Three-point estimation

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The three-point estimation technique is used in management and information systems applications for the construction of an approximate probability distribution representing the outcome of future events, based on very limited information. While the distribution used for the approximation might be a normal distribution, this is not always so and, for example a triangular distribution might be used, depending on the application.


In three-point estimation, three figures are produced initially for every distribution that is required, based on prior experience or best-guesses:

These are then combined to yield either a full probability distribution, for later combination with distributions obtained similarly for other variables, or summary descriptors of the distribution, such as the mean, standard deviation or percentage points of the distribution. The accuracy attributed to the results derived can be no better than the accuracy inherent in the three initial points, and there are clear dangers in using an assumed form for an underlying distribution that itself has little basis.


Based on the assumption that a PERT distribution governs the data, several estimates are possible. These values are used to calculate an E value for the estimate and a standard deviation (SD) as L-estimators, where:

E = (a + 4m + b) / 6
SD = (b  a) / 6

E is a weighted average which takes into account both the most optimistic and most pessimistic estimates provided. SD measures the variability or uncertainty in the estimate. In Project Evaluation and Review Techniques (PERT) the three values are used to fit a PERT distribution for Monte Carlo simulations.

The triangular distribution is also commonly used. It differs from the double-triangular by its simple triangular shape and by the property that the mode does not have to coincide with the median. The mean (expected value) is then:

E = (a + m + b) / 3.

In some applications, [1] the triangular distribution is used directly as an estimated probability distribution, rather than for the derivation of estimated statistics.

Project management

To produce a project estimate the project manager:

The E and SE values are then used to convert the project time estimates to confidence intervals as follows:

These confidence interval estimates assume that the data from all of the tasks combine to be approximately normal (see asymptotic normality). Typically, there would need to be 2030 tasks for this to be reasonable, and each of the estimates E for the individual tasks would have to be unbiased.

See also

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