ModelRisk distribution functions and the U-parameter


Every ModelRisk function that generates random samples from a univariate distribution includes an optional U-parameter to enable one to control the generation of the sampling. The U-parameter forces the function to return the value from the distribution that corresponds to a cumulative probability equal to U.

For example, the VoseNormal function can be written as follows:


in which case it will return a random sample from a Normal distribution with mean of 100 and standard deviation of 10. One can also include the optional U parameter as follows:


This function will now return the 95th percentile of the Normal distribution.

Leave space for the U parameter

ModelRisk offers a number of functions that modify a distribution. For example, the VoseXBounds(min,max) function will constrain a distribution to lie within the Min to Max range. These modifying functions are included within the distribution function after all the usual parameters. Even if you do not use the U parameter, you still need to leave space for it as follows:


This formula will generate a Normal(100,10) distribution bounded to lie within the range [90,120].

The inversion method

When distributions are correlated using copulas, the U-parameter comes from the appropriate simulated copula value.














Monte Carlo simulation in Excel. Learn more

Spreadsheet risk analysis modeling


Adding risk and uncertainty to your project schedule. Learn more

Project risk analysis


Enterprise Risk Management software (ERM)

Learn more about our enterprise risk analysis management software tool, Pelican

Enterprise risk management software introduction


For Microsoft Excel

Download your free copy of ModelRisk Basic today. Professional quality risk modeling software and no catches

Download ModelRisk Basic now


For Primavera & Microsoft Project

Download your free copy of Tamara Basic today. Professional quality project risk software and no catches.

Download Tamara Basic now