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:

$$f(x)=\frac{1}{x(\ln U-\ln L))}$$

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.