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Format: VoseBeta4(a, b, min, max, U)
The beta4 distribution is highly flexible in shape and bounded, so has been quite popular for attempting to fit to a data set for a bounded variable. In ModelRisk we offer the option of fitting the Beta4 with known bounds (our general recommendation) or without.
The PERT distribution came out of the need to describe the uncertainty in tasks during the development of the Polaris missile (Clark, 1962). The project had thousands of tasks and estimates needed to be made that were intuitive, quick and consistent in approach. The 4-parameter beta distribution was used just because it came to the author's mind (the Kumaraswamy distribution would also have been a good candidate, for example). The decision to constrain the distribution so that it's Mean = (Min + 4* Mode + Max)/6 was an approximation to their decision that the distribution should have a standard deviation of 1/6 of its range (i.e. Max - Min).
Golenko-Ginzburg (1988) describes a study that analyzed many PERT networks and concluded that 'the 'most likely' activity-time estimate m [mode] is practically useless'. They found that the location of the mode in most project tasks was approximately one third of the distance from the Min to the Max, i.e:
Mode = Min + (Max-Min)/3
Taking the Beta4(a, b, min, max) distribution again, this equates to a = 2, b = 3. Thus, from Golenko-Ginzburg's viewpoint it is sufficient to use
Beta4(2, 3, min, max)
in place of
PERT(min, mode, max)
with the added advantage that one is only asking a subject matter expert for two values.
VoseBeta4 generates values from this distribution or calculates a percentile
VoseBeta4Object constructs a distribution object for this distribution
VoseBeta4Prob returns the probability density or cumulative distribution function for this distribution
VoseBeta4Prob10 returns the log10 of the probability density or cumulative distribution function
VoseBeta4Fit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution
VoseBeta4FitObject constructs a distribution object of this distribution fitted to data
VoseBeta4FitP returns the parameters of this distribution fitted to data
