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

.. only:: html

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

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

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

.. _sphx_glr_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py:


Create a random mixture
=======================

.. GENERATED FROM PYTHON SOURCE LINES 6-12

.. code-block:: Python

    import openturns as ot
    import openturns.viewer as viewer
    from matplotlib import pylab as plt

    ot.Log.Show(ot.Log.NONE)








.. GENERATED FROM PYTHON SOURCE LINES 13-27

Create a mixture of distributions
---------------------------------

We define an affine combination of input random variables.

.. math::
   Y = 2 + 5 X_1 + X_2

where:

- :math:`X_1 \sim \mathcal{E}(\lambda=1.5)`
- :math:`X_2 \sim \mathcal{N}(\mu=4, \sigma=1)`

This notion is different from the Mixture where the combination is made on the probability density functions and not on the univariate random variable.

.. GENERATED FROM PYTHON SOURCE LINES 30-31

We create the distributions associated to the input random variables :

.. GENERATED FROM PYTHON SOURCE LINES 31-34

.. code-block:: Python

    X1 = ot.Exponential(1.5)
    X2 = ot.Normal(4.0, 1.0)








.. GENERATED FROM PYTHON SOURCE LINES 35-36

We define an offset `a0` :

.. GENERATED FROM PYTHON SOURCE LINES 36-38

.. code-block:: Python

    a0 = 2.0








.. GENERATED FROM PYTHON SOURCE LINES 39-40

We create the `weights` :

.. GENERATED FROM PYTHON SOURCE LINES 40-42

.. code-block:: Python

    weight = [5.0, 1.0]








.. GENERATED FROM PYTHON SOURCE LINES 43-44

We create the affine combination :math:`Y` :

.. GENERATED FROM PYTHON SOURCE LINES 44-47

.. code-block:: Python

    distribution = ot.RandomMixture([X1, X2], weight, a0)
    print(distribution)





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

 .. code-block:: none

    RandomMixture(Normal(mu = 6, sigma = 1) + Exponential(lambda = 0.3, gamma = 0))




.. GENERATED FROM PYTHON SOURCE LINES 48-49

We get its mean :

.. GENERATED FROM PYTHON SOURCE LINES 49-52

.. code-block:: Python

    mean = distribution.getMean()[0]
    print("Mean : %.3f" % mean)





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

 .. code-block:: none

    Mean : 9.333




.. GENERATED FROM PYTHON SOURCE LINES 53-54

its variance :

.. GENERATED FROM PYTHON SOURCE LINES 54-57

.. code-block:: Python

    variance = distribution.getCovariance()[0, 0]
    print("Variance : %.3f" % variance)





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

 .. code-block:: none

    Variance : 12.111




.. GENERATED FROM PYTHON SOURCE LINES 58-59

the 90% quantile :

.. GENERATED FROM PYTHON SOURCE LINES 59-62

.. code-block:: Python

    quantile = distribution.computeQuantile(0.9)[0]
    print("0.9-quantile : %.3f" % quantile)





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

 .. code-block:: none

    0.9-quantile : 13.825




.. GENERATED FROM PYTHON SOURCE LINES 63-64

We can get the probability of the :math:`Y` random variable to exceed 10.0 :

.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. code-block:: Python

    prb = distribution.computeSurvivalFunction(10.0)
    print("Probability : %.3f" % prb)





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

 .. code-block:: none

    Probability : 0.315




.. GENERATED FROM PYTHON SOURCE LINES 68-69

We draw its PDF :

.. GENERATED FROM PYTHON SOURCE LINES 69-72

.. code-block:: Python

    graph = distribution.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_001.png
   :alt: plot create random mixture
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 73-74

We draw its CDF :

.. GENERATED FROM PYTHON SOURCE LINES 74-78

.. code-block:: Python

    graph = distribution.drawCDF()
    view = viewer.View(graph)





.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_002.png
   :alt: plot create random mixture
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 79-89

Create a discrete mixture
-------------------------

In this paragraph we build the distribution of the value of the sum of 20 dice rolls.

.. math::
   Y = \sum_{i=1}^{20} X_i

where :math:`X_i \sim U(1,2,3,4,5,6)`


.. GENERATED FROM PYTHON SOURCE LINES 91-92

We create the distribution associated to the dice roll :

.. GENERATED FROM PYTHON SOURCE LINES 92-94

.. code-block:: Python

    X = ot.UserDefined([[i] for i in range(1, 7)])








.. GENERATED FROM PYTHON SOURCE LINES 95-96

Let's roll the dice a few times !

.. GENERATED FROM PYTHON SOURCE LINES 96-99

.. code-block:: Python

    sample = X.getSample(10)
    print(sample)





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

 .. code-block:: none

        [ v0 ]
    0 : [ 1  ]
    1 : [ 1  ]
    2 : [ 6  ]
    3 : [ 2  ]
    4 : [ 4  ]
    5 : [ 2  ]
    6 : [ 3  ]
    7 : [ 1  ]
    8 : [ 3  ]
    9 : [ 2  ]




.. GENERATED FROM PYTHON SOURCE LINES 100-102

.. code-block:: Python

    N = 20








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We create a collection of identically distributed Xi :

.. GENERATED FROM PYTHON SOURCE LINES 104-106

.. code-block:: Python

    coll = [X] * N








.. GENERATED FROM PYTHON SOURCE LINES 107-108

We create the weights and an affine combination :

.. GENERATED FROM PYTHON SOURCE LINES 108-111

.. code-block:: Python

    weight = [1.0] * N
    distribution = ot.RandomMixture(coll, weight)








.. GENERATED FROM PYTHON SOURCE LINES 112-113

We compute the probability to exceed a sum of 100 after 20 dice rolls :

.. GENERATED FROM PYTHON SOURCE LINES 113-115

.. code-block:: Python

    print("Probability : %.3g" % distribution.computeComplementaryCDF(100))





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

 .. code-block:: none

    Probability : 1.58e-05




.. GENERATED FROM PYTHON SOURCE LINES 116-117

We draw its PDF :

.. GENERATED FROM PYTHON SOURCE LINES 117-120

.. code-block:: Python

    graph = distribution.drawPDF()
    view = viewer.View(graph)




.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_003.png
   :alt: X0 PDF
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 121-122

and its CDF :

.. GENERATED FROM PYTHON SOURCE LINES 122-126

.. code-block:: Python

    graph = distribution.drawCDF()
    view = viewer.View(graph)





.. image-sg:: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_004.png
   :alt: X0 CDF
   :srcset: /auto_probabilistic_modeling/distributions/images/sphx_glr_plot_create_random_mixture_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 127-128

Display all figures

.. GENERATED FROM PYTHON SOURCE LINES 128-129

.. code-block:: Python

    plt.show()








.. _sphx_glr_download_auto_probabilistic_modeling_distributions_plot_create_random_mixture.py:

.. only:: html

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

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

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

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

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