Wind and Structures

  • 제16권4호
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  • Pages.355-372
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  • 2013
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  • 1226-6116(pISSN)
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  • 1598-6225(eISSN)
테크노프레스 (Techno-Press)
권호 표지
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The Gringorten estimator revisited

  • 투고 : 2012.03.20
  • 심사 : 2012.06.18
  • 발행 : 2013.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

The Gringorten estimator has been extensively used in extreme value analysis of wind speed records to obtain unbiased estimates of design wind speeds. This paper reviews the derivation of the Gringorten estimator for the mean plotting position of extremes drawn from parents of the exponential type and demonstrates how it eliminates most of the bias caused by the classical Weibull estimator. It is shown that the coefficients in the Gringorten estimator are the asymptotic values for infinite sample sizes, whereas the estimator is most often used for small sample sizes. The principles used by Gringorten are used to derive a new Consistent Linear Unbiased Estimator (CLUE) for the mean plotting positions for the Fisher Tippett Type 1, Exponential and Weibull distributions and for the associated standard deviations. Analytical and Bootstrap methods are used to calibrate the bias error in each of the estimators and to show that the CLUE are accurate to better than 1%.

키워드

참고문헌

  1. Castillo, E. (1988), Extreme value theory in engineering, Academic Press.
  2. Cook, N.J. (2004), "Confidence limits for extreme wind speeds in mixed climates", J. Wind Eng. Ind. Aerod., 92(1), 41-52. https://doi.org/10.1016/j.jweia.2003.09.037
  3. Cramer, H. (1946), Mathematical Methods of Statistics, Princeton University Press.
  4. Efron, B. and Tibshirani, R.J. (1993), An Introduction to the Bootstrap, Chapman and Hall, New York.
  5. Gringorten, I.I. (1963), "A plotting rule for extreme probability paper", J. Geophys. Res. 68(3), 813-814. https://doi.org/10.1029/JZ068i003p00813
  6. Gumbel, E.J. (1958), Statistics of Extremes, Columbia University Press, New York, 371 pp.
  7. Harris, R.I. (1999), "Improvements to the method of independent storms", J. Wind Eng. Ind. Aerod., 80(1-2), 1-30. https://doi.org/10.1016/S0167-6105(98)00123-8
  8. Harris, R.I. (2009), "XIMIS - a penultimate extreme value method suitable for all types of wind climate", J. Wind Eng. Ind. Aerod., 97(5-6), 271-286. https://doi.org/10.1016/j.jweia.2009.06.011
  9. Naess, A. and Clausen, PH. (2001), "Combination of the peaks-over-threshold and bootstrapping methods for extreme value prediction", Struct.Saf., 23(4), 315-330. https://doi.org/10.1016/S0167-4730(02)00015-2
  10. Weibull, W. (1939), "A statistical theory of the strength of materials", Proc. Roy. Swed. Acad. Eng. Sci., 151, 5-45.

피인용 문헌

  1. A simulation method for macro-meteorological wind speeds with a Forward Weibull parent distribution of general index vol.171, 2017, https://doi.org/10.1016/j.jweia.2017.10.004
  2. A simulation method for the macro-meteorological wind speed and the implications for extreme value analysis vol.125, 2014, https://doi.org/10.1016/j.jweia.2013.12.003
  3. Plotting positions and approximating first two moments of order statistics for Gumbel distribution: estimating quantiles of wind speed vol.19, pp.4, 2014, https://doi.org/10.12989/was.2014.19.4.371
  4. Discussion of “Revisiting moment-based characterisation for wind pressures” by G. Huang, Y. Luo, K.R. Gurley and J. Ding vol.158, 2016, https://doi.org/10.1016/j.jweia.2016.09.001