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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
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    References listed on IDEAS

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    Cited by:

    1. Subhadeep & Mukhopadhyay, 2022. "Modelplasticity and Abductive Decision Making," Papers 2203.03040, arXiv.org, revised Mar 2023.

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