Blurb::
Aleatory uncertain variable - Frechet
Description::
The Frechet distribution is also referred to as the Type II Largest Extreme Value distribution.
The distribution of maxima in sample sets from a population with a lognormal distribution will asymptotically converge to this distribution. It is commonly used to model non-negative demand variables.

The density function for the frechet distribution is:

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

where :math:`\mu = \beta\Gamma(1-\frac{1}{\alpha}),`  and
:math:`\sigma^2 = \beta^2[\Gamma(1-\frac{2}{\alpha})-\Gamma^2(1-\frac{1}{\alpha})]` 

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::
