Estimation of Three Values (PERT)
Introduction
In probability and statistics, the PERT distribution is a family of continuous probability distributions defined by the values:.
that a variable can take. This distribution is a transformation of the Beta Distribution, which has four parameters; with two additional assumptions which are that the expected value () is:.
and that the variance () is:.
Therefore, the mean of the distribution is defined as the weighted average of the minimum, most frequent and maximum values that the variable can take, with four times the weight applied to the modal value.
These assumptions about the mean and variance of the distribution were first proposed in Clark, 1962[1] to estimate the effect of task duration uncertainty on the schedule outcome of a project that is evaluated using the Program Evaluation Review Technique (PERT), hence its name. The mathematics of the distribution resulted from the authors' desire to make the standard deviation equal to approximately 1/6 of the range.[2][3].
The PERT distribution is widely used in risk analysis[4] to represent the uncertainty of the value of some quantity when one is based on subjective estimates, because the three parameters that define the distribution are intuitive to the estimator. The PERT distribution is included in most simulation software tools.
Comparison with triangular distribution
The PERT distribution offers an alternative[5] to using the Triangular Distribution that takes the same three parameters. The PERT distribution has a smoother shape than the triangular distribution, and its standard deviation is smaller; Therefore, it is usually preferred when there is greater confidence in the estimators. The triangular distribution has a mean equal to the mean of the three parameters:.
The formula places equal emphasis on extreme values that are generally less known than the most probable value and therefore may be unduly influenced by a poor estimate of an extreme. The triangular distribution also has an angular shape that does not match the smoother shape that typifies subjective knowledge.