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# 3.28. Double Triangular Distribution

Do @RISK distributions include the Double Triangular Distribution that has been recommended by AACE at http://www.aacei.org/resources/rp/?
(The relevant article is AACE recommendation number 41R-08, "Risk Analysis and Contingency Determination Using Range Estimating" by Dr. Kenneth K. Humphreys.)

With @RISK 6.x–7.x:

Use the RiskDoubleTriang(min,mode,max,lower_p) distribution.

For example, suppose that you have a 76% probability of underrun (0 to 4) and a 24% probability of overrun (4 to 10).   Then you want this formula:

=RiskDoubleTriang(0, 4, 10, 0.76)

With @RISK 5.x and earlier:

You can create a double triangular distribution by using a RiskGeneral distribution.

Suppose that you have a 76% probability of underrun (0 to 4) and a 24% probability of overrun (4 to 10). Then the RiskGeneral function would be

=RiskGeneral(0,10,{4,4},{0.38,0.08})

Please paste this into an empty cell and then click the Define Distribution icon to see the graph.

Where do the 0.38 and 0.08 come from?  In this example, the minimum (greatest possible underrun) is 0, maximum (greatest possible overrun) is 10, and the most likely value is 4 (common side between the two triangles, repeated in {...,...}). 0.38 is the maximum probability density of the first triangle, and 0.08 is the maximum probability density of the second triangle. These are found by

• 2 × (probability of underrun) ÷ (most likely minus minimum) = first value
2 × 0.76 ÷ (4 - 0) = 0.38

• 2 × (probability of overrun) ÷ (maximum minus most likely) = second value
2 × 0.24 ÷ (10 - 4) = 0.08

You don't necessarily have to use these formulas. @RISK will automatically adjust the probability densities proportionally so that the total probability of the double triangle is 1.