Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Aleatory uncertain variable  beta
This keyword is related to the topics:
Alias: none
Argument(s): INTEGER
Default: no beta uncertain variables
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required  alphas  First parameter of the beta distribution  
Required  betas  Second parameter of the beta distribution  
Required  lower_bounds  Specify minimum values  
Required  upper_bounds  Specify maximium values  
Optional  initial_point  Initial values  
Optional  descriptors  Labels for the variables 
Within the beta uncertain optional group specification, the number of beta uncertain variables, the alpha and beta parameters, and the distribution upper and lower bounds are required specifications, and the variable descriptors is an optional specification. The beta distribution can be helpful when the actual distribution of an uncertain variable is unknown, but the user has a good idea of the bounds, the mean, and the standard deviation of the uncertain variable. The density function for the beta distribution is
where is the gamma function and is the beta function. To calculate the mean and standard deviation from the alpha, beta, upper bound, and lower bound parameters of the beta distribution, the following expressions may be used.
Solving these for and gives:
Note that the uniform distribution is a special case of this distribution for parameters .
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.