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Wind and Structures Volume 16, Number 4, April 2013 , pages 355-372 DOI: https://doi.org/10.12989/was.2013.16.4.355 |
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The Gringorten estimator revisited |
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Nicholas John Cook and Raymond Ian Harris
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| Abstract | ||
| The Gringorten estimator has been extensively used in extreme value analysis of wind speedrecords 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%. | ||
| Key Words | ||
| plotting position; linear unbiased estimators; extreme values; peak-over-threshold; weibull distribution; exponential distribution; Fisher Tippett Type 1 distribution; method of independent storms | ||
| Address | ||
| Nicholas John Cook and Raymond Ian Harris : RWDI, Unit 4, Lawrence Way, Dunstable, Bedfordshire, LU6 1BD, UK | ||