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:

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

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.