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:

=VoseNormal(100,10)

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:

=VoseNormal(100,10,0.95)

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:

=VoseNormal(100,10,,VoseXBounds(90,120))

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.

 

 

 

 

 

 

 

 

 

 

 

 

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