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This paper derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. (Insur. Math. Econ. 98:92–105, 2021) as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows the constitution of classes of observations with similar tail behaviors depending on the value of the covariates, based on a recursive partition of the sample and simple model selection rules. The results we provide are obtained from concentration inequalities, and are valid for a finite sample size. A misspecification bias that arises from the use of a "Peaks over Threshold" approach is also taken into account. Moreover, the derived properties legitimate the pruning strategies, that is the model selection rules, used to select a proper tree that achieves a compromise between simplicity and goodness-of-fit. The methodology is illustrated through a simulation study, and a real data application in insurance for natural disasters. [ABSTRACT FROM AUTHOR]

Climate change and climate variation influence the occurrence of natural disasters, especially water-related disasters. Landslides are a serious hydrogeohazard in Thailand. Hence, this study aims to project the spatial changes in the landslide susceptibility area in the Nakhon Si Thammarat province of southern Thailand. The study utilizes five climate models of CMIP6 (INM-CM4-8, IITM-ESM, MPI-ESM1-2-LR, CNRM-ESM2-1 and CNRM-CM6.-1) and conducts analyses based on 2 shared socioeconomic pathways (SSPs) of tier 1, which include SSP2-4.5 and SSP5-8.5. The linear scaling bias correction technique is applied to adjust for any biases in the climate models, and the model results are combined using the ensemble mean method. To achieve the study aims, a GIS-aided physically based landslide susceptibility model is used to predict changes in spatial aspects of the landslide susceptibility area. The analysis predicted spatial changes in the landslide susceptibility area over the next 20 years (2023 to 2042). According to the analysis, the results showed that the maximum increase in landslide susceptibility areas is approximately 29%, and the maximum decrease in landslide susceptibility areas is approximately 25% under SSP2-4.5. For SSP5-8.5, the maximum increase in landslide susceptibility areas is approximately 31%, and the maximum decrease in landslide susceptibility areas is approximately 35%. Moreover, the fluctuation of rainfall strongly influences the increase or decrease in landslide susceptibility areas. However, the landslide-prone areas remain located in areas that have experienced landslides in the past. [ABSTRACT FROM AUTHOR]

• This study introduce extreme value theory (EVT) and Peaks Over Threshold (POT) methods into the calculation of takeover time thresholds; a methodology for calculating and verifying takeover time thresholds has been developed. • This study calculated the takeover time thresholds of drivers with different attributes, which can provide support for differentiated management of driver qualifications. • This study can also support regulatory authorities to assess the driver's takeover response ability and support the responsibility division of automated vehicle accidents. In conditional automated driving, the takeover response ability threshold is necessary for driver qualification assessment and liability division of automated vehicle accidents. The primary objective of this study is to establish a clear and quantifiable threshold for drivers' takeover response ability in conditional automated driving scenarios. This threshold aims to serve as a benchmark for evaluating drivers' readiness and developing safety regulations in automated driving. We designed 18 takeover events and invited 42 drivers to participate in the driving simulation experiment, and obtained their takeover time data. First, we analyze the differences of takeover time among drivers with different attributes (gender, age, driving year). Second, based on the Peaks Over Threshold and the generalized Pareto distribution model, we use the graphic method to calculate the range of takeover time threshold for drivers with different attributes. The result shows that the difference in the threshold range of takeover time between male and female drivers is relatively tiny. There are differences in the threshold range of takeover time for different age drivers, and the threshold is negatively correlated with age. Drivers with high driving experience within a safe range are allowed to have longer takeover times. Finally, the rationality of the takeover time threshold for drivers with different attributes has been verified. The return level curves are approximately linear (R2 > 0.77), indicating that the GPD model can capture the overall trend of the return level, which is changing with the probability level. This proves that the takeover time threshold is reasonable. This study uses TTC min to calibrate takeover safety, and the takeover time threshold has a good classification performance for takeover safety (accuracy > 85 %). The above content proves the rationality of the takeover time threshold. The contribution of this study is to calculate the takeover time threshold of drivers with different attributes, which can help regulatory authorities assess the driver's takeover response ability and support the liability division of automated vehicle accidents. [ABSTRACT FROM AUTHOR]

It is well known that the increase in coastal flood hazard is expected to continue due primarily to climate change. While, previous studies have advanced probabilistic approaches for estimating future coastal flood hazard, two seminal issues have received little attention: (1) sea level trend projections that arise as a consequence of climate change not being incorporated in nonstationary coastal flood frequency analysis and (2) traditional stationary approaches that estimate return periods are not suited for analysis of nonstationary water levels. In this paper, a regression approach for sea level rise estimation is proposed to detrend water levels. The peak-over-threshold approach is used to analyze the probabilistic behavior of detrended water levels via a generalized Pareto distribution. Two interpretations of return period—the expected waiting time until an exceedance event occurs and the time associated with the expected number of exceedance events equal to one—are elaborated in a nonstationary context. By incorporating the existing sea level trend projections and using two interpretations of return period, flood hazard curves with uncertainty (i.e., water levels vs. return periods) are developed to describe the probabilistic behavior of future coastal flood hazards. Two case studies are conducted: one for Boston, Massachusetts, and one for New York City, New York. [ABSTRACT FROM AUTHOR]

Motivated by empirical observations, we proposed a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution, we found that the income distribution is described by a generalized Pareto distribution (GPD) with three parameters. We observed that there is a parameter η in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically showed that, for typical market-economy countries, η is significantly close to 0, indicating that the income distribution is characterized by a two-class pattern: The bottom 90% of the population is approximated by an exponential distribution, while the richest 1%~3% is approximated by an asymptotic power law. However, we empirically found that in China during the period of the planned economy and the early stages of market reform (from 1978 to 1990), η deviated significantly from 0, indicating that the bottom of the population no longer conformed to an exponential distribution. [ABSTRACT FROM AUTHOR]

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model. [ABSTRACT FROM AUTHOR]

Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions. [ABSTRACT FROM AUTHOR]

The detection of nonstationarities in partial duration time series (PDS) depends on several factors, including the length of the time series, the selected statistical test, and the heaviness of the tail of the distribution. Because of the more limited attention received in the literature when compared to the trend detection on block maxima variables, we perform a Monte Carlo simulation study to evaluate the performance of different approaches: Spearman's rho, Mann–Kendall, ordinary least squares (OLS), Sen's slope estimator (SEN), and the nonstationary generalized Pareto distribution fit to identify the presence of trends in PDS records characterized by different sample sizes (n), shape parameter (ξ) and degrees of nonstationarity. The results point to a power gain for all tests by increasing n and the degree of nonstationarity and by reducing ξ. The use of a nonparametric test is recommended in samples with a high positive skew. Furthermore, the use of sampling rates greater than one to increase the PDS sample size is encouraged, especially when dealing with small records. The use of SEN to estimate the magnitude of a trend is preferable over OLS due to its slightly smaller probability of occurrence of type S error when ξ is positive. [ABSTRACT FROM AUTHOR]

Copyright of Canadian Water Resources Journal / Revue Canadienne des Ressources Hydriques is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the context of robust Bayesian analysis, studies mainly focus on computing the range of some quantities of interest when the prior distribution varies in a class. We use the concept of distorted bands to introduce a family of priors on the shape parameter of the Generalized Pareto distribution. We show how certain properties of the likelihood ratio order allow us to propose novel sensitivity measures for Value at Risk and Conditional Value at Risk, which are the most useful and reliable risk measures. Although we focus on the Generalized Pareto distribution, which is essential in Extreme Value Theory, the new sensitivity measures could be employed for all the distributions that verify certain conditions related to likelihood ratio order. A thorough simulation study was carried out to perform a sensitivity analysis, and two illustrative examples are also provided. [ABSTRACT FROM AUTHOR]

Estimating generalised Pareto distribution (GPD) parameters is a fundamental step in modelling the extremevalue distribution of random variables. It is generally done with the maximum likelihood method, but there are generally difficulties in estimating GPD parameters using this method as there is no closed-form solution for the first derivative of the GPD log-likelihood function. This makes the solution difficult to determine analytically. However, numerical methods can be used as an alternative. Therefore, this study estimates the solution numerically using a simple fixed-point iteration method that is intuitive for both practitioners and professionals. We obtained three fixed-point iterations when estimating GPD parameters that met the unbiased estimator and convergence criteria. The iterations allow practitioners and professionals to directly and efficiently estimate GPD parameters when modelling extreme-value distributions of random variables. [ABSTRACT FROM AUTHOR]

Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis. [ABSTRACT FROM AUTHOR]

Determining the extreme wind speed and basic wind speed in mountain areas is the fundamental topic in wind-resistant design for engineering structures. The traditional epochal approach commingles all types of wind's maximum speeds in a hybrid set regardless of their respective distributions. While the mountain wind climate is a typical mixed system that consists of local and synoptic wind events, differences in meteorological mechanisms lead to deviation in their wind speed distribution. Therefore, it is necessary to distinguish the mixed wind speed distribution and calculate the combined extreme wind speed. This study extends the extreme wind speed theory in mixed wind climates to the mountain wind field. The measured mountain wind data are classified into periodic thermally-driven winds caused by local thermal gradient, cooling windstorms driven by cold high pressure, and sudden intense winds caused by severe convection. Their respective distribution parameters are determined through the peaks-over-threshold approach with generalized Pareto distribution, and the combined extreme wind speed concluding all types of wind is obtained. The combined extreme wind speeds considering wind direction and attack angle are subsequently obtained. Results show that the combined value is a conservative estimation in mountain mixed wind climates. [ABSTRACT FROM AUTHOR]

The downside risks in stock markets may lead to huge losses and bring profound impact on businesses and governments. In order to model and predict these risks in Chinese stock markets, we propose using Gaussian mixture model to fit the risks within a given threshold, while fitting the extreme risks exceeding the threshold with a marked self-exciting point process. In the simulation study, we establish the consistencies of estimators and evaluate the performances of our proposed models by the accuracy of predicted VaR. Finally we apply our proposed models to analyze the behaviors of four real data sets. In order to illustrate our proposed approach can obtain an improved estimate for the VaR, CAViaR and the GARCH-EVT models are chosen for comparative analysis. The analysis shows that our proposed model have better performances than its competitors. [ABSTRACT FROM AUTHOR]

Extreme quantile regression provides estimates of conditional quantiles outside the range of the data. Classical quantile regression performs poorly in such cases since data in the tail region are too scarce. Extreme value theory is used for extrapolation beyond the range of observed values and estimation of conditional extreme quantiles. Based on the peaks-over-threshold approach, the conditional distribution above a high threshold is approximated by a generalized Pareto distribution with covariate dependent parameters. We propose a gradient boosting procedure to estimate a conditional generalized Pareto distribution by minimizing its deviance. Cross-validation is used for the choice of tuning parameters such as the number of trees and the tree depths. We discuss diagnostic plots such as variable importance and partial dependence plots, which help to interpret the fitted models. In simulation studies we show that our gradient boosting procedure outperforms classical methods from quantile regression and extreme value theory, especially for high-dimensional predictor spaces and complex parameter response surfaces. An application to statistical post-processing of weather forecasts with precipitation data in the Netherlands is proposed. [ABSTRACT FROM AUTHOR]

This paper aims to study the forecasting capabilities of several models under the Markov regime‐switching (MRS) and the extreme value theory (EVT) frameworks applied to daily electricity prices in the New Zealand electricity market. The MRS models in this study include up to five regimes, with time‐varying transition probabilities and incorporation of external market variables. We apply Hamilton's filter with maximum likelihood estimation for parameter estimation. The EVT peaks‐over‐threshold (EVT‐PoT) framework is also considered, and its relationship to the MRS class of models is discussed. We generate out‐of‐sample forecasts under various market scenarios. The MRS models are able to replicate real price densities under stable market conditions. The EVT‐PoT model performs well despite its lack of complexity compared to the MRS framework. We attribute this to the usage of the generalized Pareto distribution to model price extremities. [ABSTRACT FROM AUTHOR]

To measure uncertainties of site-specific extreme loads for a signature bridge, a probabilistic method is developed based on structural health monitoring data in the Bayesian context. Compared with respective design loads, the probability of the predicted extreme load exceeding the design one is used to determine whether the design load is sufficient. The generalized Pareto distribution was first employed to model extreme value information. Then, Bayesian estimation was applied to predict probabilistic distributions of extreme loads, accounting for uncertainties within the prediction process. Finally, the effectiveness of the proposed method was validated through wind speed and temperature measurements from the Nanjing Dashengguan Yangtze River Bridge. The extreme wind speed and four types of thermal loads were predicted based on site-specific monitored loading data by using Bayesian estimation of the generalized Pareto distribution. As a result, the design wind speed and design change in uniform temperature are sufficient for the signature bridge. However, the probability that the predicted extreme vertical girder temperature difference exceeds the design one is 99.96%, and the probabilities subject to the transverse girder temperature difference and tower temperature difference are almost 100%. [ABSTRACT FROM AUTHOR]

Extreme value theory motivates estimating extreme upper quantiles of a distribution by selecting some threshold, discarding those observations below the threshold and fitting a generalized Pareto distribution to exceedances above the threshold via maximum likelihood. This sharp cutoff between observations that are used in the parameter estimation and those that are not is at odds with statistical practice for analogous problems such as nonparametric density estimation, in which observations are typically smoothly downweighted as they become more distant from the value at which the density is being estimated. By exploiting the fact that the order statistics of independent and identically distributed observations form a Markov chain, this work shows how one can obtain a natural weighted composite log-likelihood function for fitting generalized Pareto distributions to exceedances over a threshold. A method for producing confidence intervals based on inverting a test statistic calibrated via parametric bootstrapping is proposed. Some theory demonstrates the asymptotic advantages of using weights in the special case when the shape parameter of the limiting generalized Pareto distribution is known to be 0. Methods for extending this approach to observations that are not identically distributed are described and applied to an analysis of daily precipitation data in New York City. Perhaps the most important practical finding is that including weights in the composite log-likelihood function can reduce the sensitivity of estimates to small changes in the threshold. [ABSTRACT FROM AUTHOR]

Confounding variables are a recurrent challenge for causal discovery and inference. In many situations, complex causal mechanisms only manifest themselves in extreme events, or take simpler forms in the extremes. Stimulated by data on extreme river flows and precipitation, we introduce a new causal discovery methodology for heavy-tailed variables that allows the effect of a known potential confounder to be almost entirely removed when the variables have comparable tails, and also decreases it sufficiently to enable correct causal inference when the confounder has a heavier tail. We also introduce a new parametric estimator for the existing causal tail coefficient and a permutation test. Simulations show that the methods work well and the ideas are applied to the motivating dataset. [ABSTRACT FROM AUTHOR]

This article studies the model proposed by Laudagé et al. (Insur Math Econ 88:77–92, 2019) and examines whether the combination between a Generalized Linear Model (GLM) and a Generalized Pareto Distribution (GPD) is valid for modeling claims severity in a practical framework. For this, we consider a real fire insurance dataset and fit the proposed model to these data. In this modeling, the threshold is of great importance since it separates the data into two parts and represents the point from which the observations become extremes. Therefore, in order to guarantee the correct choice of this threshold, one extra method is adopted in addition to that used by Laudagé et al. (2019). Furthermore, we build on the authors' results and extend them by fitting the attritional data to three well-known distributions. The results of this study show that the GLM-GPD combination outperforms the benchmark model (classical GLM) in terms of predictive power. In addition, the application of an excess of loss reinsurance treaty to these two models proves that it is more interesting for an insurer to adopt a GLM-GPD combination so as not to underestimate the risk and go bankrupt. This justifies that the combined modeling is reasonably good to describe insurance claim costs. [ABSTRACT FROM AUTHOR]

The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is shown to be minimal in all cases, so that the variability expressed by the standard error becomes the principal reliability metric. Peak-over-threshold (POT) methods are shown to always be more reliable than epoch methods due to the additional sub-epoch data. The generalized asymptotic methods are shown to always be less reliable than the sub-asymptotic methods by a factor that increases with MRI. This study reinforces the previously published theory-based arguments that GEV and GPD are unsuitable models for extreme wind speeds by showing that they also provide the least reliable predictions in practice. A new two-step Weibull-XIMIS hybrid method is shown to have superior reliability. [ABSTRACT FROM AUTHOR]

The modified Anderson-Darling test statistics have been suggested in testing the highly skewed distributions to detect more possible departures in the right (or left) tail. In this paper, we propose the corresponding modified likelihood ratio test statistics, and compare their performances for the Gumbel distribution with the modified Anderson-Darling test statistics. We also provide the approximate critical values for the generalized extreme value distribution and generalized Pareto distribution where the unknown shape parameter is present. [ABSTRACT FROM AUTHOR]

A critical stage in drought risk assessment is the measurement of drought hazard, the probability of occurrence of a potentially damaging event. The standard approach to assess drought hazard is based on the standardized precipitation index (SPI) and a drought intensity classification established according to a fixed set of SPI values. We show that this method does not allow for the assessment of region-specific hazards, and we propose an alternative method based on the extreme value theory. We model precipitation using an extreme value mixture model, with a normal distribution for the bulk, and a generalized Pareto distribution for the upper and lower tails. The model estimation allows us to identify the threshold value below which precipitation can be qualified as extreme. The quantile function is used to measure the intensity of each category of droughts and calculate the drought hazard index (DHI). By construction, the DHI value varies according to the specific characteristics of the left tail of the precipitation distribution. To test the relevance of our approach, we estimate the DHI over a gridded set of rainfall data covering West Africa, a large and climatically heterogeneous region. The results show that our mixture model fits the data better than the model used for SPI calculation. In particular, our model performs better to identify extreme precipitation in the left tail of the distribution. The DHI map highlights clusters of high drought hazard located in the central part of the region under study. [ABSTRACT FROM AUTHOR]

The objective of this research was to develop a mathematical and statistical model for long-term prediction. The Extreme Value Theory (EVT) was applied to analyze the appropriate distribution model by using the peak-over-threshold approach with Generalized Pareto Distribution (GPD) to predict daily extreme precipitation and extreme temperatures in eight provinces located in the upper northeastern region of Thailand. Generally, each province has only 1-2 meteorological stations, so spatial analysis cannot be performed comprehensively. Therefore, the reanalysis data were obtained from the NOAA Physical Sciences Laboratory. The precipitation data were used for spatial analysis at the level of 25 square kilometers, which comprises 71 grid points, whereas the temperature data were used for spatial analysis at the level of 50 square kilometers, which includes 19 grid points. According to the analysis results, GPD was appropriate for the goodness of fit test with Kolmogorov-Smirnov Statistics (KS Test) according to the estimation for the return level in the annual return periods of 2 years, 5 years, 10 years, 25 years, 50 years, and 100 years, indicating the areas with daily extreme precipitation and extreme temperatures. The analysis results would be useful for supplementing decision-making in planning to cope with risk areas as well as in effective planning for resources and prevention. [ABSTRACT FROM AUTHOR]

In addition to the characteristics of leptokurtic fat-tailed distribution, financial sequences also exhibit typical volatility and jumps. Moreover, jumps exhibit self-exciting and clustering characteristics under extreme events. However, studies on dynamic margin levels often ignore jumps. In this study, we combine the self-exciting stochastic volatility with correlated jumps (SE-SVCJ) model with a generalized Pareto distribution (GPD) to measure the optimal margin level for the stock index futures market. Value at risk (VaR) is estimated and forecasted using the SE-SVCJ-GPD, SVCJ-GPD, and generalized autoregressive conditional heteroskedasticity with GPD (GARCH-GPD) models. SE-SVCJ-GPD can undertake more risks in the long or short trading position of stock index futures contracts. Moreover, the backtesting experiment results show that the SE-SVCJ-GPD model provides a more accurate margin level forecast than the other methods in both positions. This study's findings have practical significance and theoretical value for assessing the level of risk and taking corresponding risk-prevention measures. [ABSTRACT FROM AUTHOR]

This paper details the approach of the team Kohrrelation in the 2021 Extreme Value Analysis data challenge, dealing with the prediction of wildfire counts and sizes over the contiguous US. Our approach uses ideas from extreme-value theory in a machine learning context with theoretically justified loss functions for gradient boosting. We devise a spatial cross-validation scheme and show that in our setting it provides a better proxy for test set performance than naive cross-validation. The predictions are benchmarked against boosting approaches with different loss functions, and perform competitively in terms of the score criterion, finally placing second in the competition ranking. [ABSTRACT FROM AUTHOR]

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The spatial and spatio-temporal dependence modeling to extreme value distributions have been used to analyze the extremes of daily maximum rainfall data across selected weather stations in South Africa combining generalized Pareto distribution (GPD) with the flexible Bayesian Latent Gaussian Model (LGM). The paper demonstrated the spatio-temporal GPD model for applications in extreme rainfall data that capture systematic variation through spatial and spatio-temporal modeling framework, in which the temporal constitutes the week and month as random separately. The paper uses the Bayesian integrated Nested Laplace approximation (INLA) algorithm to estimate marginal posterior means of the parameters and hyper-parameters for Bayesian spatio-temporal models. The Bayesian inferences using INLA technique were applied to obtain prediction of the return levels at each station, which incorporate uncertainty due to model estimation, as well as the randomness that is inherent in the processes. [ABSTRACT FROM AUTHOR]

We introduce a smooth-transition generalized Pareto (GP) regression model to study the time-varying dependence structure between extreme losses and a set of economic factors. In this model, the distribution of the loss size is approximated by a GP distribution, and its parameters are related to explanatory variables through regression functions, which themselves depend on a time-varying predictor of structural changes. We use this approach to study the dynamics in the monthly severity distribution of operational losses at a major European bank. Using the VIX as a transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past are indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the growth rate of the economy seems to be a relevant predictor of the likelihood of extreme losses. [ABSTRACT FROM AUTHOR]

All the available information and uncertainties should be taken into account in a model to give correct answer to a stated problem and evaluate the performance of a structure. This study deals with the impact of parameter estimation uncertainty in extreme wind speeds on the assessed reliability index using frequentist approach. The peak-over-threshold approach with an automated threshold selection method is applied and bootstrapping is used to determine the 95% confidence interval of the estimated reliability index. Based on the results practical recommendations, i.e., a framework of this procedure are derived on how to handle peak-over-threshold in extreme wind speed models for the application of the proposed performance-based wind engineering design. [ABSTRACT FROM AUTHOR]

In randomized clinical trials, methods of pairwise comparisons such as the 'Net Benefit' or the 'win ratio' have recently gained much attention when interests lies in assessing the effect of a treatment as compared to a standard of care. Among other advantages, these methods are usually praised for delivering a treatment measure that can easily handle multiple outcomes of different nature, while keeping a meaningful interpretation for patients and clinicians. For time‐to‐event outcomes, a recent suggestion emerged in the literature for estimating these treatment measures by providing a natural handling of censored outcomes. However, this estimation procedure may lead to biased estimates when tails of survival functions cannot be reliably estimated using Kaplan–Meier estimators. The problem then extrapolates to the other outcomes incorporated in the pairwise comparison construction. In this work, we suggest to extend the procedure by the consideration of a hybrid survival function estimator that relies on an extreme value tail model through the Generalized Pareto distribution. We provide an estimator of treatment effect measures that notably improves on bias and remains easily apprehended for practical implementation. This is illustrated in an extensive simulation study as well as in an actual trial of a new cancer immunotherapy. [ABSTRACT FROM AUTHOR]

Recently, there has been an increase in the occurrence of extreme high-temperature events across the China–Pakistan Economic Corridor (CPEC). Regional spatiotemporal identification and evaluation of extreme high temperatures are essential for accurate forecasting of future climate changes. When such events generate a meteorological hazard, it is important to understand their temporal and spatial features, return period, and identification criteria. Accurately identifying extreme events can help assess risk and predict their spatial–temporal variation. While past studies have focused on individual sites, extreme heat events generally manifest as spatially and temporally continuous regional events. In this study, we propose an objective identification technique based on gridded data and spatiotemporal continuity to reveal the spatiotemporal characteristics of intensity, frequency, and duration events of extreme heat events in the CPEC from May to October between 1961 and 2015. Furthermore, we estimate the return period of extreme heat in the study region using the generalized Pareto distribution (GPD). Our findings indicate that the historical extreme temperature events (intensity, frequency, and duration) in the CPEC have significantly increased. Areas with a high incidence of extreme heat events are concentrated in eastern Balochistan, northern Sindh, and southeastern Punjab. These findings suggest that disaster prevention and mitigation plans should be targeted towards areas with a high frequency of extreme heat events in the CPEC, allowing policy makers to better prepare for and respond to future events. [ABSTRACT FROM AUTHOR]

To measure uncertainties within anomaly detection and distinguish sensor faults from anomalous events, a multi-index probabilistic anomaly detection approach is proposed for large span bridges based on Bayesian estimation and evidential reasoning. To avoid false detection raised by signal spikes, an energy index is first defined and extracted from pre-processed measurements, including missing data recovery and thermal response separation. Then, a probabilistic index, namely, certainty degree, is derived from probability density functions of detection triggers – extreme values predicted by using Bayesian estimation of the generalized Pareto distribution. To distinguish sensor faults from anomalous scenarios, evidential reasoning is applied to incorporate multiple certainty degrees into a joint one under the assumption that the probability of multi-sensor failing simultaneously is extremely low. Specifically, a large joint certainty degree indicates a high occurrence probability of anomalous scenarios, while a small one together with a large individual certainty degree depicts a high probability of sensor faults. Finally, the effectiveness of the proposed anomaly detection method is validated through structural health monitoring data from the Nanjing Dashengguan Yangtze River Bridge. Measurements from four sensors, that is, three cable forces and one deflection, are selected to detect anomalies based on their high pair-wise correlations. Two case studies are presented, namely, sensor fault detection and snow disaster detection. The sensor fault is detected through a certainty degree of almost 100% for the individual index and a joint certainty degree of nearly 0. The snowstorm is detected by a joint certainty degree of 36.82%. [ABSTRACT FROM AUTHOR]

We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalized Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements. [ABSTRACT FROM AUTHOR]

In the present study, Flood Frequency Analysis (FFA) is performed on the daily inflows of a reservoir dam taken as a case study. The Peaks-Over-Threshold (POT) approach was adopted. A comparison between the default generalized Pareto distribution and the best distribution fitted to the data has been carried out. After the risk analysis, the reliability of the structure decreases to 25.60% for the chosen threshold values if the best distribution is adopted instead of the default fit. [ABSTRACT FROM AUTHOR]

This article proposes an open-set recognition model that is based on the use of extreme value statistics. For this purpose, a distance ratio is introduced that expresses how dissimilar a target point is from the known classes by considering the ratio of distances locally around the target point. It is shown that the class of generalized Pareto distributions with bounded support can be used to model the peaks of the distance ratio above a high threshold. The resulting distribution provides a probabilistic framework to perform open-set recognition. Furthermore, we describe a numerical procedure to estimate the hyperparameters of our model. This procedure is based on a new objective function that considers both the fit of the generalized Pareto distribution and the misclassification error of the known classes. Our method is applied to three image datasets and an audio dataset showing that it outperforms similar open-set recognition and anomaly detection methods. for this article are available online. [ABSTRACT FROM AUTHOR]

• Short-term electricity generation data is used to calculate PGF for Khartoum. • Peaks over threshold method is utilized to model the highest power generation. • The obtained PGF equals 4, whereas in PV potential map equals 4.8. • This factor shall facilitate PV system sizing for local engineers. In this research, the authors used the Peaks over Threshold (POT) method alongside short-term electricity generation data belonging to a 5.5 kW p off-grid photovoltaic (PV) system installed on the premises of the National Energy Research Center in Soba district, Khartoum, to estimate the panel generation factor (PGF) of the city that rests within Sudan's capital. PGF is a fundamental technical figure primarily used in the design/sizing of solar PV systems. The addressed problem here is to calculate this coefficient with an acceptable accuracy constrained by insufficient electricity generation data from a PV system operating at its maximum capacity, relying on statistical modeling methods, which is the research novelty. Accordingly, we obtained an approximate PGF of 4 utilizing the POT technique that resulted in a threshold of 19 and Generalized Pareto distribution estimators of 2.2 × 10 - 16 and 2.3 for the shape and scale parameters, respectively. In the literature, the corresponding factor value is 4.8, illustrated in Sudan's PV potential map, based on historical long-term solar irradiance satellite records. Consequently, a 16.67% Percent Error between the two values is present due to the big difference in data amount, favoring the literature. However, in front of relatively abundant data, we believe the Extreme Value Theory methodology applied here will demonstrate robustness in approximating the target factor digits and validating Sudan's map numbers. Finally, this effort shall enable local engineers to blueprint well-assessed PV systems and support the endeavors to scientifically document Sudan's PV energy capacity, which the country lacks very much. [ABSTRACT FROM AUTHOR]

Exceedance analysis aims to model extreme data that are in the tail of the distribution, with these values being greater than a threshold. In this type of modelling, the tail can usually have different types of shapes. For exceedance, the extreme value theory shows that generalized Pareto distribution (GPD) is the limit distribution of sufficiently large thresholds. The studies on extreme analysis primarily focus on estimating the probability of the occurrence of extreme events, which are the values that are in the highest quantiles of the distribution. Based on this, this work proposed a quantile regression model for the GPD distribution, where the high quantiles of the distribution are written as a function of covariates. The proposed model also allows the regression parameters to vary over time. The parameter estimation of these new models is conducted under the Bayesian paradigm. Simulations are conducted to analyze the performance of our proposed models. Results of temperature applications in the USA and Brazil (environmental data) and consumer price index in Brazil (financial data) have efficiently explained how covariates influence the quantile behaviour over time. [ABSTRACT FROM AUTHOR]

We discuss three estimation methods: the method of moments, probability weighted moments, and L-moments for the scale parameter and the extreme value index in the generalized Pareto distribution under linear normalization. Moreover, we adapt these methods to use for the generalized Pareto distribution under power and exponential normalizations. A simulation study is conducted to compare the three methods on the three models and determine which is the best, which turned out to be the probability weighted moments. A new computational technique for improving fitting quality is proposed and tested on two real-world data sets using the probability weighted moments. We looked back at various maximal data sets that had previously been addressed in the literature and for which the generalized extreme value distribution under linear normalization had failed to adequately explain them. We use the suggested procedure to find good fits. [ABSTRACT FROM AUTHOR]

In this study, inspection planning of deteriorating bridges is optimized to determine the inspection application times and methods based on various objectives. These objectives can be formulated by considering the probabilistic structural performance and service life after inspection and maintenance. Probabilistic structural performance and service life prediction are generally based on the probability of failure (or reliability). However, there are difficulties associated with optimizing inspection planning when a low probability of failure is estimated. In this study, we address inspection planning using extrapolation approaches to efficiently compute a low probability of failure. The inspection planning method proposed in this study determines the inspection application times for a given inspection method. We investigated the applicability of direct Monte Carlo simulation (MCS), subset simulation, and two extrapolation approaches (i.e., kernel density estimation (KDE) and KDE combined with generalized Pareto distribution (GPD)) for inspection planning. The probability of failure for optimum inspection planning was based on the damage detection-based state function and extended service life-based state function. These state functions were formulated by considering damage propagation, damage detection by inspections, and service life extensions by maintenance. Illustrative applications to general examples and an existing bridge are provided to investigate the effects of approaches for computing the failure probability on the accuracy and variation of the optimum inspection application times. Finally, the most appropriate approach for optimum inspection planning was determined considering the accuracy and reliability of the solution, computational efficiency, and the applicability of the probabilistic optimization process. The presented investigations revealed that KDE is more appropriate than MCS and the combination of KDE and GPD for optimum inspection planning. [ABSTRACT FROM AUTHOR]

Attempts to use the generalized extreme value distribution and generalized Pareto distribution with the maximum likelihood estimates on the extreme rainfall data at one weather station over Phitsanulok province. This paper gathered the rainfall data from January 1987 to December 2021. The estimated return level is 10, 20, 50, and 100 years. The result displays the modeling of the generalized extreme value distribution (GEV); the Gumbel distribution was a fitting proposal for extreme annual rainfall in Phitsanulok province, with µ = 24.95(1.39), σ=22.59(1.06), and ξ=0.03(0.05). In addition, the modeling of the generalized Pareto distribution (GPD) with daily rainfall data in Phitsanulok province had to fit on σ=49.08(2.99), and ξ=-0.28(0.03). Moreover, we obtained return levels with an upward trend in the change in return periods. [ABSTRACT FROM AUTHOR]

Probabilistic seismic hazard analyses (PSHA) require that at least the mean activity rate be known, as well as the distribution of magnitudes. Within the Gutenberg–Richter assumption, the magnitudes follow an exponential distribution which is upperly truncated to a maximum possible magnitude denoted m max . This parameter is often fixed from expert judgement under seismo-tectonic considerations, due to a lack of universal method. This paper proposes an alternative to the common Gutenberg Richter model based on the extreme value theory: it models the tail distribution of the magnitudes with a generalized Pareto distribution (GPD). To integrate this GPD model in a PSHA calculation for areas of low to moderate seimsicity, we propose the Randomized Gutenberg–Richter model: this is an innovative approach based on the usual exponential distribution where m max is randomized and follows a distribution defined from that previous GPD model. The inference process takes into account the time varying level of completeness of the catalogue and the uncertainty in the magnitude value itself. In order to quantify the impacts of the new model on the seismic hazard levels, we implemented it into a realistic probabilistic seismic hazard calculation. Results indicate that the Randomized Gutenberg–Richter model seems to be very useful for future PSHA models. This new recurrence model avoids having to fix a priori the maximum possible magnitude m max . This is particularly interesting as there is no widely accepted method to estimate that upper bound. [ABSTRACT FROM AUTHOR]

Monsoon-related extreme flood events are experienced regularly across India, bringing costly damage, disruption and death to local communities. This study provides a route towards estimating the likely magnitude of extreme floods (e.g., the 1-in-100-year flood) at locations without gauged data, helping engineers to design resilient structures. Gridded rainfall and evapotranspiration estimates were used with a continuous simulation hydrological model to estimate annual maximum flow rates at nine locations corresponding with river flow gauging stations in the Wainganga river basin, a data-sparse region of India. Hosking–Wallis distribution tests were performed to identify the most appropriate distribution to model the annual maxima series, selecting the Generalized Pareto and Pearson Type III distributions. The L-moments and flood frequency curves of the modeled annual maxima were compared to gauged values. The Probability Distributed Model (PDM), properly calibrated to capture the dynamics of peak flows, was shown to be effective in approximating the Generalized Pareto distribution for annual maxima, and may be useful in modeling peak flows in areas with sparse data. Confidence in the model structure, parameterization, input data and catchment representation build confidence in the modeled flood estimates; this is particularly relevant if the method is applied in a location where no gauged flows exist for verification. [ABSTRACT FROM AUTHOR]

Carburized Cr-Ni steel is widely used in the manufacture of components in many fields due to excellent performance, of which the service life has been a concern. In order to investigate the high-cycle-fatigue and very-high-cycle-fatigue properties of carburized Cr-Ni gear steel, axial loading fatigue tests were performed by QBG-100 with stress ratios of −1, 0 and 0.3. The Generalized Pareto distribution was used to evaluate the inclusion size of carburized Cr-Ni gear steel. Based on the stress ratio and the evaluated crack size, a new fatigue life prediction model for carburized Cr-Ni gear steels was constructed. The results show that the S–N characteristics of carburized Cr-Ni gear steel represent the continuously descending tendency. Based on the long crack propagation threshold and the instability propagation threshold of carburized Cr-Ni gear steel, the sizes of FGA, fisheye and surface smooth area (SSA) can be evaluated, respectively. In addition, the maximum size of surface and interior inclusion of carburized Cr-Ni gear steel are 17.50 μm and 6.46 μm with a cumulative probability of 99.9%. By validating the new established model, the prediction result is acceptable according to the good consistency between the predicted life and the experimental life. [ABSTRACT FROM AUTHOR]

Recent research in the area of univariate mixture modeling indicated that the finite mixture models based on Burr and Inverse Burr component distributions perform well in the modeling of heavy-tail insurance data. Mixture models are able to capture the multimodality which is quite a common characteristic of insurance losses. Through an extensive simulation study, we assess the performance of three different methods in building the confidence intervals for high quantiles of the mixtures of Burr and Inverse Burr distributions. First, we provide mathematical justification for linking the tail of the k-Burr and k-Inverse Burr mixtures to the maximum domain of attraction of the Fréchet distribution which allows us to employ the Generalized Pareto Distribution (GPD) in the estimation of high quantiles and their corresponding confidence intervals. Then, we compare these results to those obtained using order statistics and the bootstrap methods. We also modified the existing Peak Over Threshold (POT) algorithm for the efficient computation of the confidence intervals in the upper tail of these mixture models. A real data set on Danish Fire Losses is used to illustrate the application of these methods in practice. [ABSTRACT FROM AUTHOR]

Extreme rain events have caused numerous issues and have had a significant impact on agriculture, human activities, ecology, infrastructure, and casualties. The theory of extreme values has been widely applied in extreme precipitation modelling and a variety of other fields. This paper employs the generalized Pareto distribution, which has been widely used to analyse extreme climates, in conjunction with the peak over thresholds approach to investigate exceedances. The occurrence of intense rainfall events in Kigali city causes severe damage to human properties, infrastructure damage, people injuries, loss of life, and other various harmful consequences. Early detection of extreme rainfall in Kigali aids in the development and implementation of strategies and measures to mitigate the negative effects of extreme rainfall before it occurs. The aim of this research is to estimate the frequency and magnitude of intense rainfall events in Kigali. The daily rainfall data from Kigali Airport station collected by Rwanda Meteorological Agency from 1990 to 2019 were applied. The results showed that as the return periods increased, so did the return levels, implying that the intensity and frequency of rainfall in Kigali will increase in the future. The model's goodness was tested, and the study suggests a model that has a non‐negative shape parameter (ξ) to be good. The study's findings are extremely important for understanding the occurrence of these events and also serve as a tool for decision‐making and the development of policies aimed at mitigating the effects of such events. [ABSTRACT FROM AUTHOR]

Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis. Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM 2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction model based on long short-term memory (LSTM) is used to predict PM 2.5 concentration, achieving ideal results. [ABSTRACT FROM AUTHOR]

This article introduces lookout, a new approach to detect outliers using leave-one-out kernel density estimates and extreme value theory. Outlier detection methods that use kernel density estimates generally employ a user defined parameter to determine the bandwidth. Lookout uses persistent homology to construct a bandwidth suitable for outlier detection without any user input. We demonstrate the effectiveness of lookout on an extensive data repository by comparing its performance with other outlier detection methods based on extreme value theory. Furthermore, we introduce outlier persistence, a useful concept that explores the birth and the cessation of outliers with changing bandwidth and significance levels. The R package lookout implements this algorithm. Supplementary files for this article are available online. [ABSTRACT FROM AUTHOR]

We compute the value-at-risk of financial losses by fitting a generalized Pareto distribution to exceedances over a threshold. Following the common practice of setting the threshold as high sample quantiles, we show that, for both independent observations and time-series data, the asymptotic variance for the maximum likelihood estimation depends on the choice of threshold, unlike the existing study of using a divergent threshold. We also propose a random weighted bootstrap method for the interval estimation of VaR, with critical values computed by the empirical distribution of the absolute differences between the bootstrapped estimators and the maximum likelihood estimator. While our asymptotic results unify the inference with nondivergent and divergent thresholds, the finite sample studies via simulation and application to real data show that the derived confidence intervals well cover the true VaR in insurance and finance. [ABSTRACT FROM AUTHOR]