.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_distributions_plot_random_mixture_distribution.py:


Create a random mixture of distributions
========================================

In this example we are going to build an affine combination of input random variables.

.. math:: 
   Y = 2 + 5 X_1 + X_2

where:

- :math:`X1 \sim \mathcal{E}(\lambda=1.5)`
- :math:`X2 \sim \mathcal{N}(\mu=4, \sigma=1)`

This notion is different from the Mixture where the combination is made on the probability density functions and not on the univariate random variable.


.. 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 distributions associated to the input random variables


.. code-block:: default

    X1 = ot.Exponential(1.5)
    X2 = ot.Normal(4.0, 1.0)








offset


.. code-block:: default

    a0 = 2.0








Create the weights


.. code-block:: default

    weight = [5.0, 1.0]








create the affine combination


.. code-block:: default

    distribution = ot.RandomMixture([X1, X2], weight, a0)
    distribution






.. raw:: html

    <p>RandomMixture(Normal(mu = 6, sigma = 1) + Exponential(lambda = 0.3, gamma = 0))</p>
    <br />
    <br />

ask its mean


.. code-block:: default

    distribution.getMean()






.. raw:: html

    <p>[9.33333]</p>
    <br />
    <br />

ask its variance


.. code-block:: default

    distribution.getCovariance()[0, 0]





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

 Out:

 .. code-block:: none


    12.11111111111111



ask the 90% quantile


.. code-block:: default

    distribution.computeQuantile(0.9)






.. raw:: html

    <p>[13.8253]</p>
    <br />
    <br />

ask its probability to exceeds 3


.. code-block:: default

    distribution.computeSurvivalFunction(3.0)





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

 Out:

 .. code-block:: none


    0.9998938620694351



draw PDF


.. code-block:: default

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




.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_random_mixture_distribution_001.png
    :alt: plot random mixture distribution
    :class: sphx-glr-single-img





draw PDF


.. code-block:: default

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




.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_random_mixture_distribution_002.png
    :alt: plot random mixture distribution
    :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.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.py <plot_random_mixture_distribution.py>`



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

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


.. only:: html

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

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