.. _variables-uniform_uncertain:

"""""""""""""""""
uniform_uncertain
"""""""""""""""""


Aleatory uncertain variable - uniform




**Topics**


continuous_variables, aleatory_uncertain_variables



.. toctree::
   :hidden:
   :maxdepth: 1

   variables-uniform_uncertain-lower_bounds
   variables-uniform_uncertain-upper_bounds
   variables-uniform_uncertain-initial_point
   variables-uniform_uncertain-descriptors


**Specification**

- *Alias:* None

- *Arguments:* INTEGER

- *Default:* no uniform uncertain variables


**Child Keywords:**

+-------------------------+--------------------+--------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword     | Dakota Keyword Description                    |
|                         | Group              |                    |                                               |
+=========================+====================+====================+===============================================+
| Required                                     | `lower_bounds`__   | Specify minimum values                        |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Required                                     | `upper_bounds`__   | Specify maximium values                       |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `initial_point`__  | Initial values for variables                  |
+----------------------------------------------+--------------------+-----------------------------------------------+
| Optional                                     | `descriptors`__    | Labels for the variables                      |
+----------------------------------------------+--------------------+-----------------------------------------------+

.. __: variables-uniform_uncertain-lower_bounds.html
__ variables-uniform_uncertain-upper_bounds.html
__ variables-uniform_uncertain-initial_point.html
__ variables-uniform_uncertain-descriptors.html



**Description**


The number of uniform uncertain variables and their distribution lower and upper
bounds are required specifications, while variable descriptors is an optional specification.
The uniform distribution has the density function:

.. math:: f(x) = \frac{1}{U-L},

where

:math:`U`  and :math:`L` are the upper and lower bounds of the uniform distribution, respectively. The mean of the uniform distribution is :math:`\frac{U+L}{2}` 
and the variance is :math:`\frac{(U-L)^2}{12}` .




**Theory**


This distribution is a special case of the more general beta distribution.

For some methods, including vector and centered parameter studies, an
initial point is needed for the uncertain variables. When not given
explicitly, these variables are initialized to their means.



