An evaluation of the self-determined probability-weighted moment method for estimating extreme wind speeds

For the estimation of probability distribution parameters, the method of self-determined probability-weighted moments (SD-PWM) has previously been introduced as a refinement on the original method of probability-weighted moments (PWM). Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward. In addition, certain associated algorithms are difficult to interpret and contain formulations that do not appear to properly enforce the definitions of self-determined probability-weighted moments. Therefore, new algorithms have been developed to both clarify and simplify the determination of SD-PWM parameter estimates. As an application of the SD-PWM algorithms, the estimation of extreme wind speeds is considered using the Gumbel and generalized extreme value (GEV) distributions. The estimation results are compared to similar results obtained via PWM, the method of moments and the maximum likelihood method. The analyses suggest SD-PWM may be a reasonable tool for analyzing the ability of a particular distribution to describe a sample. Relative to the method of moments and PWM estimates, the SD-PWM estimates compare well based on fits of the cumulative distributions. While the SD-PWM estimates exhibit increased variability relative to the method of moment (MOM) estimates, SD-PWM wind speed estimates are generally conservative relative to the MOM estimates.