This chapter describes the calculations required to create random samples from distributions. This is fundamental to modellers who wish to use the Excel/VBA approach, but relevant only as a background for those using @RISK (who may choose to skim or skip this chapter). In traditional statistics (and in Excel), distribution functions return a measure of relative or cumulative probability at a particular value of the variable (rather than a random sample), whereas in @RISK, distribution functions directly return samples (rather than probability information).

As described in Chapter 8 (see Figure 8.8), random samples can be created explicitly by inversion of the cumulative distribution function, involving two steps:

- The creation of a random sample from a (standard) uniform continuous distribution, i.e. of a random value between zero and one (0% and 100%). In Excel, this can be done using the
**RAND**() function. - The calculation of the associated percentile of the distribution.

Recall from Chapter 9 that a cumulative distribution is a function, *F*, that evaluates the cumulated probability, *P*, up to the point *x*:

where Par1, Par2… are the parameters of the distribution (e.g. *μ*, *σ*, *α*, *β*, *λ*, Min, ML, Max).

The inversion process involves finding, for any value of *P*, the corresponding *x*-value. Although one may conceive of this as requiring ...

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