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


Aleatory uncertain variable - loguniform

Topics

This keyword is related to the topics:

Specification

Alias: none

Argument(s): INTEGER

Default: no loguniform uncertain variables

Required/Optional Description of Group Dakota Keyword Dakota Keyword Description
Required lower_bounds Specify minimum values
Required upper_bounds Specify maximium values
Optional initial_point

Initial values

Optional descriptors

Labels for the variables

Description

If the logarithm of an uncertain variable X has a uniform distribution, that is $\log X \sim U(L_{LU},U_{LU})$, then X is distributed with a loguniform distribution. The distribution lower bound is $L_{LU}$ and upper bound is $L_{LU}$ The loguniform distribution has the density function:

\[f(x) = \frac{1}{x(ln U_{LU} - ln {L_{LU}})}\]

Theory

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.