Spatial clustering of heavy clustering in ERA-5 precipitation over Europe}

<p>Extreme precipitation often cause floods and lead to important societal and economical damages. Rainfall is subject to local orography features and their intensities can be highly variable. In this context, identifying climatically coherent regions for extremes is paramount to understand and analyze rainfall at the correct spatial scale. We assume that the region of interest can be partitioned into homogeneous regions. In other words, sub-regions with common marginal distribution except a scale factor. As an example, considering extremes as block maxima or excesses over a threshold, a sub-region corresponds to a constant shape parameter. We develop a non-parametric clustering algorithm based on a ratio of Probability Weighted Moments to identify these homogeneous regions and gather weather stations. By construction this ratio does not depend on the location and scale parameters for the Generalized Extreme Value and Generalized Pareto distributions. Our method has the advantage to only rely on raw precipitation data and not on station covariates.</p><p>A simulation data study is performed based on the extended GPD distribution that appears to well capture low, moderate and heavy rainfall intensities. Sensitivity to the number of clusters is analyzed. Results of simulation reveal that the method detects homogeneous regions. We apply our clustering algorithm on ERA-5 precipitation over Europe. We obtain coherent homogeneous regions consistent with local orography. The marginal precipitation behaviour is analyzed through regional fitting of an extended GPD.</p>

Modeling of Extreme Values via Exponential Normalization Compared with Linear and Power Normalization

Several new asymmetric distributions have arisen naturally in the modeling extreme values are uncovered and elucidated. The present paper deals with the extreme value theorem (EVT) under exponential normalization. An estimate of the shape parameter of the asymmetric generalized value distributions that related to this new extension of the EVT is obtained. Moreover, we develop the mathematical modeling of the extreme values by using this new extension of the EVT. We analyze the extreme values by modeling the occurrence of the exceedances over high thresholds. The natural distributions of such exceedances, new four generalized Pareto families of asymmetric distributions under exponential normalization (GPDEs), are described and their properties revealed. There is an evident symmetry between the new obtained GPDEs and those generalized Pareto distributions arisen from EVT under linear and power normalization. Estimates for the extreme value index of the four GPDEs are obtained. In addition, simulation studies are conducted in order to illustrate and validate the theoretical results. Finally, a comparison study between the different extreme models is done throughout real data sets.

Inference on P(Y

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25

Experimental Study of Slam Forces on External Turrets With Different Top Angles

The external turret is widely used for mooring FPSOs. However, external turrets can be exposed to slamming and it leads to generate FPSO’s whipping. To analyze the fatigue strength of the FPSOs, probability distributions of slam forces acting when slamming happens are necessary. In this study, we focus on slam force filtered by 10Hz low-pass filter. Then, we examined the probability distribution of peak slam forces, the effect of the top angle on slam forces, and the difference of two types (fixed and oscillator-mounted) tests. For three turret models with different top angle (180°, 160°, and 140°), two types of model tests were carried out. To confirm the experiment’s validity and reliability, we compared these model tests with the previous study. The slam forces measured on a conical (140°) turret were consistent with the estimated curve in the previous study. The comparison of two types of tests indicated that fixed turret tests were an easy and valid way of measuring the slam forces on external turrets. 3-hour return values calculated by five methods were used to examine the characteristic of each turret. And these values were compared with 3-hour mean maxima to examine the difference between the five methods and experimental results. As a result, the use of Generalized Extreme Values and Generalized Pareto distributions is more suitable than using Rayleigh distribution in estimating return values of slam forces on external turrets.

Reliability Inference for the Multicomponent System Based on Progressively Type II Censored Samples from Generalized Pareto Distributions

In this paper, the reliability of a k-component system, in which all components are subject to common stress, is considered. The multicomponent system will continue to survive if at least s out of k components’ strength exceed the common stress. The system reliability is investigated by utilizing the maximum likelihood estimator based on progressively type II censored samples from generalized Pareto distributions. The confidence interval of the system reliability can be obtained by using asymptotic normality with Fisher information matrix or bootstrap method approximation. An intensive simulation study is conducted to evaluate the performance of maximum likelihood estimators of the model parameters and system reliability for a variety of cases. For the confidence interval of the system reliability, simulation results indicate the bootstrap method approximation outperforms over the asymptotic normality approximation in terms of coverage probability.

Application of Extreme Value Theory for Before-After Road Safety Analysis

Because of well-recognized quality and quantity problems associated with historical crash data, traffic conflict techniques have been increasingly used in before-after safety analysis in recent years. This study proposes using an extreme value theory (EVT) approach to conduct traffic conflict-based before-after analysis. The capability of providing confident estimation of extreme events by the EVT approach drives the before-after analysis to shift from normal traffic conflicts to more serious conflicts, which are relatively rare but have more in common with actual crashes. The approach is applied to evaluate the safety effects of converting channelized right-turn lanes into smart channels, based on traffic conflicts defined by time to collision (TTC) and collected from three treatment intersections and one control intersection in the city of Penticton, British Columbia. Odds ratios and treatment effects are calculated from extreme-serious conflicts, the frequencies of which are estimated from the generalized Pareto distributions of traffic conflicts with TTC⩽0.5 s. The results show approximately 34% reduction in total extreme-serious conflicts (i.e., combining merging conflicts and rear-end conflicts), indicating overall a remarkable safety improvement following the smart channel treatment. This finding is consistent with the analysis result based on traffic conflicts with TTC⩽3.0 s. It is also found that the reduction in extreme-serious merging conflicts is small and insignificant. This is caused by the phenomenon that TTC values of merging conflicts become smaller after the treatment, and it is possibly because drivers become more aggressive with the better view of approaching cross-street traffic provided by the smart channel.