Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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Aleatory uncertain variable - triangular


This keyword is related to the topics:


Alias: none

Argument(s): INTEGER

Default: no triangular uncertain variables

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

Optional descriptors

Labels for the variables


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. Within the triangular uncertain optional group specification, the number of triangular uncertain variables, the modes, and the distribution lower and upper bounds are required specifications, and variable descriptors is an optional specification.

The density function for the triangular distribution is:

\[f(x) = \frac{2(x-L_T)}{(U_T-L_T)(M_T-L_T)}\]

if $L_T\leq x \leq M_T$, and

\[f(x) = \frac{2(U_T-x)}{(U_T-L_T)(U_T-M_T)}\]

if $M_T\leq x \leq U_T$, and 0 elsewhere. In these equations, $L_T$ is the lower bound, $U_T$ is the upper bound, and $M_T$ is the mode of the triangular distribution.