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3.29. Entering Parameters for Gamma Distribution

Applies to:
@RISK 6.x/7.x

I'm trying to use a RiskGamma distribution, but the parameters don't seem to match what I found in another source.

A two-parameter gamma distribution has one shape parameter and one scale parameter. @RISK specifies them in that order, as shape = α (alpha) and scale = β (beta).

But there are other ways to specify the parameters, simply by using different Greek letters or even by using different parameters. Wikipedia, for instance, lists three ways: shape k and scale θ (theta), shape α or k and rate β (β = 1/θ, rate= 1/scale), or shape k and mean μ = kθ = k/β.

Don't be confused by the different letters. Comparing to Wikipedia, @RISK α (alpha) matches Wikipedia's k, and @RISK β (beta) matches Wikipedia's θ (theta), not Wikipedia's β (beta). @RISK's β is a scale parameter, but Wikipedia's β is a different parameter called rate, which is the reciprocal of the scale parameter θ. Thus @RISK reports the mean of the gamma distribution as αβ, considering β as a scale parameter, and that matches Wikipedia's αθ. Wikipedia also gives a mean of α/β, because the rate β is 1/θ where θ is the scale parameter corresponding to @RISK's β parameter.

I have parameters from an outside source. How do I enter them in @RISK?

Here's what to enter for the α and β parameters of the RiskGamma distribution;

If you have shape and scale, regardless what letters are used by your outside source, set α = shape and β = scale.
If you have shape and rate, set α = shape and β = 1/rate.
If you have shape and mean, set α = shape and β = mean/shape.

Last edited: 2018-12-28

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