.. _variables-loguniform_uncertain:

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loguniform_uncertain
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Aleatory uncertain variable - loguniform




**Topics**


continuous_variables, aleatory_uncertain_variables



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

   variables-loguniform_uncertain-lower_bounds
   variables-loguniform_uncertain-upper_bounds
   variables-loguniform_uncertain-initial_point
   variables-loguniform_uncertain-descriptors


**Specification**

- *Alias:* None

- *Arguments:* INTEGER

- *Default:* no loguniform 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-loguniform_uncertain-lower_bounds.html
__ variables-loguniform_uncertain-upper_bounds.html
__ variables-loguniform_uncertain-initial_point.html
__ variables-loguniform_uncertain-descriptors.html



**Description**



If the logarithm of an uncertain variable :math:`X` has a uniform
distribution, that is :math:`\log X \sim \mathcal{U}(L, U),` then
:math:`X` is distributed with a loguniform distribution. The
distribution lower bound is :math:`L` and upper bound is
:math:`U` The loguniform distribution has the density function:

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

..
   TODO: Is above discussion of bounds correct?




**Theory**


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.