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**Distribution Parameters from "Alt" Distributions**

**Applies to:**

@RISK 5.x–7.x

When I specify a distribution in terms of percentiles or "alt parameters", how does @RISK figure out the parameters of the distribution?

That's a good question. If you have a RiskPertAlt or RiskTriangAlt, for example, @RISK finds what parameters of a standard RiskPert or RiskTriang would give the percentiles you specified. But there's no formula. Instead, @RISK has to use a process of successive approximations to find the right parameters for the RiskPert. And it's the same for all the other Alt distributions, as well as RiskTrigen, which specifies two of a triangle's three parameters as percentiles.

What about RiskUniformAlt?

Unlike all the other Alt functions, formulas do exist to convert RiskUniformAlt to the equivalent non-Alt function. Consider RiskUniformAlt(C1,x1,c,x2) where C1 and C2 are cumulative ascending percentiles >0 and <1. How is that converted to the equivalent RiskUniform(min,max)?

The CDF (cumulative distribution function) for RiskUniformAlt is a straight line passing through your desired percentiles (x1,C1) and (x2,C2). But the same straight line also passes through (min,0) and (max,1), although you don't yet know the values of min and max, and therefore the equation of the CDF is

C = (x − min) / (max − min)

Substituting the two desired percentiles gives C1⋅(max − min) = x1 − min and C2⋅(max − min) = x2 − min. Solving those as simultaneous equations in min and max gives the formulas

min = (x1⋅C2 − x2⋅C1) / (C2 − C1) and

max = min + (x2 − x1) / (C2 − C1).

The attached workbook shows an example.

How can I find out what parameters @RISK computes for non-Alt functions other than RiskUniform?

You can't get them exactly, but you can get them approximately.

- Run a simulation with a large number of iterations, such as 100,000. (For best performance, place your Alt function alone in a workbook, and don't have your actual model open while you simulate.)
- If the distribution isn't displayed at the end of simulation, click Browse Results.
- Click "Fit Distributions to This Simulated Result", near the end of the row of small icons below the graph.
- In the
*Fit Distributions to Data*dialog, on the*Distributions to Fit*tab, click the Select button, and choose "Clear All". Then tick the box for just the non-Alt distribution you are trying to fit: BetaGeneral for BetaGeneral Alt, Triang for TriangAlt or Trigen, and so on. - Click the Fit button. You'll see the fitted function above the graph on the next window. Click "Write to Cell", and in the
*Write to Cell*dialog select "@RISK Function Format" = Standard.

Last edited: 2018-06-13

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