Dakota Reference Manual  Version 6.15
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exponential_uncertain


Aleatory uncertain variable - exponential

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): 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