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Approximating Continuous Probability Distributions Using the 10th, 50th, and 90th Percentiles

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  • Robert Hammond
  • J. Bickel

Abstract

In economic decision analyses, continuous uncertainties are often represented by discrete probability distributions. In this article, we analyze the ability of discretizations based on the 10th, 50th, and 90th percentiles to match the mean, variance, skewness, and kurtosis of a wide range of distributions in the Johnson distribution system. In addition, we develop new discretization methods that improve upon current practice. Finally, we demonstrate that all of these methods are special cases from a continuum of weightings and show under which conditions each is most appropriate. Our results provide guidelines for the methods’ applications and limits to their usefulness.

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  • Robert Hammond & J. Bickel, 2013. "Approximating Continuous Probability Distributions Using the 10th, 50th, and 90th Percentiles," The Engineering Economist, Taylor & Francis Journals, vol. 58(3), pages 189-208.
    • Handle: RePEc:taf:uteexx:v:58:y:2013:i:3:p:189-208
    DOI: 10.1080/0013791X.2013.793761
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    Cited by:

    1. Woodruff, Joshua & Dimitrov, Nedialko B., 2018. "Optimal discretization for decision analysis," Operations Research Perspectives, Elsevier, vol. 5(C), pages 288-305.
    2. Maram Salem & Zeinab Amin & Moshira Ismail, 2020. "Progressively Censored Reliability Sampling Plans Based on Mean Product Lifetime," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 1-33, May.

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