..
   Copyright 2021 IRT Saint-Exupéry, https://www.irt-saintexupery.com

   This work is licensed under the Creative Commons Attribution-ShareAlike 4.0
   International License. To view a copy of this license, visit
   http://creativecommons.org/licenses/by-sa/4.0/ or send a letter to Creative
   Commons, PO Box 1866, Mountain View, CA 94042, USA.

.. _gen_distribution_algos:

Probability distribution algorithms
===================================

.. warning::
   Some algorithms may require the :ref:`installation <installation>` of |g| with :ref:`all its features <dependencies>`
   and some others may depend on :ref:`plugins <plugins>`.

.. note::
   All the features of the wrapped algorithm libraries may not be exposed through |g|.



.. raw:: html

    <style>
    th {
      cursor: pointer;
    }

    th, td {
      text-align: center;
    }

    tr:hover {
        border: 1px solid black;
    }

    tr:nth-child(even) {
      background-color: #f2f2f2
    }
    </style>

    <script>
    function sortTable(n) {
      var table, rows, switching, i, x, y, shouldSwitch, dir, switchcount = 0;
      table = document.getElementById("myTable");
      switching = true;
      dir = "asc";
      while (switching) {
        switching = false;
        rows = table.rows;
        for (i = 1; i < (rows.length - 1); i++) {
          shouldSwitch = false;
          x = rows[i].getElementsByTagName("TD")[n];
          y = rows[i + 1].getElementsByTagName("TD")[n];
          if (dir == "asc") {
            if (x.innerHTML.toLowerCase() > y.innerHTML.toLowerCase()) {
              shouldSwitch= true;
              break;
            }
          } else if (dir == "desc") {
            if (x.innerHTML.toLowerCase() < y.innerHTML.toLowerCase()) {
              shouldSwitch = true;
              break;
            }
          }
        }
        if (shouldSwitch) {
          rows[i].parentNode.insertBefore(rows[i + 1], rows[i]);
          switching = true;
          switchcount ++;
        } else {
          if (switchcount == 0 && dir == "asc") {
            dir = "desc";
            switching = true;
          }
        }
      }
    }
    </script>



.. _OTComposedDistribution_options:

OTComposedDistribution
----------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.composed`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />






























    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**distributions** : *Sequence[OTDistribution]*

The distributions.

.. raw:: html

    </li>

    <li>

**variable** : *str*

The name of the variable, if any;
otherwise,
concatenate the names of the random variables
defined by ``distributions``.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**copula** : *CopulaModel | str, optional*

A copula model.


By default it is set to independent_copula.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTDiracDistribution_options:

OTDiracDistribution
-------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.dirac`





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    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />






















































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation applied
to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**variable_value** : *float, optional*

The value of the random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTDistribution_options:

OTDistribution
--------------



Module: :class:`gemseo.uncertainty.distributions.openturns.distribution`





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    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**interfaced_distribution** : *str*

The name of the probability distribution,
typically the name of a class wrapped from an external library,
such as 'Normal' for OpenTURNS or 'norm' for SciPy.

.. raw:: html

    </li>

    <li>

**parameters** : *ParametersType*

The parameters of the probability distribution.

.. raw:: html

    </li>

    <li>

**variable** : *str*

The name of the random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**standard_parameters** : *StandardParametersType | None, optional*

The standard representation
of the parameters of the probability distribution.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation applied
to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTExponentialDistribution_options:

OTExponentialDistribution
-------------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.exponential`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




























































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the exponential random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the exponential random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**loc** : *float, optional*

The location of the exponential random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**rate** : *float, optional*

The rate of the exponential random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation
applied to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTNormalDistribution_options:

OTNormalDistribution
--------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.normal`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




























































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the normal random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the normal random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**mu** : *float, optional*

The mean of the normal random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**sigma** : *float, optional*

The standard deviation
of the normal random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation
applied to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTTriangularDistribution_options:

OTTriangularDistribution
------------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.triangular`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />


































































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the triangular random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the triangular random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**maximum** : *float, optional*

The maximum of the random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**minimum** : *float, optional*

The minimum of the triangular random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**mode** : *float, optional*

The mode of the triangular random variable.


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation
applied to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _OTUniformDistribution_options:

OTUniformDistribution
---------------------



Module: :class:`gemseo.uncertainty.distributions.openturns.uniform`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




























































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the uniform random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the uniform random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**lower_bound** : *float | None, optional*

A lower bound to truncate the distribution.
If None, no lower truncation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**maximum** : *float, optional*

The maximum of the uniform random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**minimum** : *float, optional*

The minimum of the uniform random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**threshold** : *float, optional*

A threshold in [0,1].


By default it is set to 0.5.


.. raw:: html

    </li>

    <li>

**transformation** : *str | None, optional*

A transformation
applied to the random variable,
e.g. 'sin(x)'. If None, no transformation.


By default it is set to None.


.. raw:: html

    </li>

    <li>

**upper_bound** : *float | None, optional*

An upper bound to truncate the distribution.
If None, no upper truncation.


By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPComposedDistribution_options:

SPComposedDistribution
----------------------



Module: :class:`gemseo.uncertainty.distributions.scipy.composed`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />






























    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**distributions** : *Sequence[SPDistribution]*

The distributions.

.. raw:: html

    </li>

    <li>

**variable** : *str*

The name of the variable, if any;
otherwise,
concatenate the names of the random variables
defined by ``distributions``.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**copula** : *CopulaModel | str, optional*

A copula model.


By default it is set to independent_copula.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPDistribution_options:

SPDistribution
--------------



Module: :class:`gemseo.uncertainty.distributions.scipy.distribution`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />










































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**interfaced_distribution** : *str*

The name of the probability distribution,
typically the name of a class wrapped from an external library,
such as 'Normal' for OpenTURNS or 'norm' for SciPy.

.. raw:: html

    </li>

    <li>

**parameters** : *ParametersType*

The parameters of the probability distribution.

.. raw:: html

    </li>

    <li>

**variable** : *str*

The name of the random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the random variable.
standard_parameters (dict, optional): The standard representation
of the parameters of the probability distribution.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**standard_parameters** : *StandardParametersType | None, optional*




By default it is set to None.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPExponentialDistribution_options:

SPExponentialDistribution
-------------------------



Module: :class:`gemseo.uncertainty.distributions.scipy.exponential`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the exponential random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the exponential random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**loc** : *float, optional*

The location of the exponential random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**rate** : *float, optional*

The rate of the exponential random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPNormalDistribution_options:

SPNormalDistribution
--------------------



Module: :class:`gemseo.uncertainty.distributions.scipy.normal`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the normal random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the normal random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**mu** : *float, optional*

The mean of the normal random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**sigma** : *float, optional*

The standard deviation of the normal random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPTriangularDistribution_options:

SPTriangularDistribution
------------------------



Module: :class:`gemseo.uncertainty.distributions.scipy.triangular`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />










































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the triangular random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the triangular random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**maximum** : *float, optional*

The maximum of the triangular random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**minimum** : *float, optional*

The minimum of the triangular random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    <li>

**mode** : *float, optional*

The mode of the triangular random variable.


By default it is set to 0.5.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



.. _SPUniformDistribution_options:

SPUniformDistribution
---------------------



Module: :class:`gemseo.uncertainty.distributions.scipy.uniform`





.. raw:: html

    <link rel="stylesheet" href="../_static/css/theme.css" type="text/css" />
    <link rel="stylesheet" href="../_static/css/gemseo.css" type="text/css" />




































    <dl class="field-list simple">
    <dt class="field-odd">Required parameters</dt>
    <dd class="field-odd"><ul class="simple">

    <li>

**variable** : *str*

The name of the uniform random variable.

.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>



    <dl class="field-list simple">
    <dt class="field-odd">Optional parameters</dt>
    <dd class="field-odd"><ul class="simple">


    <li>

**dimension** : *int, optional*

The dimension of the uniform random variable.


By default it is set to 1.


.. raw:: html

    </li>

    <li>

**maximum** : *float, optional*

The maximum of the uniform random variable.


By default it is set to 1.0.


.. raw:: html

    </li>

    <li>

**minimum** : *float, optional*

The minimum of the uniform random variable.


By default it is set to 0.0.


.. raw:: html

    </li>

    </ul>
    </dd>
    </dl>