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The Generalized Johnson Quantile-Parameterized Distribution System

Author

Listed:
  • Christopher C. Hadlock

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

  • J. Eric Bickel

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

Abstract

Johnson quantile-parameterized distributions (J-QPDs) are parameterized by any symmetric percentile triplet (SPT) (e.g., the 10th–50th–90th) and support bounds. J-QPDs are smooth, highly flexible, and amenable to Monte Carlo simulation via inverse transform sampling. However, semibounded J-QPDs are limited to lognormal tails. In this paper we generalize the kernel distribution of J-QPD beyond the standard normal, generating new fat-tailed distribution systems that are more flexible than J-QPD. We also show how to augment the SPT/bound parameters with a tail parameter, lending separate control over the distribution body and tail. We then present advantages of our new generalized system over existing systems in the contexts of both expert elicitation and fitting to empirical data.

Suggested Citation

  • Christopher C. Hadlock & J. Eric Bickel, 2019. "The Generalized Johnson Quantile-Parameterized Distribution System," Decision Analysis, INFORMS, vol. 16(1), pages 67-85, March.
    • Handle: RePEc:inm:ordeca:v:16:y:2019:i:1:p:67-85
    DOI: 10.1287/deca.2018.0376
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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. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    3. Christopher C. Hadlock & J. Eric Bickel, 2017. "Johnson Quantile-Parameterized Distributions," Decision Analysis, INFORMS, vol. 14(1), pages 35-64, March.
    4. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
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    Cited by:

    1. Vicki M. Bier & Simon French, 2020. "From the Editors: Decision Analysis Focus and Trends," Decision Analysis, INFORMS, vol. 17(1), pages 1-8, March.
    2. 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.
    3. Perepolkin, Dmytro & Goodrich, Benjamin & Sahlin, Ullrika, 2021. "The tenets of indirect inference in Bayesian models," OSF Preprints enzgs, Center for Open Science.
    4. 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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