Dakota Reference Manual: gamma_uncertain

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gamma_uncertain

Aleatory uncertain variable - gamma

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## Specification

Alias: none

Argument(s): INTEGER

Default: no gamma uncertain variables

Child Keywords:

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

## Description

The gamma distribution is sometimes used to model time to complete a task, such as a repair or service task. It is a very flexible distribution with its shape governed by alpha and beta.

The density function for the gamma distribution is given by:

and . Note that the exponential distribution is a special case of this distribution for parameter .

## Theory

When used with some methods such as design of experiments and multidimensional parameter studies, distribution bounds are inferred to be [0, ].

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.