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Selection of Probability Distributions in Characterizing Risk of Extreme Events

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  • James H. Lambert
  • Nicholas C. Matalas
  • Con Way Ling
  • Yacov Y. Haimes
  • Duan Li

Abstract

Use of probability distributions by regulatory agencies often focuses on the extreme events and scenarios that correspond to the tail of probability distributions. This paper makes the case that assessment of the tail of the distribution can and often should be performed separately from assessment of the central values. Factors to consider when developing distributions that account for tail behavior include (a) the availability of data, (b) characteristics of the tail of the distribution, and (c) the value of additional information in assessment. The integration of these elements will improve the modeling of extreme events by the tail of distributions, thereby providing policy makers with critical information on the risk of extreme events. Two examples provide insight into the theme of the paper. The first demonstrates the need for a parallel analysis that separates the extreme events from the central values. The second shows a link between the selection of the tail distribution and a decision criterion. In addition, the phenomenon of breaking records in time‐series data gives insight to the information that characterizes extreme values. One methodology for treating risk of extreme events explicitly adopts the conditional expected value as a measure of risk. Theoretical results concerning this measure are given to clarify some of the concepts of the risk of extreme events.

Suggested Citation

  • James H. Lambert & Nicholas C. Matalas & Con Way Ling & Yacov Y. Haimes & Duan Li, 1994. "Selection of Probability Distributions in Characterizing Risk of Extreme Events," Risk Analysis, John Wiley & Sons, vol. 14(5), pages 731-742, October.
    • Handle: RePEc:wly:riskan:v:14:y:1994:i:5:p:731-742
    DOI: 10.1111/j.1539-6924.1994.tb00283.x
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    References listed on IDEAS

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    1. James Mitsiopoulos & Yacov Y. Haimes, 1989. "Generalized Quantification of Risk Associated with Extreme Events," Risk Analysis, John Wiley & Sons, vol. 9(2), pages 243-254, June.
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    Cited by:

    1. Hoa X. Pham & Asaad Y. Shamseldin & Bruce W. Melville, 2021. "Projection of future extreme precipitation: a robust assessment of downscaled daily precipitation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(1), pages 311-329, May.
    2. Bruno Spilak & Wolfgang Karl Härdle, 2022. "Tail-Risk Protection: Machine Learning Meets Modern Econometrics," Springer Books, in: Cheng-Few Lee & Alice C. Lee (ed.), Encyclopedia of Finance, edition 0, chapter 92, pages 2177-2211, Springer.
    3. Bruno Spilak & Wolfgang Karl Hardle, 2020. "Tail-risk protection: Machine Learning meets modern Econometrics," Papers 2010.03315, arXiv.org, revised Aug 2021.

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