution.computeComplementaryCDF(100)





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

 Out:

 .. code-block:: none


    1.576207331110968e-05



draw PDF


.. code-block:: default

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




.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_random_mixture_distribution_discrete_001.png
    :alt: X0 PDF
    :class: sphx-glr-single-img





draw CDF


.. code-block:: default

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



.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_random_mixture_distribution_discrete_002.png
    :alt: X0 CDF
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.142 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_random_mixture_distribution_discrete.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_random_mixture_distribution_discrete.py <plot_random_mixture_distribution_discrete.py>`



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

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


.. only:: html

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

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