Extrapolation of extreme loads using turbulent wind samples of various mean speeds and random starting points is addressed using probability distribution functions that are suitably distorted to fit the peak extremes. The tail of the extreme value distribution of the simulated loads is required to fit accurately and this tail is extrapolated to a exceedance probability to determine the characteristic load. The Gumbel distribution with a quadratic distortion is especially addressed due to its asymptotic theoretical validity for Gaussian loads. The blade root moments and the hub moments are studied here with respect to their behavior under extrapolation using a quadratic Gumbel distribution. Verification with a large number of random seeds at various mean wind speeds is done, so as to assess the accuracy of the extrapolation and the convergence of the extrapolated load. Methods of accounting for the variance in the extrapolated load with changes in the random wind seeds are proposed.