Dakota Reference Manual  Version 6.4 Large-Scale Engineering Optimization and Uncertainty Analysis
frechet_uncertain

Aleatory uncertain variable - Frechet

## Topics

This keyword is related to the topics:

## Specification

Alias: none

Argument(s): INTEGER

Default: no frechet uncertain variables

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

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:

where and

## Theory

When used with design of experiments and multidimensional parameter studies, distribution bounds are inferred. These bounds are [0, ].

For vector and centered parameter studies, an inferred initial starting point is needed for the uncertain variables. These variables are initialized to their means for these studies.