Dakota Reference Manual: gumbel_uncertain

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gumbel_uncertain

Aleatory uncertain variable - gumbel

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no gumbel uncertain variables

Child Keywords:

| Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description
--- | --- | --- | --- | ---
| Required | alphas | First parameter of the gumbel distribution
| Required | betas | Second parameter of the gumbel distribution
| Optional | initial_point | Initial values for variables
| Optional | descriptors | Labels for the variables

## Description

The Gumbel distribution is also referred to as the Type I Largest Extreme Value distribution. The distribution of maxima in sample sets from a population with a normal distribution will asymptotically converge to this distribution. It is commonly used to model demand variables such as wind loads and flood levels.

The density function for the Gumbel distribution is given by:

and .

## Theory

When used with some methods such as design of experiments and multidimensional parameter studies, distribution bounds are inferred to be [ , ]

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.