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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py>`
        to download the full example code

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

.. _sphx_glr_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py:


Estimate tail dependence coefficients on the wave-surge data
============================================================

.. GENERATED FROM PYTHON SOURCE LINES 6-11

In this example we estimate the tail dependence coefficient of a bivariate sample
applied to the concurrent measurements of two oceanographic variables (wave and surge heights) at a single location off south-west England.
Readers should refer to [coles2001]_ to get more details.

First, we load the wave-surge dataset.

.. GENERATED FROM PYTHON SOURCE LINES 11-24

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as otv
    from openturns.usecases import coles

    data = coles.Coles().wavesurge
    print(data[:5])

    graph = ot.Graph("Concurent wave and surge heights", "wave (m)", "surge (m)", True, "")
    cloud = ot.Cloud(data)
    cloud.setColor("red")
    graph.add(cloud)
    view = otv.View(graph)




.. image-sg:: /auto_data_analysis/estimate_dependency_and_copulas/images/sphx_glr_plot_estimate_dependence_wavesurge_001.png
   :alt: Concurent wave and surge heights
   :srcset: /auto_data_analysis/estimate_dependency_and_copulas/images/sphx_glr_plot_estimate_dependence_wavesurge_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

        [ wave   surge  ]
    0 : [  1.5   -0.009 ]
    1 : [  1.83  -0.053 ]
    2 : [  2.44  -0.024 ]
    3 : [  1.68   0     ]
    4 : [  1.49   0.079 ]




.. GENERATED FROM PYTHON SOURCE LINES 25-30

We plot the graph of the function :math:`u \mapsto \chi(u)` and the graph of the function
:math:`u \mapsto \bar{\chi}(u)`. We conclude that both variables are asymptotially dependent
as :math:`\chi > 0` and that they are positively correlated as :math:`\hat{\chi} > 0`.
We can visually deduce the upper tail dependence coefficient :math:`\chi \simeq 0.26` and
the upper extremal dependence coefficient :math:`\bar{\chi} \simeq 0.5`.

.. GENERATED FROM PYTHON SOURCE LINES 30-38

.. code-block:: Python

    graph1 = ot.VisualTest.DrawUpperTailDependenceFunction(data)
    graph2 = ot.VisualTest.DrawUpperExtremalDependenceFunction(data)
    grid = ot.GridLayout(1, 2)
    grid.setGraph(0, 0, graph1)
    grid.setGraph(0, 1, graph2)
    view = otv.View(grid)





.. image-sg:: /auto_data_analysis/estimate_dependency_and_copulas/images/sphx_glr_plot_estimate_dependence_wavesurge_002.png
   :alt: , Upper tail dependence function, Upper extremal dependence function
   :srcset: /auto_data_analysis/estimate_dependency_and_copulas/images/sphx_glr_plot_estimate_dependence_wavesurge_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 39-40

.. code-block:: Python

    otv.View.ShowAll()








.. _sphx_glr_download_auto_data_analysis_estimate_dependency_and_copulas_plot_estimate_dependence_wavesurge.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

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

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

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