Performance of the generalized least-squares method for the Gumbel distribution and its application to annual maximum wind speeds

The Gumbel model is often used to fit annual maximum wind speed or wind velocity pressure. The commonly used fitting methods include the method of moments, the method of maximum likelihood, the method of L-moments, and the Lieblein BLUE (i.e., generalized least-squares method (GLSM)). Previously, the coefficients of the estimators for the latter method have not been available for large sample size, and the relative performance of the GLSM to other fitting methods such as the method of L-moments is unknown. In this study, we evaluate these coefficients for a sample size up to 100, and identify trends in the calculated coefficients. The relative performance of commonly used fitting methods for the Gumbel distribution, including the GLSM, is evaluated in terms of efficiency, bias, and root-mean square error. We illustrate their application and impact on the estimated return period values of the annual maximum wind speed for 14 locations in Canada.