Application of the Self-Determined Probability-Weighted Moment Method to Extreme Wind Speed Estimation

For the estimation of probability distribution parameters, Haktanir (1997) introduced the method of selfdetermined probability weighted moments (SD-PWM) as a refinement on the original method of probability weighted moments (PWM) defined by Greenwood et al., (1979). Tables have been created summarizing the solution of the relevant equations for certain probability distributions, but application of these is awkward. In addition, certain algorithms presented by Haktanir are difficult to interpret and contain formulations that do not appear to properly enforce the definitions of self-determined probability weighted moments. Therefore, algorithms are developed here to both clarify and simplify the determination of SD-PWM parameter estimates for five distributions: Gumbel, generalized extremevalue (GEV), log-logistic (LL), three parameter log normal (LN3), and Pearson type three (P3). As an application of the SD-PWM algorithms, the estimation of extreme wind speeds has been considered using the Gumbel, GEV, and LL 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, as originally hypothesized by Haktanir. Additionally, for the GEV and LL distributions, SDPWM appears to be an improvement over PWM. Relative to the MOM estimates, the SD-PWM estimates compare well based on overall errors and upper tail errors. While the SD-PWM estimates exhibit increased variability relative to the MOM estimates, SD-PWM wind speed estimates are generally conservative relative to the MOM estimates