Applies to: @RISK, all releases

Specifying a Triangular Distribution When You Don’t Know the Mode or Median

You can use a triangular distribution in @RISK even if you don’t know the most likely value (mode).

• Depending on what information you do have, there are two supported approaches.

Using the mean (expected value)
The mean of a triangular distribution is:

mean = (min + m.likely + max) / 3

Rearranging gives:

m.likely = 3 × mean − min − max

Steps:

1. Compute m.likely using the formula above.

2. Open the Define Distribution window.

3. Choose the Triangular distribution.

4. Enter min, the computed m.likely, and max.

Important: If the computed m.likely is less than min or greater than max, then no valid triangular distribution exists with those inputs.

Using the median (50th percentile)
@RISK lets you define a triangular distribution using percentiles instead of the mode.

Method 1 (via Define Distribution window):

1. 1. Open the Define Distribution window and select the Triangular distribution.

   2. Click the Parameters box (showing “Standard”), then check Alternate Parameters.

   3. In Parameter Selection, select Min and Max as parameters.

   4. For M. likely, select Percentiles and enter 50.

   5. Click OK, then enter min, median, and max.

Method 2 (Alternate Parameters tab):

1. 1. Open Define Distribution and go to the Alt. Parameters tab.

   2. Select TriangAlt.

   3. Choose Alternate parameters.

   4. In the Triang Parameters dialog, select Min and Max, then click OK.

Both methods allow you to define a triangular distribution without knowing the mode, using information you do have.