IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v4y2007i3p156-166.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.1070.0093
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.1070.0093?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lynn B. Davidson & Dale O. Cooper, 1980. "Implementing Effective Risk Analysis at Getty Oil Company," Interfaces, INFORMS, vol. 10(6), pages 62-75, December.
    2. Powell, Mark R. & Wilson, James D., 1997. "Risk Assessment for National Natural Resource Conservation Programs," Discussion Papers 10859, Resources for the Future.
    3. Dewispelare, Aaron R. & Herren, L. Tandy & Clemen, Robert T., 1995. "The use of probability elicitation in the high-level nuclear waste regulation program," International Journal of Forecasting, Elsevier, vol. 11(1), pages 5-24, March.
    4. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    5. Donald L. Keefer & William A. Verdini, 1993. "Better Estimation of PERT Activity Time Parameters," Management Science, INFORMS, vol. 39(9), pages 1086-1091, September.
    6. Powell, Mark & Wilson, James, 1997. "Risk Assessment for National Natural Resource Conservation Programs," RFF Working Paper Series dp-97-49, Resources for the Future.
    7. Garthwaite, Paul H. & Kadane, Joseph B. & O'Hagan, Anthony, 2005. "Statistical Methods for Eliciting Probability Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 680-701, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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 & 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, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Robert K. Hammond & J. Eric Bickel, 2013. "Reexamining Discrete Approximations to Continuous Distributions," Decision Analysis, INFORMS, vol. 10(1), pages 6-25, March.
    2. Kotz, Samuel & van Dorp, J. René, 2005. "A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 383-394, March.
    3. Alwynelle (Nell) S. AM, 1999. "Invited Editorial: Risk Assessment Challenges at USDA," Risk Analysis, John Wiley & Sons, vol. 19(3), pages 323-326, June.
    4. Ozgoc-Caglar, C. Derya & Farnsworth, Richard L., 2008. "A Multiple Criteria Decision System to Improve Performance of Federal Conservation Programs," 2008 Conference (52nd), February 5-8, 2008, Canberra, Australia 5986, Australian Agricultural and Resource Economics Society.
    5. Wilson, Kevin J., 2017. "An investigation of dependence in expert judgement studies with multiple experts," International Journal of Forecasting, Elsevier, vol. 33(1), pages 325-336.
    6. Durbach, Ian N. & Stewart, Theodor J., 2012. "A comparison of simplified value function approaches for treating uncertainty in multi-criteria decision analysis," Omega, Elsevier, vol. 40(4), pages 456-464.
    7. Jin-Huei Yeh & Jying-Nan Wang & Chung-Ming Kuan, 2014. "A noise-robust estimator of volatility based on interquantile ranges," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 751-779, November.
    8. James W. Taylor, 2005. "Generating Volatility Forecasts from Value at Risk Estimates," Management Science, INFORMS, vol. 51(5), pages 712-725, May.
    9. Moors, J.J.A. & Schuld, M.H. & Mathijssen, A.C.A., 1995. "A new method for assessing judgmental distributions," Other publications TiSEM 7ad88666-4ed3-42bf-a563-d, Tilburg University, School of Economics and Management.
    10. Moors, J.J.A. & Schuld, M.H. & Mathijssen, A.C.A., 1995. "A new method for assessing judgmental distributions," Research Memorandum FEW 708, Tilburg University, School of Economics and Management.
    11. D. K. Mohanty & Avik Pradhan & M. P. Biswal, 2020. "Chance constrained programming with some non-normal continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1281-1298, December.
    12. Wisse, Bram & Bedford, Tim & Quigley, John, 2008. "Expert judgement combination using moment methods," Reliability Engineering and System Safety, Elsevier, vol. 93(5), pages 675-686.
    13. 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.
    14. Saurabh Bansal & Genaro J. Gutierrez, 2020. "Estimating Uncertainties Using Judgmental Forecasts with Expert Heterogeneity," Operations Research, INFORMS, vol. 68(2), pages 363-380, March.
    15. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    16. Durbach, Ian N. & Stewart, Theodor J., 2011. "An experimental study of the effect of uncertainty representation on decision making," European Journal of Operational Research, Elsevier, vol. 214(2), pages 380-392, October.
    17. Anil Gaba & Dana G. Popescu & Zhi Chen, 2019. "Assessing Uncertainty from Point Forecasts," Management Science, INFORMS, vol. 65(1), pages 90-106, January.
    18. Durbach, Ian N. & Stewart, Theodor J., 2012. "Modeling uncertainty in multi-criteria decision analysis," European Journal of Operational Research, Elsevier, vol. 223(1), pages 1-14.
    19. M Revie & T Bedford & L Walls, 2010. "Evaluation of elicitation methods to quantify Bayes linear models," Journal of Risk and Reliability, , vol. 224(4), pages 322-332, December.
    20. A Jessop, 2011. "Using imprecise estimates for weights," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1048-1055, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ordeca:v:4:y:2007:i:3:p:156-166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.