loguniform_uncertain

Aleatory uncertain variable - loguniform

Topics

continuous_variables, aleatory_uncertain_variables

Specification

• Alias: None

• Arguments: INTEGER

• Default: no loguniform uncertain variables

Child Keywords:

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 for variables
Optional		descriptors	Labels for the variables

Description

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

\[f(x) = \frac{1}{ x \left( \ln U - \ln L) \right) }\]

Theory

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.