Wind and Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Errors in GEV analysis of wind epoch maxima from Weibull parents

  • Harris, R.I. (RWDI-Anemos Ltd.)
  • Received : 2005.03.09
  • Accepted : 2006.03.06
  • Published : 2006.06.25
⟨ Previous Next ⟩

Abstract

Parent wind data are often acknowledged to fit a Weibull probability distribution, implying that wind epoch maxima should fall into the domain of attraction of the Gumbel (Type I) extreme value distribution. However, observations of wind epoch maxima are not fitted well by this distribution and a Generalised Extreme Value (GEV) analysis leading to a Type III fit empirically appears to be better. Thus there is an apparent paradox. The reasons why advocates of the GEV approach seem to prefer it are briefly summarised. This paper gives a detailed analysis of the errors involved when the GEV is fitted to epoch maxima of Weibull origin. It is shown that the results in terms of the shape parameter are an artefact of these errors. The errors are unavoidable with the present sample sizes. If proper significance tests are applied, then the null hypothesis of a Type I fit, as predicted by theory, will almost always be retained. The GEV leads to an unacceptable ambiguity in defining design loads. For these reasons, it is concluded that the GEV approach does not seem to be a sensible option.

Keywords

References

  1. Castillo, E. (1988), Extreme Value Theory in Engineering, Academic Press, London
  2. Cook, N.J. and Harris, R.I. (2001), 'Discussion on application of the generalized pareto distribution to extreme value analysis in wind engineering', by Holmes, J.D. and Moriarty, W.W. J. Wind Eng. Ind. Aerodyn., 89, 215-224 https://doi.org/10.1016/S0167-6105(00)00063-5
  3. Cook, N.J. and Harris, R.I. (2004), 'Exact and general penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents', Structural Safety, 26, 391-420 https://doi.org/10.1016/j.strusafe.2004.01.002
  4. Cook, N.J. and Harris, R.I., 'Postscript to exact and general FTl penultimate distributions of extreme wind speeds drawn from tail-equivalent Weibull parents', Offered to Structural Safety
  5. Cook, N.J., Harris, R.I., and Whiting, R. (2003), 'Extreme wind speeds in mixed climates revisited', JWEIA, 91, 403-422 https://doi.org/10.1016/S0167-6105(02)00397-5
  6. Fisher, R.A. and Tippett, L.M.C. (1928), 'Limiting forms of the frequency distributions of the largest or smallest number in a sample', Proc. Camb. Phil. Soc., 24, 180-190
  7. Galambos, J. (1978), The Asymptotic Theory of Extreme Order Statistics, Wiley, New York
  8. Gomes, M.I.L. (1984), 'Penultimate limiting forms in extreme value theory', Ann. Inst. Statist. Math., 36, 71-85 https://doi.org/10.1007/BF02481954
  9. Gumbel, E.J. (1958), Statistics of Extremes, Columbia University Press, New York
  10. Harris, R.I. (2004), 'Extreme value analysis of epoch maxima-convergence and choice of asymptote', J. Wind Eng. Ind. Aerodyn., 92, 897-918 https://doi.org/10.1016/j.jweia.2004.05.003
  11. Holmes, J.D. (2003), 'Discussion on generalized extreme gust wind speeds', J. Wind Eng. Ind. Aerodyn., 91, 965-967 https://doi.org/10.1016/S0167-6105(03)00016-3
  12. Hosking, J.R.M., Wallis, J.R., and Wood, E.F. (1985), 'Estimation of the generalized extreme value distribution by the method of probability weighted moments', Technometrics, 27, 251-261 https://doi.org/10.2307/1269706
  13. Press, W.H., et al. (1989), Numerical Recipies, Cambridge University Press, Cambridge
  14. Von Mises, R. (1936), 'La distribution de la plus grandes des n valeurs', Rev. Math. De l'Union Interbalkanique, Athens, 1, 1

Cited by

  1. Extreme wind speeds from long-term synthetic records vol.115, 2013, https://doi.org/10.1016/j.jweia.2012.12.008
  2. Use of two-component Weibull mixtures in the analysis of wind speed in the Eastern Mediterranean vol.87, pp.8, 2010, https://doi.org/10.1016/j.apenergy.2010.02.033
  3. Probability distributions for offshore wind speeds vol.52, pp.1, 2011, https://doi.org/10.1016/j.enconman.2010.06.015
  4. Analysis of wind speed distributions: Wind distribution function derived from minimum cross entropy principles as better alternative to Weibull function vol.49, pp.5, 2008, https://doi.org/10.1016/j.enconman.2007.10.008
  5. Use of MinMaxEnt distributions defined on basis of MaxEnt method in wind power study vol.49, pp.4, 2008, https://doi.org/10.1016/j.enconman.2007.07.045
  6. XIMIS, a penultimate extreme value method suitable for all types of wind climate vol.97, pp.5-6, 2009, https://doi.org/10.1016/j.jweia.2009.06.011
  7. Technical note: Calibration of EVA methods for peak-over-threshold wind data using Bootstrapping vol.120, 2013, https://doi.org/10.1016/j.jweia.2013.07.005
  8. Three issues concerning the statistics of mean and extreme wind speeds vol.125, 2014, https://doi.org/10.1016/j.jweia.2013.12.009
  9. A joint probability distribution model of directional extreme wind speeds based on the t-Copula function vol.25, pp.3, 2006, https://doi.org/10.12989/was.2017.25.3.261
  10. Inverse Log-logistic distribution for Extreme Wind Speed modeling: Genesis, identification and Bayes estimation vol.6, pp.6, 2006, https://doi.org/10.3934/energy.2018.6.926