.. only:: html

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

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

    .. _sphx_glr_auto_probabilistic_modeling_distributions_plot_composite_distribution.py:


Create a composite distribution
===============================

In this example we are going to create a distribution defined as the push-forward distribution of a scalar distribution by a transformation.


If we note :math:`\mathcal{L}_0` a scalar distribution, :math:`f: \mathbb{R} \rightarrow \mathbb{R}` a mapping, then it is possible to create the push-forward distribution :math:`\mathcal{L}` defined by

.. math::
   \mathcal{L} = f(\mathcal{L}_0)



.. 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 an 1-d distribution


.. code-block:: default

    antecedent = ot.Normal()








Create an 1-d transformation


.. code-block:: default

    f = ot.SymbolicFunction(['x'], ['sin(x)+cos(x)'])








Create the composite distribution


.. code-block:: default

    distribution = ot.CompositeDistribution(f, antecedent)
    graph = distribution.drawPDF()
    view = viewer.View(graph)




.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_composite_distribution_001.png
    :alt: plot composite distribution
    :class: sphx-glr-single-img





Using the simplified construction


.. code-block:: default

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




.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_composite_distribution_002.png
    :alt: plot composite distribution
    :class: sphx-glr-single-img





Using chained operators


.. code-block:: default

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



.. image:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_composite_distribution_003.png
    :alt: plot composite distribution
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.218 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_composite_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_composite_distribution.py <plot_composite_distribution.py>`



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

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


.. only:: html

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

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