HomeTechniques and Tips@RISK DistributionsCumulative Probability

# 3.18. Cumulative Probability

Applies to: @RISK 5.x and newer

Excel has functions like NORM.DIST (NORMDIST in older Excels) to return the cumulative probability in a normal distribution. Does @RISK have anything like that?

Yes, @RISK has functions to find the cumulative probability for any distribution. Instead of a separate cumulative-probability function for each distribution, @RISK uses the same function for cumulative probability of any distribution.

Actually, there are two functions, one to obtain simulation results and one to query the theoretical distribution.

• Suppose you have an @RISK input or output, or even just an Excel formula, in cell AB123. To obtain the cumulative probability to the left of x = 14, for the most recent simulation, use the function =RiskXtoP(AB123,14). This function won't return a meaningful value until after a simulation has been run.

• For @RISK distributions, you can access the theoretical distribution. For example, if you have =RiskNormal(100,10) in cell XY234, the function =RiskXtoP(XY234,120) will return 0.97725, give or take, but varying from one simulation to the next. But the "theo" function, =RiskTheoXtoP(XY234,120) will return the exact theoretical cumulative probability, limited only by the accuracy of floating point. The theoretical value is not dependent on running a simulation. With the "theo" functions, you can even embed the distribution right in the function, as for instance =RiskTheoXtoP(RiskNormal(100,10), 120).

Instead of the probability from –∞ to an x value, how can I get the probability between two x values?

Just subtract the two cumulative probabilities. For example, the cumulative probability of cell PQ456 between x = 7 and 22 would be =RiskXtoP(PQ456,22) – RiskXtoP(PQ456,7).

How do I get the probability density, which Excel returns when the last argument of NORM.DIST is FALSE?

The probability density is simply the height of the curve at a given x value. Use RiskTheoXtoY instead of RiskTheoXtoP. (The RiskTheoXtoY function was added in @RISK 6.0 and is not available in @RISK 5.x.)

Last edited: 2017-05-04