Dakota Reference Manual: frechet_uncertain

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frechet_uncertain

Aleatory uncertain variable - Frechet

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## Specification

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

## 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:

and

## Theory

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.