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 the triangular distribution and its use to describe uncertainty of bounded input phenomena. The trapezoidal distribution, explicitly suggested by Pouliquen (1970) in the framework of risk and uncertainty analysis, 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. While the trapezoidal and the triangular distributions are restricted to linear geometric forms in the successive stages of the distribution, the generalized trapezoidal (GT) distribution introduced by van Dorp and (2003) allows for a non-linear behavior at its tails and Kotz a linear incline (or decline) in the central stage. In this paper we shall 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. 1 Corresponding Author. Department of Engineering Management and Systems Engineering, School of Engineering and Applied Science, The George Washington University, 1776 G Street, N.W. , Suite 110, Washington D.C. 20052. Phone: 202-994-6638, Fax: 202-994-0245, E-mail: [email protected]. 2Departamento de Dirección y Gestión de Empresas. University of Almería (Spain). E-mail: [email protected] 3Departamento de Econom a Aplicada. í University of Almería (Spain). E-mail: [email protected] 4Departamento de M todos Cuantitativos para la Economía y la Empresa. University of Granada (Spain). E-mail: é [email protected] Johan René van Dorp, Salvador Cruz Rambaud, José García Pérez, and Rafael Herrerías Pleguezuelo (2007). "An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage", Decision Analysis Journal, Vol. 4, pp. 156 166. MANUSCRIPT TEXT 2