Modified PERT distribution | Vose Software

# Modified PERT distribution

Format: ModPERT(min, mode, max, g)

The Modified PERT distribution was first proposed in Vose (2000). It is a modification of the PERT distribution with minimum a, most likely b and maximum c to produce shapes with varying degrees of uncertainty for the a,b,c values by changing the assumption about the mean:

In the standard PERT, g = 4, which is the PERT network assumption that the best estimate of the duration of a task = (a + 4b + c) /6. However, if we increase the value of g, the distribution becomes progressively more peaked and concentrated around b (and therefore less uncertain). Conversely, if we decrease g the distribution becomes flatter and more uncertain. The figure below illustrates the effect of three different values of g for a modified PERT(5,7,10) distribution.

This modified PERT distribution can be very useful in modeling expert opinion. The expert is asked to estimate the same three values as before (i.e. minimum, most likely and maximum). Then the g parameter is varied and the expert is asked to select the shape that fits his/her opinion most accurately.

Most commonly, a g value of between 2.5 and 3.0 is used as this gives a balance between showing a significant peak at the most likely value, but without under-emphasizing the probability of the tail values.

An alternative to the modified PERT distribution is the Beta Subjective in which one explicitly specifies the mean of the distribution as well as the min, mode and max.

## ModelRisk functions added to Microsoft Excel for the Modified PERT distribution

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

VoseModPERT constructs a distribution object for this distribution.

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

VoseModPERTProb10 returns the log10 of the probability density or cumulative distribution function.

## Reference

Vose, D (2000). Quantitative Risk Analysis - a guide to Monte Carlo simulation modelling