Dakota Reference Manual  Version 6.15
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gamma_uncertain


Aleatory uncertain variable - gamma

Topics

This keyword is related to the topics:

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:

\[ f(x) = \frac{ {x}^{\alpha-1} \exp \left( \frac{-x}{\beta} \right) } { \beta^{\alpha}\Gamma(\alpha) }, \]

$\mu = \alpha\beta,$ and $\sigma^2 = \alpha\beta^2$. Note that the exponential distribution is a special case of this distribution for parameter $\alpha = 1$.

Theory

When used with some methods such as design of experiments and multidimensional parameter studies, distribution bounds are inferred to be [0, $\mu + 3 \sigma$].

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.