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.
Highlights
In the field of valuation in general, and in a more specific field such as that of agricultural valuation, the two distribution functions method is wellknown
Valuation, the two distribution functions method is wellknown. This was an original idea of Ballestero (1971, 1973) and was later developed by Caballer (1993) and Romero (1977), who contributed some practical applications, and is described in several textbooks: Ballestero (1991a, 1991b) and Caballer (1994)
Some works currently under review attempt to introduce statistical tests for the representativeness of the indices and the adaptation of the distributions that model them (García et al, 2003b). All these works and others included in the references of these papers attempt to introduce mathematical models in the discipline of valuation
Summary
In the field of valuation in general, and in a more specific field such as that of agricultural valuation, the two distribution functions method is wellknown. The aim of this work is to develop, in the method of the two distribution functions, a poly-stage model of valuation that generates a confidence interval for the value to be determined, which will be called the negotiation interval.
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