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

2007; Institute for Operations Research and the Management Sciences; Volume: 4; Issue: 3 Linguagem: Inglês

10.1287/deca.1070.0093

1545-8504

Johan René van Dorp, Salvador Cruz Rambaud, José Garcı́a Pérez, Rafael Herrerı́as Pleguezuelo,

Control Systems and Identification

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.