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

.. only:: html

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

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

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

.. _sphx_glr_auto_data_analysis_distribution_fitting_plot_model_singular_multivariate_distribution.py:


Model a singular multivariate distribution
==========================================

.. GENERATED FROM PYTHON SOURCE LINES 7-11

From time to time we need to model singular nD distributions
(e.g. the joint distribution of KL coefficients for curves resulting from the transport of a low dimensional random vector).
A way to do that is to use an EmpiricalBernsteinCopula with a bin number equal to the sample size
(also called the empirical beta copula in this case)

.. GENERATED FROM PYTHON SOURCE LINES 11-18

.. code-block:: default


    import openturns as ot
    import openturns.viewer as viewer
    import math as m
    ot.Log.Show(ot.Log.NONE)
    ot.RandomGenerator.SetSeed(0)








.. GENERATED FROM PYTHON SOURCE LINES 19-20

routine to draw a distribution cloud and a sample

.. GENERATED FROM PYTHON SOURCE LINES 20-39

.. code-block:: default



    def draw(dist, Y):
        g = ot.Graph()
        g.setAxes(True)
        g.setGrid(True)
        c = ot.Cloud(dist.getSample(10000))
        c.setColor("red")
        c.setPointStyle("bullet")
        g.add(c)
        c = ot.Cloud(Y)
        c.setColor("black")
        c.setPointStyle("bullet")
        g.add(c)
        g.setBoundingBox(ot.Interval(
            Y.getMin()-0.5*Y.computeRange(), Y.getMax()+0.5*Y.computeRange()))
        return g









.. GENERATED FROM PYTHON SOURCE LINES 40-41

generate some multivariate data to estimate, with correlation

.. GENERATED FROM PYTHON SOURCE LINES 41-49

.. code-block:: default

    f = ot.SymbolicFunction(["U", "xi1", "xi2"], [
                            "sin(U)/(1+cos(U)^2)+0.05*xi1", "sin(U)*cos(U)/(1+cos(U)^2)+0.05*xi2"])
    U = ot.Uniform(-0.85*m.pi, 0.85*m.pi)
    xi = ot.Normal(2)
    X = ot.BlockIndependentDistribution([U, xi])
    N = 200
    Y = f(X.getSample(N))








.. GENERATED FROM PYTHON SOURCE LINES 50-51

estimation by multivariate kernel smoothing

.. GENERATED FROM PYTHON SOURCE LINES 51-54

.. code-block:: default

    multi_ks = ot.KernelSmoothing().build(Y)
    view = viewer.View(draw(multi_ks, Y))




.. image-sg:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_model_singular_multivariate_distribution_001.png
   :alt: plot model singular multivariate distribution
   :srcset: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_model_singular_multivariate_distribution_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 55-56

estimation by empirical beta copula

.. GENERATED FROM PYTHON SOURCE LINES 56-63

.. code-block:: default

    beta_copula = ot.EmpiricalBernsteinCopula(Y, len(Y))
    marginals = [ot.KernelSmoothing().build(Y.getMarginal(j))
                 for j in range(Y.getDimension())]
    beta_dist = ot.ComposedDistribution(marginals, beta_copula)
    view = viewer.View(draw(beta_dist, Y))

    viewer.View.ShowAll()



.. image-sg:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_model_singular_multivariate_distribution_002.png
   :alt: plot model singular multivariate distribution
   :srcset: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_model_singular_multivariate_distribution_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  0.524 seconds)


.. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_model_singular_multivariate_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_model_singular_multivariate_distribution.py <plot_model_singular_multivariate_distribution.py>`



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

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


.. only:: html

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

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