Project management under uncertainty beyond beta: The generalized bicubic distribution

The beta distribution has traditionally been employed in the PERT methodology and generally used for modeling bounded continuous random variables based on expert's judgment. The impossibility of estimating four parameters from the three values provided by the expert when the beta distribution is assumed to be the underlying distribution has been widely debated. This paper presents the generalized bicubic distribution as a good alternative to the beta distribution since, when the variance depends on the mode, the generalized bicubic distribution approximates the kurtosis of the Gaussian distribution better than the beta distribution. In addition, this distribution presents good properties in the PERT methodology in relation to moderation and conservatism criteria. Two empirical applications are presented to demonstrate the adequateness of this new distribution.