Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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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

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

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:

\[f(x) = \frac{{x}^{\alpha-1}{e}^{\frac{-x}{\beta}}}{\beta^{\alpha}\Gamma(\alpha)}\]

where $\mu_{GA} = \alpha\beta$ and $\sigma^2_{GA} = \alpha\beta^2$. Note that the exponential distribution is a special case of this distribution for parameter $\alpha = 1$.

Theory

When used with design of experiments and multidimensional parameter studies, distribution bounds are inferred. These bounds are [0, $\mu + 3 \sigma$].

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.