Dakota Reference Manual: exponential_uncertain

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exponential_uncertain

Aleatory uncertain variable - exponential

## Topics

This keyword is related to the topics:

- continuous_variables
- aleatory_uncertain_variables

## 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:

where and .

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, ].

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