gamma_uncertain

Aleatory uncertain variable - gamma

Topics

continuous_variables, aleatory_uncertain_variables

Specification

  • Alias: None

  • Arguments: 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:

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

where \(\mu = \alpha\beta,\) 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.