ModelRisk distribution functions and the U-parameter | Vose Software

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.