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**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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