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Calculating Exceedance Probabilities Using a Distributionally Robust Method

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journal contribution
posted on 19.04.2017, 14:49 by Farzad Faridafshin, Bogdan Grechuk, Arvid Naess
Calculation of exceedance probabilities or the inverse problem of finding the level corresponding to a given exceedance probability occurs in many practical applications. For instance, it is often of interest in offshore engineering to evaluate the wind, wave, current, and sea ice properties with annual exceedance probabilities of, e.g., 10−1, 10−2, and 10−3, or so-called 10-year, 100-year, and 1000-year values. A methodology is provided in this article to calculate a tight upper bound of the exceedance probability, given any probability distribution from a wide range of commonly used distributions. The approach is based on a generalization of the Chebyshev inequality for the class of distributions with a logarithmically concave cumulative distribution function, and has the potential to relieve the often-debated exercise of determining an appropriate probability distribution function based on limited data, particularly in terms of tail behavior. Two numerical examples are provided for illustration.

History

Citation

Structural Safety, 2017, 67, pp. 132–141

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Structural Safety

issn

0167-4730

Acceptance date

15/02/2017

Copyright date

2017

Available date

22/05/2018

Publisher version

http://www.sciencedirect.com/science/article/pii/S0167473016301916

Notes

The file associated with this record is embargoed until 12 months after the date of publication. The final published version may be available through the links above.

Language

en