Dakota Reference Manual: beta_uncertain

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beta_uncertain

Aleatory uncertain variable - beta

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no beta uncertain variables

Child Keywords:

| 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 for variables
| Optional | descriptors | Labels for the variables

## Description

The number of beta uncertain variables, the alpha and beta parameters, and the distribution upper and lower bounds are required specifications, while 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 .

## Theory

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.