Blurb::
Aleatory uncertain variable - exponential

Description::
The exponential distribution is often used for modeling failure rates.

The density function for the exponential distribution is given by:

.. math:: f(x) = \frac{1}{\beta} \exp \left( \frac{-x}{\beta} \right),

where :math:`\mu_{E} = \beta`  and :math:`\sigma^2_{E} = \beta^2` .


Note that this distribution is a special case of the more general gamma distribution.

Topics::
continuous_variables, aleatory_uncertain_variables

Examples::

Theory::
When used with some methods such as design of experiments and
multidimensional parameter studies, distribution bounds are inferred
to be [0, :math:`\mu + 3 \sigma` ].

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.

Faq::

See_Also::
