.. only:: html

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

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

    .. _sphx_glr_auto_data_analysis_distribution_fitting_plot_estimate_normal.py:


Fit a parametric distribution
=============================

In this example we estimate the parameters of a distribution from a given sample.
Once we are settled on a good candidate, we use the corresponding factory to fit 
the distribution. Each distribution factory has one or several estimators available. 
They are all derived from either the Maximum Likelihood method or from the method of moments (see :ref:`parametric_estimation`). 



.. 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)










The Normal distribution
-----------------------

The parameters are estimated by the method of moments.


We consider a sample, here created from a standard normal distribution :


.. code-block:: default

    sample = ot.Normal().getSample(1000)








We can estimate a normal distribution with `ǸormalFactory` :


.. code-block:: default

    distribution = ot.NormalFactory().build(sample)








We take a look at the estimated parameters with the `getParameter` method :


.. code-block:: default

    print(distribution.getParameter())





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

 Out:

 .. code-block:: none

    [0.00320214,1.02733]




We draw the fitted distribution


.. code-block:: default

    graph = distribution.drawPDF()
    graph.setTitle("Fitted Normal distribution")
    view = viewer.View(graph)




.. image:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_001.png
    :alt: Fitted Normal distribution
    :class: sphx-glr-single-img





The Student distribution
------------------------

The parameters of the Student law are estimated by a mixed method of moments and reduces MLE. 


We generate a sample from a Student distribution with parameters :math:`\nu=5.0`, :math:`\mu = -0.5` and a scale parameter :math:`\sigma=2.0`.


.. code-block:: default

    sample = ot.Student(5.0, -0.5, 2.0).getSample(1000)








We use the factory to build an estimated distribution :


.. code-block:: default

    distribution = ot.StudentFactory().build(sample)








We can obtain the estimated parameters with the `getParameter` method :


.. code-block:: default

    print(distribution.getParameter())






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

 Out:

 .. code-block:: none

    [3.65576,-0.515215,1.84614]




Draw fitted distribution


.. code-block:: default

    graph = distribution.drawPDF()
    graph.setTitle("Fitted Student distribution")
    view = viewer.View(graph)




.. image:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_002.png
    :alt: Fitted Student distribution
    :class: sphx-glr-single-img





The Pareto distribution
-----------------------

By default the parameters of the Pareto distribution are estimated by least squares.


We use a sample from a Pareto distribution with a scale parameter :math:`\beta=1.0`, a shape parameter :math:`\alpha > 1.0` and a location parameter :math:`\gamma = 0.0`.


.. code-block:: default

    sample = ot.Pareto(1.0, 1.0, 0.0).getSample(1000)








Draw fitted distribution


.. code-block:: default

    distribution = ot.ParetoFactory().build(sample)

    print(distribution.getParameter())

    graph = distribution.drawPDF()
    graph.setTitle("Fitted Pareto distribution")
    view = viewer.View(graph)


    plt.show()



.. image:: /auto_data_analysis/distribution_fitting/images/sphx_glr_plot_estimate_normal_003.png
    :alt: Fitted Pareto distribution
    :class: sphx-glr-single-img


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

 Out:

 .. code-block:: none

    [0.787856,0.944192,0.246677]





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

   **Total running time of the script:** ( 0 minutes  0.328 seconds)


.. _sphx_glr_download_auto_data_analysis_distribution_fitting_plot_estimate_normal.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_estimate_normal.py <plot_estimate_normal.py>`



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

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


.. only:: html

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

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