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3.40. Four-Parameter Pert Distribution

Applies to: @RISK 5.x–7.x

Does @RISK have a four-parameter Pert distribution, with a shape parameter?

The RiskPert distribution has three parameters: min, mode (most likely), and max. Some authorities, such as Wolfram, mention a four-parameter Pert distribution, the fourth parameter λ being the shape, and you may see references to a "Beta-Pert" on some Web sites. Implicitly, with RiskPert the value of λ is 4.

The Pert distribution is closely related to the Beta distribution, and in fact RiskPert is a special case of RiskBetaGeneral.

@RISK doesn't let you enter a shape parameter directly, but you get the equivalent of a four-parameter Pert distribution with a RiskBetaSubj(min, mode, μ, max) function, where

μ = (min + max + λ·mode) / (λ + 2).

To modify a regular three-parameter RiskPert(min, mode, max) by adding a shape parameter λ, change it to

RiskBetaSubj(min, mode, (min+max+λ*mode)/(λ+2), max).

If you have the min, mode, max, and λ in cells B1 through B4, then you can put the formula

=(B1 + B3 + B4*B2)/(B4 + 2)

in cell B5, and use =RiskBetaSubj(B1,B2,B5,B3). A simple example is attached.

Last edited: 2016-08-29


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