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Wind and Structures
  Volume 19, Number 4, October 2014, pages 371-387

Plotting positions and approximating first two moments of order statistics for Gumbel distribution: estimating quantiles of wind speed
H.P. Hong and S.H. Li

    Probability plotting positions are popular and used as the basis for distribution fitting and for inspecting the quality of the fit because of its simplicity. The plotting positions that lead to excellent approximation to the mean of the order statistics should be used if the objective of the fitting is to estimate quantiles. Since the mean depends on the sample size and is not amenable for simple to use closed form solution, many plotting positions have been presented in the literature, including a new plotting position that is derived based on the weighted least-squares method. In this study, the accuracy of using the new plotting position to fit the Gumbel distribution for estimating quantiles is assessed. Also, plotting positions derived by fitting the mean of the order statistics for all ranks is proposed, and an approximation to the covariance of the order statistics for the Gumbel (and Weibull) variate is given. Relative bias and root-mean-square-error of the estimated quantiles by using the proposed plotting position are shown. The use of the proposed plotting position to estimate the quantiles of annual maximum wind speed is illustrated.
Key Words
    Gumbel distribution; Weibull distribution; least-squares methods; plotting positions
H.P. Hong and S.H. Li: Department of Civil and Environmental Engineering, University of Western Ontario, Canada N6A 5B9

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