HomeTechniques and Tips@RISK DistributionsTriangular Distribution: Specify Mean or Median Instead of Most Likely

# 3.27. Triangular Distribution: Specify Mean or Median Instead of Most Likely

Applies to: @RISK, all releases

I'd like to use the triangular distribution in @RISK, but I don't know the mode (m.likely), only the mean. Can I specify a triangular distribution using the mean?

Yes. The mean of a triangular distribution equals (min+m.likely+max)/3. Therefore

m.likely = 3*mean – min – max

Compute m.likely using that formula, and enter it along with min and max in the Define Distribution window.

(If the formula yields a value for m.likely that is less than min or greater than max, then mathematically no triangular distribution exists with the specified min, mean, and max.)

I'd like to use the triangular distribution in @RISK, but I don't know the mode (m.likely), only the median (50th percentile). Can I specify a triangular distribution using the median?

Yes.  Many distributions, including RiskTriang( ), let you specify one or more parameters as percentiles. Here's one method:

1. Open the Define Distribution window and select the Triang distribution.
2. Click in the box to the right of Parameters (the box contains "Standard"), then click the drop-down arrow that appears, and check (tick) "Alternate Parameters".
3. The window expands with a "Parameter Selection" section.  Select the radio buttons to the left of Min and Max, but to the right of M. likely select Percentiles and if necessary enter 50.
4. Click OK.  Now in the Define Distribution window you can specify min, median (50th percentile), and max.

Here's an alternative method:

1. Open the Define Distribution window and select the Alt. Parameters tab, then TriangAlt.
2. At the left, next to Parameters, click on Alternate, then click the drop-down arrow that appears.
3. In the Triang Parameters dialog, select the radio buttons next to Min and Max, then click OK.

Last edited: 2015-06-19