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Johnson Quantile-Parameterized Distributions

Author

Listed:
  • Christopher C. Hadlock

    (Graduate Program in Operations Research and Industrial Engineering, The University of Texas, Austin, Austin, Texas 78712)

  • J. Eric Bickel

    (Graduate Program in Operations Research and Industrial Engineering, The University of Texas, Austin, Austin, Texas 78712)

Abstract

It is common decision analysis practice to elicit quantiles of continuous uncertainties and then fit a continuous probability distribution to the corresponding probability-quantile pairs. This process often requires curve fitting and the best-fit distribution will often not honor the assessed points. By strategically extending the Johnson Distribution System, we develop a new distribution system that honors any symmetric percentile triplet of quantile assessments (e.g., the 10th-50th-90th) in conjunction with specified support bounds. Further, our new system is directly parameterized by the assessed quantiles and support bounds, eliminating the need to apply a fitting procedure. Our new system is practical, flexible, and, as we demonstrate, able to match the shapes of numerous commonly named distributions.

Suggested Citation

  • Christopher C. Hadlock & J. Eric Bickel, 2017. "Johnson Quantile-Parameterized Distributions," Decision Analysis, INFORMS, vol. 14(1), pages 35-64, March.
    • Handle: RePEc:inm:ordeca:v:14:y:2017:i:1:p:35-64
    DOI: 10.1287/deca.2016.0343
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    References listed on IDEAS

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    1. Thomas W. Keelin, 2016. "The Metalog Distributions," Decision Analysis, INFORMS, vol. 13(4), pages 243-277, December.
    2. Camilo Dagum, 2008. "A New Model of Personal Income Distribution: Specification and Estimation," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 1, pages 3-25, Springer.
    3. Michael Vander Wielen & Ryan Vander Wielen, 2015. "The General Segmented Distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(10), pages 1994-2009, May.
    4. 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.
    5. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    6. J. J. A. Moors & R. Th. A. Wagemakers & V. M. J. Coenen & R. M. J. Heuts & M. J. B. T. Janssens, 1996. "Characterizing systems of distributions by quantile measures," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 50(3), pages 417-430, November.
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    Cited by:

    1. Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    2. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of indirect inference in Bayesian models," OSF Preprints enzgs, Center for Open Science.
    3. Perepolkin, Dmytro & Lindsröm, Erik & Sahlin, Ullrika, 2023. "Quantile-parameterized distributions for expert knowledge elicitation," OSF Preprints tq3an, Center for Open Science.

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