triangular_uncertain

Aleatory uncertain variable - triangular

Topics

continuous_variables, aleatory_uncertain_variables

Specification

• Alias: None

• Arguments: INTEGER

• Default: no triangular uncertain variables

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Required		modes	Distribution parameter
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

The triangular distribution is often used when one does not have much data or information, but does have an estimate of the most likely value and the lower and upper bounds. The number of triangular uncertain variables, the modes, and the distribution lower and upper bounds are required specifications, whilevariable descriptors is an optional specification.

The density function for the triangular distribution is:

\[f(x) = \frac{2(x-L)}{(U-L)(M-L)}\]

if \(L\leq x \leq M\) , and

\[f(x) = \frac{2(U-x)}{(U-L)(U-M)}\]

if \(M\leq x \leq U\) , and 0 elsewhere. In these equations, \(L\) is the lower bound, \(U\) is the upper bound, and \(M\) is the mode of the triangular distribution.