Simplified models for uncertainty quantification of extreme events using Monte Carlo technique

• Simplified models of standard error for extreme value quantiles are developed. • Uncertainty of extreme event using three probability distributions are discussed. • Reliability of simplified models is validated using theoretical solutions. • Cases study in extreme event analysis of wind and precipitation are performed. The accurate prediction of extreme events based on measured data is an important task because it can facilitate infrastructure reliability design, risk assessment, and disaster mitigation. However, owing to limited sample size, considerable uncertainties are introduced to extreme value predictions with respect to different probabilities of exceedance. This paper proposes an uncertainty quantification analysis algorithm for extreme value statistics using the Monte Carlo technique. The study is focused on three widely used probability distributions fitted by the maximum likelihood method: generalized extreme value, generalized Pareto, and Pearson Type III. Three simplified models of the standard error for extreme value quantiles are explicitly developed as a function of the sample size, return period, and distribution parameters. These models eliminate the constraints resulting from the assumption of normality as well as provide more straightforward and accurate expressions that are convenient for engineering applications. The results indicate that the standard error increases with the return period as well as the shape and scale parameters of the distribution; however, it decreases with the sample size. The developed simplified models were applied to extreme event analyses of wind speed and precipitation at several typical sites. To clarify the practicability and rationality of the method, a wind hazard map for non-typhoon winds was developed for mainland China.