Iterative valuation process in the method of the two beta distributions

Abstract

In the literature on PERT methodology, four subfamilies of beta distributions have appeared: classical, of constant variance, mesokurtic and Caballer. To date, these four subfamilies have been used independently to resolve economic valuation problems. The only differences between using one or another lie in the means or variances obtained by each. For example, following a criterion of prudence the maximum variance is required, and for a riskier criterion the minimum variance is preferred. With respect to the mean, we are interested in the one closest to the centre of the interval, i.e. the model that provides a more centered expected value and hence more moderate estimations. This work focuses on the field of valuation, more specifically on the valuation method of the two distribution functions (recommended when there are limited data). The aim of this work was to develop an iterative process that uses the four families of beta distributions simultaneously with the objective of using all the information provided by each of them. The practical application of this process can conclude either with an interval of possible values or a precise valuation. Then the concepts of stability and convergence of the valuation process appear.