exponential_uncertain

Aleatory uncertain variable - exponential

Topics

continuous_variables, aleatory_uncertain_variables

Specification

  • Alias: None

  • Arguments: INTEGER

  • Default: no exponential uncertain variables

Child Keywords:

Required/Optional

Description of Group

Dakota Keyword

Dakota Keyword Description

Required

betas

Parameter of the exponential distribution

Optional

initial_point

Initial values for variables

Optional

descriptors

Labels for the variables

Description

The exponential distribution is often used for modeling failure rates.

The density function for the exponential distribution is given by:

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

where \(\mu_{E} = \beta\) and \(\sigma^2_{E} = \beta^2\) .

Note that this distribution is a special case of the more general gamma distribution.

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.