Generalized Trapezoid Uniform distribution | Vose Software

Generalized Trapezoid Uniform distribution

Format: GTU(min, leftmode, rightmode,max,m,n)

The Trapezoid Uniform distribution is a generalization of the Triangle distribution, well-suited for subjective estimation. It's probability density function (PDF) has a flat part in the middle rather than a peak at the mode. It consists of three stages, and its PDF plot looks like a trapezoid.

It takes four parameters: min, left mode, right mode and max. For the limiting case min=left mode and max=right mode this becomes a uniform distribution, and for left mode=right mode this becomes a triangle distribution.

The Generalized Trapezoidal distribution allows the slopes to be curved, governed by two extra parameters m and n: m for the curvature on the left and n on the right. The values m=1 and n=1 correspond to straight slopes.


The Generalized Trapezoidal distribution may be used to model processes that are characterized by a growth, steady and decline stage.

The Generalized Trapezoidal distribution can also provide a flexible alternative to the PERT and triangle for subjective estimation.


Van dorp (2003) provides a thorough explanation of the derivation and use of the GTU.

ModelRisk functions added to Microsoft Excel for the Generalized Trapezoid Uniform distribution

VoseGTU generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseGTUObject constructs a distribution object for this distribution.

VoseGTUProb returns the probability density or cumulative distribution function for this distribution.

VoseGTUProb10 returns the log10 of the probability density or cumulative distribution function.


Generalized Trapezoidal distribution equations