.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_probabilistic_modeling/distributions/plot_truncated_distribution.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        Click :ref:`here <sphx_glr_download_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py>`
        to download the full example code

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

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_truncated_distribution.py:


Truncate a  distribution
========================

.. GENERATED FROM PYTHON SOURCE LINES 6-20

In this example we are going to define truncated distributions.

It is possible to truncate a distribution in its lower area, or its upper area or in both lower and upper areas.

In 1-d, assuming a and b bounds, its probability density function is defined as:

.. math::
   \forall y \in \mathbb{R}, p_Y(y) =
         \begin{array}{|ll}
           0 &  \mbox{for } y \geq b  \mbox{ or }  y \leq a\\
           \displaystyle \frac{1}{F_X(b) - F_X(a)}\, p_X(y) & \mbox{for } y\in[a,b]
         \end{array}

Is is also possible to truncate a multivariate distribution.

.. GENERATED FROM PYTHON SOURCE LINES 22-32

.. code-block:: default

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

    # the original distribution
    distribution = ot.Gumbel(0.45, 0.6)
    graph = distribution.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_001.png
   :alt: plot truncated distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 33-34

truncate on the left

.. GENERATED FROM PYTHON SOURCE LINES 34-39

.. code-block:: default

    truncated = ot.TruncatedDistribution(
        distribution, 0.2, ot.TruncatedDistribution.LOWER)
    graph = truncated.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_002.png
   :alt: plot truncated distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 40-41

truncate on the right

.. GENERATED FROM PYTHON SOURCE LINES 41-46

.. code-block:: default

    truncated = ot.TruncatedDistribution(
        distribution, 1.5, ot.TruncatedDistribution.UPPER)
    graph = truncated.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_003.png
   :alt: plot truncated distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 47-48

truncated on both bounds

.. GENERATED FROM PYTHON SOURCE LINES 48-52

.. code-block:: default

    truncated = ot.TruncatedDistribution(distribution, 0.2, 1.5)
    graph = truncated.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_004.png
   :alt: plot truncated distribution
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 53-54

Define a multivariate distribution

.. GENERATED FROM PYTHON SOURCE LINES 54-59

.. code-block:: default

    dimension = 2
    size = 70
    sample = ot.Normal(dimension).getSample(size)
    ks = ot.KernelSmoothing().build(sample)








.. GENERATED FROM PYTHON SOURCE LINES 60-61

Truncate it between (-2;2)^n

.. GENERATED FROM PYTHON SOURCE LINES 61-64

.. code-block:: default

    bounds = ot.Interval([-2.0] * dimension, [2.0] * dimension)
    truncatedKS = ot.Distribution(ot.TruncatedDistribution(ks, bounds))








.. GENERATED FROM PYTHON SOURCE LINES 65-66

Draw its PDF

.. GENERATED FROM PYTHON SOURCE LINES 66-72

.. code-block:: default

    graph = truncatedKS.drawPDF(
        [-2.5] * dimension, [2.5] * dimension, [256] * dimension)
    graph.add(ot.Cloud(truncatedKS.getSample(200)))
    graph.setColors(["blue", "red"])
    view = viewer.View(graph)
    plt.show()



.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_005.png
   :alt: [X0,X1] iso-PDF
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_truncated_distribution_005.png
   :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    /home/devel/project/build/python/src/site-packages/openturns/viewer.py:442: UserWarning: No contour levels were found within the data range.
      contourset = self._ax[0].contour(X, Y, Z, **contour_kw)





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

   **Total running time of the script:** ( 0 minutes  0.388 seconds)


.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_truncated_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_truncated_distribution.py <plot_truncated_distribution.py>`



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

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


.. only:: html

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