What to Do If You Can’t Find the Distribution You Want on the Palette Or, Journeying to Strange, New Distributions

See the @RISK risk analysis distribution paletteThere are thirty-nine distributions on the palette in @RISK for Excel. Sure, a couple are essentially doubles (Lognorm/Lognorm2 etc) and one is a Frequency x Severity concept (Compound) rather than strictly being a particular distribution. But basically there is plenty of choice there! However, what can you do if you have a particular distribution in mind but it isn’t on the list? There are plenty of esoteric risk analysis applications out there that require distributions beyond the realm of the palette.

Thankfully, one of the distributions you can access is the Uniform distribution. This boring rectangle is your key to any distribution you can think of when combined with an inverse CDF.

In a previous life I modelled very heavy-tailed processes (Operational Risk losses) for a large retail bank using Extreme Value Theory. One of the possible limiting distributions (in this case for sample maxima) is the Generalised Extreme Value Distribution (GEV). The Inverse CDF of the GEV is of the form:

σ (μ+(-ln(U(0,1))-ξ-1)/ξ)

Thus sampling from a Uniform(0,1) variable in this function will generate samples from a GEV with parameters μ,σ and ξ. Specific information on the GEV could then be generated by making the cell an output or using the RiskMakeInput function if required. Either way you’ve just created a distribution that isn’t on the standard palette for use in your modeling.

Any distribution can be constructed in the same way, so fear not if the distribution palette at first appears inadequate for your risk assessment needs. It’s not!

Rishi Prabhakar
Palisade Training Team

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