.. _variables-geometric_uncertain:

"""""""""""""""""""
geometric_uncertain
"""""""""""""""""""


Aleatory uncertain discrete variable - geometric




**Topics**


discrete_variables, aleatory_uncertain_variables



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

   variables-geometric_uncertain-probability_per_trial
   variables-geometric_uncertain-initial_point
   variables-geometric_uncertain-descriptors


**Specification**

- *Alias:* None

- *Arguments:* INTEGER

- *Default:* no geometric uncertain variables


**Child Keywords:**

+-------------------------+--------------------+---------------------------+-----------------------------------------------+
| Required/Optional       | Description of     | Dakota Keyword            | Dakota Keyword Description                    |
|                         | Group              |                           |                                               |
+=========================+====================+===========================+===============================================+
| Required                                     | `probability_per_trial`__ | Geometric distribution parameter              |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `initial_point`__         | Initial values for variables                  |
+----------------------------------------------+---------------------------+-----------------------------------------------+
| Optional                                     | `descriptors`__           | Labels for the variables                      |
+----------------------------------------------+---------------------------+-----------------------------------------------+

.. __: variables-geometric_uncertain-probability_per_trial.html
__ variables-geometric_uncertain-initial_point.html
__ variables-geometric_uncertain-descriptors.html



**Description**


The geometric distribution represents the number of successful trials that might occur before a failure is observed.

The density function for the geometric distribution is given by:

.. math:: f(x) = {p}{(1-p)^{x}},

where :math:`p` is the probability of failure per trial.



