Nonparametric extrapolation of extreme quantiles: a comparison study

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

Nonparametric Estimation of Extreme Quantiles with an Application to Longevity Risk

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain.

Extreme Quantiles Dynamic Line Rating Forecasts and Application on Network Operation

This paper presents a study on dynamic line rating (DLR) forecasting procedure aimed at developing a new methodology able to forecast future ampacity values for rare and extreme events. This is motivated by the belief that to apply DLR network operators must be able to forecast their values and this must be based on conservative approaches able to guarantee the safe operation of the network. The proposed methodology can be summarised as follows: firstly, probabilistic forecasts of conductors’ ampacity are calculated with a non-parametric model, secondly, the lower part of the distribution is replaced with a new distribution calculated with a parametric model. The paper presents also an evaluation of the proposed methodology in network operation, suggesting an application method and highlighting the advantages. The proposed forecasting methodology delivers a high improvement of the lowest quantiles’ reliability, allowing perfect reliability for the 1% quantile and a reduction of roughly 75% in overconfidence for the 0.1% quantile.

Future extreme precipitation frequency in the eastern Mediterranean: a new approach exploiting climate model projections

<p>Understanding extreme precipitation under changing climatic conditions is crucial to manage weather- and flood-related hazards. Global and regional climate models are able to provide coarse scale information on future conditions under different emission scenarios, but large uncertainties affect the projected precipitation amounts, extremes in particular, so that frequency analyses cannot be quantitatively trusted. This study uses, for the first time, the Simplified Metastatistical Extreme Value (SMEV) approach to directly exploit synoptic scale information, better represented by climate models, for obtaining projections of future extreme precipitation frequency.</p><p>We use historical rainfall data from >400 stations in Israel and Jordan to (a) provide a climatology of extreme daily precipitation (e.g., the 100-year return period amounts) in the steep climatic gradients of the region and (b) improve understanding of the SMEV description under changing climate. We demonstrate that, using SMEV, it is possible to (c) present the sensitivity of extreme quantiles to occurrence and intensity of Mediterranean lows and other synoptic systems, and (d) project future extreme quantiles starting from synoptic scale information generated by earlier climate-model-based studies. Under our working hypotheses, we project a general decrease of extreme precipitation quantiles for the RCP8.5 scenario; an increase is detected in the coastal region and the Negev arid lands. We discuss the apparent contrast of these results with previous findings.</p>