.. DO NOT EDIT.
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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/distributions/discrete_1d/plot_distribution_discrete_1D.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_distributions_discrete_1d_plot_distribution_discrete_1D.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_distributions_discrete_1d_plot_distribution_discrete_1D.py:


Distribution Discrete 1D example
=================================

This examples shows the use of the univariate discrete distributions class. In particular:

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- How to define one of the univariate discrete distributions supported by UQpy
- How to extract the moments of the distribution
- How to draw random samples from the distribution

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Import the necessary modules.

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.. code-block:: default


    import matplotlib.pyplot as plt
    from UQpy.distributions.collection.Binomial import Binomial








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Example of a 1D discrete distribution
--------------------------------------

Define a univariate binomial distribution.
By using the :code:`__bases__` attribute we can verify that the Binomial distribution extends the
:class:`DistributionDiscrete1D` baseclass, while in order to define the :class:`Binomial` distribution, two
parameters are required, namely, :code:`n` and :code:`p`.

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.. code-block:: default


    print(Binomial.__bases__)
    dist = Binomial(n=5, p=0.4)






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

 .. code-block:: none

    (<class 'UQpy.distributions.baseclass.DistributionDiscrete1D.DistributionDiscrete1D'>,)




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Print the mean, standard deviation, skewness, and kurtosis of the distribution.
-------------------------------------------------------------------------------
Using the moments method existing in all univariate distributions, the user can retrieve the available
moments. The order in which the moments are extracted can be seen in the moments_list variable.

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.. code-block:: default


    moments_list = ['mean', 'variance', 'skewness', 'kurtosis']
    m = dist.moments()
    print('Moments with inherited parameters:')
    for i, moment in enumerate(moments_list):
        print(moment + ' = {0:.2f}'.format(m[i]))





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

 .. code-block:: none

    Moments with inherited parameters:
    mean = 2.00
    variance = 1.20
    skewness = 0.18
    kurtosis = -0.37




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Generate 5000 random samples from the binomial distribution.
-------------------------------------------------------------

The number of samples is provided as `nsamples` (default :math:`1`).
The user can fix the seed of the pseudo random generator via input random_state.

Important: the output of rvs is a `(nsamples, 1)` ndarray.

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.. code-block:: default


    y1 = dist.rvs(nsamples=5000)
    print('Shape of output provided by rvs is (nsamples, dimension), i.e. here:')
    print(y1.shape)
    plt.hist(y1[:, 0], bins=50)
    plt.xlabel('x')
    plt.ylabel('count')
    plt.show()









.. image-sg:: /auto_examples/distributions/discrete_1d/images/sphx_glr_plot_distribution_discrete_1D_001.png
   :alt: plot distribution discrete 1D
   :srcset: /auto_examples/distributions/discrete_1d/images/sphx_glr_plot_distribution_discrete_1D_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    Shape of output provided by rvs is (nsamples, dimension), i.e. here:
    (5000, 1)





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

   **Total running time of the script:** ( 0 minutes  0.064 seconds)


.. _sphx_glr_download_auto_examples_distributions_discrete_1d_plot_distribution_discrete_1D.py:

.. only:: html

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


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/distributions/discrete_1d/plot_distribution_discrete_1D.ipynb
        :alt: Launch binder
        :width: 150 px



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

      :download:`Download Python source code: plot_distribution_discrete_1D.py <plot_distribution_discrete_1D.py>`

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

      :download:`Download Jupyter notebook: plot_distribution_discrete_1D.ipynb <plot_distribution_discrete_1D.ipynb>`


.. only:: html

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

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