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Determining the Accuracy of the Triangular and PERT Distributions

Author

Listed:
  • Imran A. Khan

    (Operations Research & Industrial Engineering, The University of Texas, Austin, Texas 78712)

  • J. Eric Bickel

    (Operations Research & Industrial Engineering, The University of Texas, Austin, Texas 78712; Information, Risk, and Operations Management, The University of Texas, Austin, Texas 78712)

  • Robert K. Hammond

    (Information, Risk, and Operations Management, The University of Texas, Austin, Texas 78712)

Abstract

The Triangular and PERT (Program Evaluation Review Technique) distribution probability density functions are commonly used in decision and risk analyses. These distributions are popular because they are each specified by only three points (two support bounds and the mode) that are believed to be easy to assess from experts or data. In this paper, we carefully analyze how close the Triangular and PERT distributions are to other distributions sharing the same support and mode and show that the errors induced by the Triangular and PERT distributions are significant. We further show that distributions that are characterized by the median tend to provide a better fit than do those that are characterized by the mode.

Suggested Citation

  • Imran A. Khan & J. Eric Bickel & Robert K. Hammond, 2023. "Determining the Accuracy of the Triangular and PERT Distributions," Decision Analysis, INFORMS, vol. 20(2), pages 151-165, June.
    • Handle: RePEc:inm:ordeca:v:20:y:2023:i:2:p:151-165
    DOI: 10.1287/deca.2022.0464
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    References listed on IDEAS

    as
    1. Christopher C. Hadlock & J. Eric Bickel, 2017. "Johnson Quantile-Parameterized Distributions," Decision Analysis, INFORMS, vol. 14(1), pages 35-64, March.
    2. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    3. Robert K. Hammond & J. Eric Bickel, 2013. "Reexamining Discrete Approximations to Continuous Distributions," Decision Analysis, INFORMS, vol. 10(1), pages 6-25, March.
    4. Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    Full references (including those not matched with items on IDEAS)

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