IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v8y2011i3p206-219.html

Quantile-Parameterized Distributions

Author

Listed:
  • Thomas W. Keelin

    (Keelin Reeds Partners, Menlo Park, California 94025)

  • Bradford W. Powley

    (Department of Management Science and Engineering, School of Engineering, Stanford University, Stanford, California 94305)

Abstract

This paper introduces a new class of continuous probability distributions that are flexible enough to represent a wide range of uncertainties such as those that commonly arise in business, technology, and science. In many such cases, the nature of the uncertainty is more naturally characterized by quantiles than by parameters of familiar continuous probability distributions. In the practice of decision analysis, it is common to fit a hand-drawn curve to quantile outputs from probability elicitations on a continuous uncertain quantity and to then discretize the curve. The resulting discrete probability distribution is an approximation that cuts off the distribution's tails and eliminates intermediate values. Quantile-parameterized distributions address this problem by using quantiles themselves to parameterize a continuous probability distribution. We define quantile-parameterized distributions, illustrate their flexibility and range of applicability, and conclude with practical considerations when parameterizing distributions using inconsistent quantile assessments.

Suggested Citation

  • Thomas W. Keelin & Bradford W. Powley, 2011. "Quantile-Parameterized Distributions," Decision Analysis, INFORMS, vol. 8(3), pages 206-219, September.
    • Handle: RePEc:inm:ordeca:v:8:y:2011:i:3:p:206-219
    DOI: 10.1287/deca.1110.0213
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.1110.0213
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.1110.0213?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. Victor Richmond R. Jose & Robert L. Winkler, 2009. "Evaluating Quantile Assessments," Operations Research, INFORMS, vol. 57(5), pages 1287-1297, October.
    2. James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
    3. Allen C. Miller, III & Thomas R. Rice, 1983. "Discrete Approximations of Probability Distributions," Management Science, INFORMS, vol. 29(3), pages 352-362, March.
    4. Ronald A. Howard, 1988. "Decision Analysis: Practice and Promise," Management Science, INFORMS, vol. 34(6), pages 679-695, June.
    5. James E. Smith, 1993. "Moment Methods for Decision Analysis," Management Science, INFORMS, vol. 39(3), pages 340-358, March.
    6. Craig W. Kirkwood, 1976. "Parametrically Dependent Preferences for Multiattributed Consequences," Operations Research, INFORMS, vol. 24(1), pages 92-103, February.
    7. Donald L. Keefer & Samuel E. Bodily, 1983. "Three-Point Approximations for Continuous Random Variables," Management Science, INFORMS, vol. 29(5), pages 595-609, May.
    8. Thomas S. Wallsten & David V. Budescu, 1983. "State of the Art---Encoding Subjective Probabilities: A Psychological and Psychometric Review," Management Science, INFORMS, vol. 29(2), pages 151-173, February.
    9. Karvanen, Juha, 2006. "Estimation of quantile mixtures via L-moments and trimmed L-moments," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 947-959, November.
    10. Carl S. Spetzler & Carl-Axel S. Staël Von Holstein, 1975. "Exceptional Paper--Probability Encoding in Decision Analysis," Management Science, INFORMS, vol. 22(3), pages 340-358, November.
    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. Subhadeep & Mukhopadhyay, 2022. "Modelplasticity and Abductive Decision Making," Papers 2203.03040, arXiv.org, revised Mar 2023.

    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. 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.
    2. Tanaka, Ken'ichiro & Toda, Alexis Akira, 2015. "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis," University of California at San Diego, Economics Working Paper Series qt7g23r5kh, Department of Economics, UC San Diego.
    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. Yijing Li & Prakash P. Shenoy, 2012. "A Framework for Solving Hybrid Influence Diagrams Containing Deterministic Conditional Distributions," Decision Analysis, INFORMS, vol. 9(1), pages 55-75, March.
    5. 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.
    6. Soltani, Mohamad & Samorani, Michele & Kolfal, Bora, 2019. "Appointment scheduling with multiple providers and stochastic service times," European Journal of Operational Research, Elsevier, vol. 277(2), pages 667-683.
    7. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    8. Kjetil Høyland & Stein W. Wallace, 2001. "Generating Scenario Trees for Multistage Decision Problems," Management Science, INFORMS, vol. 47(2), pages 295-307, February.
    9. Kashyap, Ravi, 2019. "The perfect marriage and much more: Combining dimension reduction, distance measures and covariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    10. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    11. Logan, Douglas M., 1990. "5.4. Decision analysis in engineering-economic modeling," Energy, Elsevier, vol. 15(7), pages 677-696.
    12. James S. Dyer & James E. Smith, 2021. "Innovations in the Science and Practice of Decision Analysis: The Role of Management Science," Management Science, INFORMS, vol. 67(9), pages 5364-5378, September.
    13. Woodruff, Joshua & Dimitrov, Nedialko B., 2018. "Optimal discretization for decision analysis," Operations Research Perspectives, Elsevier, vol. 5(C), pages 288-305.
    14. Ignacio Rios & Andres Weintraub & Roger J.-B. Wets, 2016. "Building a stochastic programming model from scratch: a harvesting management example," Quantitative Finance, Taylor & Francis Journals, vol. 16(2), pages 189-199, February.
    15. Konstantin Pavlikov & Stan Uryasev, 2018. "CVaR distance between univariate probability distributions and approximation problems," Annals of Operations Research, Springer, vol. 262(1), pages 67-88, March.
    16. Hardaker, J. B., 1982. "Fundamental Aspects Of Risk And Uncertainty In Agriculture," Agrekon, Agricultural Economics Association of South Africa (AEASA), vol. 21(2), October.
    17. 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.
    18. Steffen Keck & Wenjie Tang, 2018. "Gender Composition and Group Confidence Judgment: The Perils of All-Male Groups," Management Science, INFORMS, vol. 64(12), pages 5877-5898, December.
    19. Lau, Hon-Shiang & Somarajan, C., 1995. "A proposal on improved procedures for estimating task-time distributions in PERT," European Journal of Operational Research, Elsevier, vol. 85(1), pages 39-52, August.
    20. Baker, Erin & Keisler, Jeffrey M., 2011. "Cellulosic biofuels: Expert views on prospects for advancement," Energy, Elsevier, vol. 36(1), pages 595-605.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:8:y:2011:i:3:p:206-219. 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.