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

Author

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  • Johan René van Dorp

    (Department of Engineering Management and Systems Engineering, The George Washington University, Washington, D.C. 20052)

  • Salvador Cruz Rambaud

    (Departamento de Dirección y Gestión de Empresas, University of Almería, Almería, Spain)

  • José García Pérez

    (Departamento de Economía Aplicada, University of Almería, Almería, Spain)

  • Rafael Herrerías Pleguezuelo

    (Departamento de Métodos Cuantitativos para la Economía y la Empresa, University of Granada, Granada, Spain)

Abstract

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.

Suggested Citation

  • Johan René van Dorp & Salvador Cruz Rambaud & José García Pérez & Rafael Herrerías Pleguezuelo, 2007. "An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage," Decision Analysis, INFORMS, vol. 4(3), pages 156-166, September.
    • Handle: RePEc:inm:ordeca:v:4:y:2007:i:3:p:156-166
    DOI: 10.1287/deca.1070.0093
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    References listed on IDEAS

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    1. L. Robin Keller & Ali Abbas & Manel Baucells & Vicki M. Bier & David Budescu & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Ahti Salo & George Wu, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(4), pages 327-330, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & Kevin F. McCardle & Gregory S. Parnell & Ahti Salo, 2007. "From the Editors..," Decision Analysis, INFORMS, vol. 4(4), pages 173-175, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
    2. Ali E. Abbas & David V. Budescu & Hsiu-Ting Yu & Ryan Haggerty, 2008. "A Comparison of Two Probability Encoding Methods: Fixed Probability vs. Fixed Variable Values," Decision Analysis, INFORMS, vol. 5(4), pages 190-202, December.
    3. López Martín, M.M. & García García, C.B. & García Pérez, J. & Sánchez Granero, M.A., 2012. "An alternative for robust estimation in Project Management," European Journal of Operational Research, Elsevier, vol. 220(2), pages 443-451.
    4. L. Robin Keller & Kelly M. Kophazi, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(2), pages 57-59, June.
    5. L. Robin Keller & Kelly M. Kophazi, 2010. "From the Editors..," Decision Analysis, INFORMS, vol. 7(2), pages 151-154, June.

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