Rafael Herrerías Pleguezuelo

A note on the reasonableness of PERT hypotheses

In this paper the expression for the mean in the PERT method is considered. This mean involves a parameter k, that sometimes has been set to 4. Insisting on the similarity between the beta and the normal distributions, certain hypotheses are proposed that lead to k necessarily being exactly 4. More specifically, by using the moments of the second and fourth orders, it is shown that the usual beta distribution in the PERT method is mesokurtic (@c=3) and of constant variance (@s^2=136).

An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage

Recent advances in computation technology for decision/simulation and uncertainty analyses have revived interest in the triangular distribution and its use to describe uncertainty of bounded input phenomena. The trapezoidal distribution is a generalization of the triangular distribution that allows for the specification of the modal value by means of a range of values rather than a single point estimate. Whereas the trapezoidal and the triangular distributions are restricted to linear geometric forms in the successive stages of the distribution, the generalized trapezoidal (GT) distribution allows for a nonlinear behavior at its tails and a linear incline (or decline) in the central stage. In this paper we develop two novel elicitation procedures for the parameters of a special case of the GT family by restricting ourselves to a uniform (horizontal) central stage in accordance with the central stage of the original trapezoidal distribution.

Using generator function system to check independence of random variables

This study presents a criterion to determine the stochastic dependence or independence between the variables of a random vector or between two of its subvectors, either from the joint density function or from the generator function system for such a density. This criterion generalizes the condition discussed by HERRERIAS R., PALACIOS F. and CALLEJON J.(1997). There is a noteworthy simplicity of calculations, as the stochastic dependence or independence of random variables is seen as a consequence of the analytical dependence or independence in the generator function system.