.. only:: html

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

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

    .. _sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_visualize_copula_validation.py:


Graphical copula validation
===========================

In this example we are going to visualize an estimated copula versus the data in the rank space.


.. 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 data


.. code-block:: default

    marginals = [ot.Normal()] * 2
    dist = ot.ComposedDistribution(marginals, ot.ClaytonCopula(3))
    N = 500
    sample = dist.getSample(N)








The estimated copula


.. code-block:: default

    estimated = ot.ClaytonCopulaFactory().build(sample)








Cloud in the rank space


.. code-block:: default

    ranksTransf = ot.MarginalTransformationEvaluation(marginals, ot.MarginalTransformationEvaluation.FROM)
    rankSample = ranksTransf(sample)
    rankCloud = ot.Cloud(rankSample, 'blue', 'plus', 'sample')








Graph with rank sample and estimated copula


.. code-block:: default

    myGraph = ot.Graph('Parametric estimation of the copula', 'X', 'Y', True, 'topleft')
    myGraph.setLegendPosition('bottomright')
    myGraph.add(rankCloud)

    # Then draw the iso-curves of the estimated copula
    minPoint = [0.0]*2
    maxPoint = [1.0]*2
    pointNumber = [201]*2
    graphCop = estimated.drawPDF(minPoint, maxPoint, pointNumber)
    contour_estCop = graphCop.getDrawable(0)

    # Erase the labels of the iso-curves
    contour_estCop.setDrawLabels(False)

    # Change the levels of the iso-curves
    nlev = 21
    levels = ot.Point(nlev)
    for i in range(nlev):
        levels[i] = 0.25 * nlev / (nlev - i)
    contour_estCop.setLevels(levels)
    # Change the legend of the curves
    contour_estCop.setLegend('Gumbel copula')

    # Change the color of the iso-curves
    contour_estCop.setColor('red')

    # Add the iso-curves graph into the cloud one
    myGraph.add(contour_estCop)
    view = viewer.View(myGraph)
    plt.show()




.. image:: /auto_data_analysis/estimate_dependency_and_copulas/images/sphx_glr_plot_visualize_copula_validation_001.png
    :alt: Parametric estimation of the copula
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.126 seconds)


.. _sphx_glr_download_auto_data_analysis_estimate_dependency_and_copulas_plot_visualize_copula_validation.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_visualize_copula_validation.py <plot_visualize_copula_validation.py>`



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

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


.. only:: html

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

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