Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Aleatory uncertain variable  gumbel
This keyword is related to the topics:
Alias: none
Argument(s): INTEGER
Default: no gumbel uncertain variables
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  
Optional  descriptors  Labels for the variables 
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:
where and .
When used with design of experiments and multidimensional parameter studies, distribution bounds are inferred. These bounds are [ , ]
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.