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

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

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_deconditioned_distribution.py:


Create a deconditioned distribution
===================================

.. GENERATED FROM PYTHON SOURCE LINES 7-35

In this example we are going to build the distribution of the random vector :math:`\inputRV`
defined by the conditional distribution of:

.. math::

   \inputRV|\vect{\Theta}

where :math:`\vect{\Theta}` is the output of the random variable :math:`\vect{Y}` through the link
function :math:`f`:

.. math::

   \vect{\Theta} & = f(\vect{Y})\\
   \vect{Y} & \sim \cL_{\vect{Y}}

This example creates a :class:`~openturns.DeconditionedDistribution` which offers all the methods
attached to the distributions.

We consider the case where :math:`X` is of dimension 1 and follows a uniform distribution defined
by:

===============  =========================================================  ===============================
Variable         Distribution                                               Parameter
===============  =========================================================  ===============================
:math:`X`        :class:`~openturns.Uniform` (:math:`a, b`)                 :math:`(a,b) = (Y, 1+Y^2)`
:math:`Y`        :class:`~openturns.Uniform` (:math:`c, d`)                 :math:`(c,d) = (-1, 1)`
===============  =========================================================  ===============================


.. GENERATED FROM PYTHON SOURCE LINES 37-40

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv








.. GENERATED FROM PYTHON SOURCE LINES 41-42

Create the :math:`Y` distribution.

.. GENERATED FROM PYTHON SOURCE LINES 42-44

.. code-block:: Python

    YDist = ot.Uniform(-1.0, 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 45-46

Create the link function :math:`f: y \rightarrow (y, 1+y^2)`.

.. GENERATED FROM PYTHON SOURCE LINES 46-48

.. code-block:: Python

    f = ot.SymbolicFunction(["y"], ["y", "1+y^2"])








.. GENERATED FROM PYTHON SOURCE LINES 49-51

Create the conditional distribution of :math:`\vect{X}|\vect{\Theta}`: as the parameters have no
importance, we use the default distribution.

.. GENERATED FROM PYTHON SOURCE LINES 51-53

.. code-block:: Python

    XgivenThetaDist = ot.Uniform()








.. GENERATED FROM PYTHON SOURCE LINES 54-55

Create the deconditioned distribution of :math:`X`.

.. GENERATED FROM PYTHON SOURCE LINES 55-59

.. code-block:: Python

    XDist = ot.DeconditionedDistribution(XgivenThetaDist, YDist, f)
    XDist.setDescription([r"$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$"])
    XDist






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    DeconditionedDistribution
    <ul>
      <li>name=DeconditionedDistribution</li>
      <li>dimension=1</li>
      <li>weight=1</li>
      <li>range=[-0.998771, 1.99754]</li>
      <li>description=[$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$]</li>
      <li>isParallel=true</li>
      <li>isCopula=false</li>
    </ul>

    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 60-61

Get a sample:

.. GENERATED FROM PYTHON SOURCE LINES 61-63

.. code-block:: Python

    XDist.getSample(5)






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table>
      <tr><td></td><th>$X|\mathbf{\boldsymbol{\Theta}} = f(Y)$</th></tr>
      <tr><th>0</th><td>0.9728113</td></tr>
      <tr><th>1</th><td>-0.655941</td></tr>
      <tr><th>2</th><td>1.050775</td></tr>
      <tr><th>3</th><td>1.277257</td></tr>
      <tr><th>4</th><td>-0.101663</td></tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 64-65

Draw the PDF.

.. GENERATED FROM PYTHON SOURCE LINES 65-69

.. code-block:: Python

    graph = XDist.drawPDF()
    view = otv.View(graph)





.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_deconditioned_distribution_001.svg
   :alt: plot deconditioned distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_deconditioned_distribution_001.svg
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 70-71

.. code-block:: Python

    view.ShowAll()








.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_deconditioned_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_deconditioned_distribution.ipynb <plot_deconditioned_distribution.ipynb>`

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

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

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_deconditioned_distribution.zip <plot_deconditioned_distribution.zip>`