Three-Point Estimate Distribution | Vose Software

# Three-Point Estimate Distribution

Format: ThreePointEstimate(Min, Mode, x, P)

The simplest subjective estimates (using distributions like Triangle, PERT, Modified PERT) require that one provides a minimum, most likely and maximum value for the variable. The minimum and most likely values are usually easy to think about, but the maximum is very often more difficult.

This distribution replaces the maximum with a percentile, for example the P80 (the value you think there is an 80% chance the variable will not exceed).The input parameters are:

Min – the minimum value the variable can take

Mode - the most likely value the variable will take

x: a value

P: the probability you believe the variable will be below x

For example, VoseThreePointEstimate(1, 3, 8, 80%) as shown in the graph above defines a variable that takes a minimum value of 1, a most likely value of 3, and has an 80% chance of being below 8.

## Remarks

The Three Point Estimate distribution is constructed by fitting a Modified PERT distribution to the input values with the constraint that the Gamma parameter equals 3, which gives a naturally shaped distribution.

The distribution was first proposed for use by the risk analyst David Vose. It is used extensively in the Tamara project risk analysis software.

## ModelRisk functions added to Microsoft Excel for the Three-Parameter Estimate distribution

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

VoseThreePointEstimateObject constructs a distribution object for this distribution.

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

VoseThreePointEstimateProb10 returns the log10 of the probability density or cumulative distribution function.

No fitting functions are provided for this distribution as it is not designed to be fit to data.

## Three-Point Estimate Distribution equations

Same as the Modified PERT distribution with g = 3 and Max determined by numerically solving the equation:

VoseModPERT(Min,Mode,Max,3,P) = x