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See also: Distributions in ModelRisk, Vose Select Distribution, Distributions introduction
In every distribution function an extra optional parameter U is included, to enable one to control the generation of the sampling. For example, the Risk Event function can be written as follows:
=VoseRiskEvent(0.2,VoseLognormalObject(3,2),0.95)
This function constructs the distribution of a risk event which has a 20% chance of occurring with an impact of Lognormal(3,2). The third (U) parameter of 0.95 makes the function return the 95th percentile of this risk event.
When the U parameter is omitted, the function generates random values of the distribution.
In addition to returning percentiles of a distribution, the U parameter is very important for linking to copula functions so that you can generate correlated random variables.
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 ModelRisk distribution functions randomly generate numbers from a chosen distribution using the inversion method, where every distribution has its own set of parameters (shape, scale or location parameters). This method first constructs a cumulative distribution curve for the distribution, as shown in the figure.
Then a random number is
generated between zero and one (using the Mersenne
Twister random number generator), and this value is used to find the
variable value that corresponds to a cumulative probability equal to the
random number that was generated.
In this figure, a U value of 0.7 is used with a Pareto(20, 0.95) distribution returning the 70th percentile of the distribution equal to 1.00895.