HomeTechniques and Tips@RISK DistributionsCauchy Distribution

# 3.36. Cauchy Distribution

Applies to: @RISK 5.0 and newer

Does @RISK have a Cauchy distribution?

Yes, beginning with @RISK 7.5 you can specify a Cauchy distribution (also known as a Lorentz or Lorentzian distribution) in the regular Define Distributions dialog: RiskCauchy(γ,β) where γ is the location parameter and β is the scale parameter.

@RISK 7.0 and earlier did not have a Cauchy distribution among the pre-programmed list. If you can't upgrade to the current version of @RISK, you can easily create one yourself from a t distribution. According to Evans, Hastings, Peacock Statistical Distributions 3/e (Wiley, 2000), pages 49–50:

"The Cauchy variate C:a,b is related to the standard Cauchy variate C:0,1 by C:a,b ~ a+b(C:0,1). ... The standard Cauchy variate is a special case of the Student's t variate with one degree of freedom."

Therefore, to get a Cauchy distribution with location parameter (median) in cell A1 and scale parameter in A2, use this formula in @RISK 5.5 through 7.0:

=RiskMakeInput(A1 + A2*RiskStudent(1))

In @RISK 5.0, use:

=RiskMakeInput(A1 + A2*RiskStudent(1), RiskStatic(A1))

Notes:

• The RiskMakeInput( ) wrapper tells @RISK that graphs, reports, and sensitivity analysis should show the Cauchy distribution from the formula, as opposed to the Student's t distribution.

• The mean of a Cauchy distribution is undefined, so when a simulation isn't running you would normally see #VALUE in the cell. By using the RiskStatic property function, you tell @RISK to display the median in the cell when a simulation isn't running. Beginning with @RISK 5.5, the RiskStatic function is not necessary because @RISK will use 0 as the mean for RiskStudent(1).

• The output graph may look like just a spike, because the default automatic scaling includes the few extreme values as well as the great mass in the center. If that happens, right-click on the x axis labels and select Axis Options to adjust the scaling.

The attached workbook illustrates the Cauchy distribution for @RISK 7.0 and earlier.

Last edited: 2016-07-12