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Dakota Reference Manual
Version 6.16
Explore and Predict with Confidence
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Aleatory uncertain variable - Frechet
This keyword is related to the topics:
Alias: none
Argument(s): INTEGER
Default: no frechet uncertain variables
Child Keywords:
| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description | |
|---|---|---|---|---|
| Required | alphas | First parameter of the Frechet distribution | ||
| Required | betas | Second parameter of the Frechet distribution | ||
| Optional | initial_point | Initial values for variables | ||
| Optional | descriptors | Labels for the variables | ||
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:
and ![$\sigma^2 = \beta^2[\Gamma(1-\frac{2}{\alpha})-\Gamma^2(1-\frac{1}{\alpha})]$](form_436.png)
When used with some methods such as design of experiments and multidimensional parameter studies, distribution bounds are inferred to be [0,
].
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.