Nonparametric extrapolation of extreme quantiles: a comparison study

Abstract The extrapolation of quantiles beyond or below the largest smallest observation plays an important role in hydrological practice, design hydraulic structures, water resources management, risk assessment. Traditionally, extreme are obtained using parametric methods that require to make a priori assumption about distribution generated data. This approach has several limitations mainly when applied tails distribution. Semiparametric nonparametric methods, on other hand, allow more flexibility and they may overcome problems approach. Therefore, we present here comparison between three selected semi/nonparametric namely Hutson (Stat Comput, 12(4):331–338, 2002) Scholz (Nonparametric tail extrapolation. Tech. Rep. ISSTECH-95-014, Boeing Information Support Services, Seattle, WA, United States America, 1995) kernel density estimation. While first third have already applications hydrology, is proposed this context for time. After describing their compare performance different sample lengths return periods. We use synthetic samples extracted from four distributions whose maxima belong Gumbel, Weibull, Fréchet domain attraction. Then, same real precipitation dataset compared with Eventually, detailed discussion results presented guide researchers choice most suitable method. None fact, outperforms others; performances, instead, vary greatly type, period, size.