HomeTechniques and Tips@RISK DistributionsExtreme Value Distributions: Gumbel and Fréchet

3.31. Extreme Value Distributions: Gumbel and Fréchet

Applies to: @RISK 5.x and newer

@RISK does not use the type of Extreme Value distribution that I need. Is there any way I can get the other type of Extreme Value distribution out of @RISK?

The Extreme Value distribution falls into two major types: Type I is also called Gumbel, and Type II is also called Fréchet; both are offered in @RISK.

Gumbel Distribution (Type I Extreme Value)

There are two sub-types of Gumbel distribution.

The Maximum Extreme Value distribution is implemented in @RISK's RiskExtValue(α,β) function, which has been available since early versions of RISK.

The Minimum Extreme Value distribution is implemented in @RISK 6.0 and newer as the RiskExtValueMin(α,β) function. In earlier versions of @RISK, use RiskExtValue( ), but put a minus sign in front of the function and another minus sign in front of the first argument. For example, for a Minimum Extreme Value distribution with α=1, β=2, use RiskExtValueMin(1,2) in @RISK 6.0 and newer, or –(RiskExtValue(–1,2)) in @RISK 5.7 and earlier.

Fréchet Distribution (Type II Extreme Value)

The Fréchet distribution is defined in @RISK 7.5 and newer.

If you have an older @RISK and can't upgrade to the latest, you can use the technique in Add Your Own Distribution to @RISK to create one. You'll need the CDF, which is exp[–z–α], where z = (x–γ)/β. γ is the location parameter, β is the scale parameter, and α is the shape parameter.

Additional keywords: ExtValue distribution, ExtValueMin distribution

Last edited: 2016-07-12

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