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Download a pdf copy of this help file here |
See also: Distributions in ModelRisk, Vose Select Distribution, Distributions introduction
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. 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.
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.