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This study applies both stationary and nonstationary generalized extreme value (GEV) models to analyze annual extreme temperature patterns in four stations of Southern Highlands region of Tanzania: Iringa, Mbeya, Rukwa, and Ruvuma over a 30‐year period. Parameter estimates reveal varied distribution characteristics, with the location parameter μ ranging from 28.98 to 33.44, and shape parameter ξ indicating both bounded and heavy‐tailed distributions. These results highlight the potential for extreme temperature conditions, such as heatwaves and droughts, particularly in regions with heavy‐tailed distributions. Return level estimates show increasing temperature extremes, with 100‐year return levels reaching 33.95 °C in Ruvuma. Nonstationary models that incorporate time‐varying location and scale parameters significantly improve model fit, particularly in Mbeya, where such a model outperforms the stationary model (p value = 0.0092). Trend analyses identify significant temperature trends in Mbeya (p value = 0.0123) and Ruvuma (p value = 0.0015), emphasizing the need for adaptive climate strategies. These findings underscore the importance of accounting for nonstationarity in climate models to better understand and predict temperature extremes. [ABSTRACT FROM AUTHOR]

The performance of marine radar constant false alarm rate (CFAR) detection method is significantly influenced by the modeling of sea clutter distribution and detector decision rules. The false alarm rate and detection rate are therefore unstable. In order to address low CFAR detection performance and the modeling problem of non-uniform, non-Gaussian, and non-stationary sea clutter distribution in marine radar images, in this paper, a CFAR detection method in generalized extreme value distribution modeling based on marine radar space-time filtering background clutter is proposed. Initially, three-dimensional (3D) frequency wave-number (space-time) domain adaptive filter is employed to filter the original radar image, so as to obtain uniform and stable background clutter. Subsequently, generalized extreme value (GEV) distribution is introduced to integrally model the filtered background clutter. Finally, Inclusion/Exclusion (IE) with the best performance under the GEV distribution is selected as the clutter range profile CFAR (CRP-CFAR) detector decision rule in the final detection. The proposed method is verified by utilizing real marine radar image data. The results indicate that when the P f a is set at 0.0001, the proposed method exhibits an average improvement in P D of 2.3% compared to STAF-RCBD-CFAR, and a 6.2% improvement compared to STCS-WL-CFAR. When the P f a is set at 0.001, the proposed method exhibits an average improvement in P D of 6.9% compared to STAF-RCBD-CFAR, and a 9.6% improvement compared to STCS-WL-CFAR. [ABSTRACT FROM AUTHOR]

Statistical descriptions of extreme met-ocean conditions are essential for the safe and reliable design and operation of structures in marine environments. The significant wave height ( H S ) is one of the most essential wave parameters for coastal and offshore structural design. Recent studies have reported that a time-varying component exists globally in the H S . Therefore, the non-stationary behavior of an annual maximum series of H S is important for various ocean engineering applications. This study aims to analyze the frequency of H S over the northern Indian Ocean by modeling the non-stationarity in the H S series using a non-stationary Generalized Extreme Value (GEV) distribution. The hourly maximum H S data (with a spatial resolution of 0.5° longitude × 0.5° latitude) collected from the global atmospheric reanalysis dataset of the European Centre for Medium-Range Weather Forecasts (ECMWF) is used for the study. To model the annual maximum series of H S using a non-stationary GEV distribution, two physical covariates (El-Ni n ~ o Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD)) and time covariates are introduced into the location and scale parameters of the GEV distribution. The return levels of various frequencies of H S are estimated under non-stationary conditions. From the results, average increases of 13.46%, 13.66%, 13.85%, and 14.02% are observed over the study area for the 25-year, 50-year, 100-year, and 200-year return periods, respectively. A maximum percentage decrease of 33.3% and a percentage increase of 167% are observed in the return levels of various return periods. The changes in the non-stationary return levels over time highlight the importance of modeling the non-stationarity in H S . [ABSTRACT FROM AUTHOR]

The generalized extreme value (GEV) distribution is a popular model for analyzing and forecasting extreme weather data. To increase prediction accuracy, spatial information is often pooled via a latent Gaussian process (GP) on the GEV parameters. Inference for GEV‐GP models is typically carried out using Markov Chain Monte Carlo (MCMC) methods, or using approximate inference methods such as the integrated nested Laplace approximation (INLA). However, MCMC becomes prohibitively slow as the number of spatial locations increases, whereas INLA is applicable in practice only to a limited subset of GEV‐GP models. In this article, we revisit the original Laplace approximation for fitting spatial GEV models. In combination with a popular sparsity‐inducing spatial covariance approximation technique, we show through simulations that our approach accurately estimates the Bayesian predictive distribution of extreme weather events, is scalable to several thousand spatial locations, and is several orders of magnitude faster than MCMC. A case study in forecasting extreme snowfall across Canada is presented. [ABSTRACT FROM AUTHOR]

This study introduced the application of concepts and methods from extreme value theory (EVT) to estimate the probability that daily minimum temperatures exceed springtime critical temperature thresholds for Pinot noir buds and young shoots as a function of springtime phenology. The springtime frost risk estimates were computed spatially for Pinot noir throughout the Willamette Valley (WV) American Viticultural Area (AVA) using a gridded dataset of historical daily minimum surface air temperature data. EVT-based springtime frost risk maps can inform vineyard-management operations by identifying those locations throughout a wine region with a low risk for any cold injury where remedial action is likely not necessary when there is a forecasted frost event. Frost risk estimates were computed for 1991–2021 and 1991–2022 to examine a potentially changed risk profile for springtime frost events throughout the WV AVA due to the April 2022 advective frost event. The April 2022 advective frost event influenced the risk profile throughout the AVA such that an event of its magnitude is now modelled to occur more frequently. The EVT-based risk analysis can be readily updated each year as new data become available. While spatially varying budbreak calculations facilitated computation of the spring frost risk estimates, the EVT approach profiled in this study does not necessarily depend on potentially uncertain predetermined budbreak date estimates. Gridded maps of extreme daily minimum temperature exceedances, reclassified relative to the springtime phenology critical temperature thresholds for Pinot noir, were readily combined with a ripening potential map to identify optimal areas for vineyard site selection throughout the WV AVA. When simultaneously evaluating Pinot noir ripening potential with springtime frost risk using historical data, the limiting factor for vineyard site selection throughout the WV AVA was frost risk, not ripening potential. The study approach is also applicable for other winegrape-growing regions, assessments of winter freeze risk and summertime heatwaves, and with non-gridded observed temperature datasets. [ABSTRACT FROM AUTHOR]

Climate variability, particularly, that of temperature and precipitation, has received a great deal of attention worldwide. In the present work, we have carried out a thorough statistical modelling of precipitation and temperature extremes by taking century-long (1901–2002) datasets into consideration for Himachal Pradesh, India. Globally, the patterns of extreme weather events have changed from longer and hotter heat waves to heavier rains. A fragile ecosphere, climatic change, and the unique geology of Himachal Pradesh have all led to a sharp increase in natural disasters in the hill state over time. The climate of the state varies by altitude. Since precipitation and temperature are the main driving forces behind climate change, quantifying these two variables over a range of return periods is crucial in policymaking for minimizing the potential harm brought on by variations in these atmospheric elements. The statistical modelling of the meteorological data and probabilistic forecasting were done using extreme value theory (EVT), an advanced statistical modelling approach that is widely acknowledged. The generalized extreme value (GEV) analysis approach of EVT is utilized for the probabilistic forecasting of the extremities. The extreme values and their probable occurrence are estimated once every 50, 80, 100, 120, 200, 250, 300, and 500 years, respectively. By estimating the probabilities of extreme events, we can better understand the potential risks and impacts of climate change and develop strategies to manage and mitigate these risks. [ABSTRACT FROM AUTHOR]

The study investigates the application of Extreme Value Theory in modelling stock prices, aiming to capture the tail behaviour and extreme movements that conventional distributions often fail to represent accurately. The use of Extreme Value Theory has gained considerable attention in the field of finance due to its ability to model rare events, such as financial crises or market crashes. By incorporating Extreme Value Theory, researchers aim to improve risk management, portfolio optimization, and pricing of financial derivatives. In this study, the Log-normal, Weibull, Gamma, and Normal distributions were used to model the stock price closing data, with a specific focus on extreme value distributions. Both graphical explorations and goodness-of-fit criteria were considered together to evaluate the suitability of these distributions. When assessing the data, it was observed that the Weibull distribution provided the best fit for the given stock price closing data. [ABSTRACT FROM AUTHOR]

The effective use of available information in extreme value analysis is critical because extreme values are scarce. Thus, using the r largest order statistics (rLOS) instead of the block maxima is encouraged. Based on the four-parameter kappa model for the rLOS (rK4D), we introduce a new distribution for the rLOS as a special case of the rK4D. That is the generalized logistic model for rLOS (rGLO). This distribution can be useful when the generalized extreme value model for rLOS is no longer efficient to capture the variability of extreme values. Moreover, the rGLO enriches a pool of candidate distributions to determine the best model to yield accurate and robust quantile estimates. We derive a joint probability density function, the marginal and conditional distribution functions of new model. The maximum likelihood estimation, delta method, profile likelihood, order selection by the entropy difference test, cross-validated likelihood criteria, and model averaging were considered for inferences. The usefulness and practical effectiveness of the rGLO are illustrated by the Monte Carlo simulation and an application to extreme streamflow data in Bevern Stream, UK. [ABSTRACT FROM AUTHOR]

Analyzing the statistical behavior of the assets' returns has shown to be an interesting approach to perform asset selection. In this work, we explore a stress-strength reliability approach to perform asset selection based on probabilities of the type P(X < Y) when both X and Y follow a generalized extreme value (GEV) distribution with three parameters. At first, we derive new analytical and closed form relations in terms of the extreme value H-function, which have been obtained under fewer parameter restrictions compared to similar results in the literature. To show the performance of our results, we include a Monte-Carlo simulation study and we investigate the application of the reliability measure P(X < Y) in selecting financial assets with returns characterized by the distributions X and Y. Therefore, rather than the conventional approach of comparing the expected values of X and Y based on modern portfolio theory, we delve into the metric P(X < Y) as an alternative parameter for assessing better returns. [ABSTRACT FROM AUTHOR]

The problem of estimating return levels of river discharge, relevant in flood frequency analysis, is tackled by relying on the extreme value theory. The Generalized Extreme Value (GEV) distribution is assumed to model annual maxima values of river discharge registered at multiple gauging stations belonging to the same river basin. The specific features of the data from the Upper Danube basin drive the definition of the proposed statistical model. Firstly, Bayesian P-splines are considered to account for the non-linear effects of station-specific covariates on the GEV parameters. Secondly, the problem of functional and variable selection is addressed by imposing a grouped horseshoe prior to the coefficients to encourage the shrinkage of non-relevant components to zero. A cross-validation study is organized to compare the proposed modeling solution to other models, showing its potential to reduce the uncertainty of the ungauged predictions without affecting their calibration. [ABSTRACT FROM AUTHOR]

This study introduced the application of concepts and methods from extreme value theory (EVT) to estimate the probability that daily minimum temperatures exceed springtime critical temperature thresholds for Pinot noir buds and young shoots as a function of springtime phenology. The springtime frost risk estimates were computed spatially for Pinot noir throughout the Willamette Valley (WV) American Viticultural Area (AVA) using a gridded dataset of historical daily minimum surface air temperature data. EVT-based springtime frost risk maps can inform vineyard-management operations by identifying those locations throughout a wine region with a low risk for any cold injury where remedial action is likely not necessary when there is a forecasted frost event. Frost risk estimates were computed for 1991–2021 and 1991–2022 to examine a potentially changed risk profile for springtime frost events throughout the WV AVA due to the April 2022 advective frost event. The April 2022 advective frost event influenced the risk profile throughout the AVA such that an event of its magnitude is now modelled to occur more frequently. The EVT-based risk analysis can be readily updated each year as new data become available. While spatially varying budbreak calculations facilitated computation of the spring frost risk estimates, the EVT approach profiled in this study does not necessarily depend on potentially uncertain predetermined budbreak date estimates. Gridded maps of extreme daily minimum temperature exceedances, reclassified relative to the springtime phenology critical temperature thresholds for Pinot noir, were readily combined with a ripening potential map to identify optimal areas for vineyard site selection throughout the WV AVA. When simultaneously evaluating Pinot noir ripening potential with springtime frost risk using historical data, the limiting factor for vineyard site selection throughout the WV AVA was frost risk, not ripening potential. The study approach is also applicable for other winegrape-growing regions, assessments of winter freeze risk and summertime heatwaves, and with non-gridded observed temperature datasets.

Extreme precipitation shows non-stationarity, meaning that its distribution can change with time or other large-scale variables. For a classical frequency-intensity analysis this effect is often neglected. Here, we propose a model including the influence of North Atlantic Oscillation, time, surface temperature and a blocking index. The model features flexibility to use annual maxima as well as seasonal maxima to be fitted in a generalized extreme value setting. To further increase the efficiency of data usage, maxima from different accumulation durations are aggregated so that information for extremes on different time scales can be provided. Our model is trained to individual station data with temporal resolutions ranging from one minute to one day across Germany. Models are chosen with a stepwise BIC model selection and verified with a cross-validated quantile skill index. The verification shows that the new model performs better than a reference model without large-scale information. Also, the new model enables insights into the effect of large-scale variables on extreme precipitation. Results suggest that the probability of extreme precipitation increases with time since 1950 in all seasons. High probabilities of extremes are positively correlated with blocking situations in summer and with temperature in winter. However, they are negatively correlated with blocking situations in winter and temperature in summer. [ABSTRACT FROM AUTHOR]

This paper presents an expansion of the generalized extreme value distribution to new distribution classes, specifically the Alpha Power Transformation Generalized Extreme Value (APTGEV) distribution. This extension is achieved by combining the Extreme Value theory and the alpha power transformation technique. We employ the maximum likelihood method in conjunction with the Newton-Raphson procedure to estimate the parameters in these proposed distributions. In the final stages of our research, we simulate these new distributions and apply them to real-world data. For this study, we have chosen extreme rainfall data from a weather station in the Si Samrong District Sukhothai Province of Thailand as our dataset. These extended distribution classes are designed to provide greater flexibility and adaptability in understanding complex data patterns, and their application to real-world data offers valuable insights into their effectiveness. [ABSTRACT FROM AUTHOR]

In the conditions of rising air temperature and changing precipitation regimes in Central Europe and Slovakia over the last two decades, it is necessary to analyse drought, develop high-quality tools for drought detection, and understand its reactions to the emerging drought situation. One of the frequently used meteorological drought indices is the Standardized Precipitation and Evapotranspiration Index (SPEI). Several parameters can be modified in different steps of the calculation process of SPEI. In the article, we analyse the influence of selected adjustable parameters on the index results. Our research has shown that the choice of a statistical distribution (Log-logistic, Pearson III, or Generalized Extreme Value) for fitting water balance can affect the feasibility of calculating distribution parameters (and thus the index) from the provided input data, as well as lead to either underestimation or overestimation of the index. The normality test of SPEI can be used as a tool for the detection and elimination of highly skewed indices and cases when the indices were not well determined by the distribution function. This study demonstrated improved results when using the GEV distribution, despite the common use of the Log-logistic distribution. With the Pearson III distribution, unusually high or low SPEI values (|SPEI| > 6) were detected. [ABSTRACT FROM AUTHOR]

Progressive first-failure censoring has been widely-used in practice when the experimenter desires to remove some groups of test units before the first-failure is observed in all groups. Practically, some test groups may haphazardly quit the experiment at each progressive stage, which cannot be determined in advance. As a result, in this article, we propose a progressively first-failure censored sampling with random removals, which allows the removal of the surviving group(s) during the execution of the life test with uncertain probability, called the beta-binomial probability law. Generalized extreme value lifetime model has been widely-used to analyze a variety of extreme value data, including flood flows, wind speeds, radioactive emissions, and others. So, when the sample observations are gathered using the suggested censoring plan, the Bayes and maximum likelihood approaches are used to estimate the generalized extreme value distribution parameters. Furthermore, Bayes estimates are produced under balanced symmetric and asymmetric loss functions. A hybrid Gibbs within the Metropolis-Hastings method is suggested to gather samples from the joint posterior distribution. The highest posterior density intervals are also provided. To further understand how the suggested inferential approaches actually work in the long run, extensive Monte Carlo simulation experiments are carried out. Two applications of real-world datasets from clinical trials are examined to show the applicability and feasibility of the suggested methodology. The numerical results showed that the proposed sampling mechanism is more flexible to operate a classical (or Bayesian) inferential approach to estimate any lifetime parameter. [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]

Pest outbreaks, harmful algal blooms and population collapses are extreme events with critical consequences for ecosystems. Therefore, understanding the ecological mechanisms underlying these extreme events is crucial. We evaluated theoretical predictions on the size scaling and variance of extreme population abundance by combining (i) the generalized extreme value (GEV) theory and (ii) the resource‐limited metabolic restriction hypothesis for population abundance. Using the phytoplankton data from the L4 station in the English Channel, we showed a negative size scaling of the expected value of maximal density, whose confidence interval included the predicted metabolic scaling (α = −1) supporting theoretical predictions. The role of resources and temperature in the distribution of the size–abundance pattern and residuals was well characterized by the GEV distribution. This comprehensive modelling framework will allow to elucidate community structure and fluctuations and provide unbiased return times estimates, thereby improving the prediction accuracy of the timing of the population outbreaks. [ABSTRACT FROM AUTHOR]

In extreme values theory, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. The GEV distribution is a family of continuous probability distributions, which has wide applicability in several areas, including hydrology, engineering, science, ecology, and finance. However, the GEV distribution is not suitable for modeling extreme bimodal data. In this paper, we propose an extension of the GEV distribution that incorporates an additional parameter. The additional parameter introduces bimodality and aries tail weight, i.e., this proposed extension is more flexible than the GEV distribution. Inference for the proposed distribution was performed under the likelihood paradigm. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. Finally, the proposed distribution is applied to environmental data sets, illustrating their capabilities in challenging cases in extreme value theory. [ABSTRACT FROM AUTHOR]

The risk-return relationship is of fundamental significance in the field of economics and finance. It is used to structure investment strategies, allocate resources, as well as assist in the construction of policy and regulatory frameworks. The accurate forecast of the risk-return relationship ensures sound financial decisions, whereas an inaccurate one can underestimate risk and thus lead to losses. The GARCH-M approach is one of the foremost models used in South African literature to investigate the risk-return relationship. This study made a novel and significant contribution, on a local and international level, as it was the first study to investigate GARCH-M type models with different innovation distributions. This study analyzed the JSE ALSI returns of the South African market for the sample period from 05 October 2004 to 05 October 2021. Results revealed that the EGARCH (1, 1)-M with the Skewed Student-t distribution (Skew-t) is optimal relative to the standard GARCH, APARCH and GJR. However, the EGARCH-M Skew-t failed to capture the financial data's asymmetric, volatile and random nature. To improve forecast accuracy, this study applied different nonnormal innovation distributions: the Pearson Type Ⅳ distribution (PIVD), Generalized Extreme Value distribution (GEVD), Generalized Pareto distribution (GPD) and Stable. Model diagnostics revealed that the nonnormal innovation distributions adequately captured asymmetry. The Value at Risk and backtesting procedure found that the PIVD, followed by Stable, outperformed the Extreme Value Theory distributions (GEVD and GPD). Thus, investors, risk managers and policymakers would opt to use the EGARCH-M in combination with the PIVD when modelling the risk-return relationship. The main contribution of this study was to confirm that applying GARCH type models with the conventional and normal type distributions, to a volatile emerging market, is considered ineffective. Therefore, this study recommended the exploration of other innovation distributions, that were not included in the scope of this study, for future research purposes.

The potential weight of accumulated snow on the roof of a structure has long been an important consideration in structure design. However, the historical approach of modeling the weight of snow on structures is incompatible for structures with surfaces and geometry where snow is expected to slide off of the structure, such as standalone solar panels. This paper proposes a "storm-level" adaptation of previous structure-related snow studies that is designed to estimate short-term, rather than season-long, accumulations of the snow water equivalent or snow load. One key development associated with this paper includes a climate-driven random forests model to impute missing snow water equivalent values at stations that measure only snow depth in order to produce continuous snow load records. Additionally, the paper compares six different approaches of extreme value estimation on short-term snow accumulations. The results of this study indicate that, when considering the 50-year mean recurrence interval (MRI) for shortterm snow accumulations across different weather station types, the traditional block maxima approach, the mean-adjusted quantile method with a gamma distribution approach, and the peak over threshold Bayesian approach tend to most often provide MRI estimates near the median of all six approaches considered in this study. Further, this paper also shows, via bootstrap simulation, that the peak over threshold extreme value estimation using automatic threshold selection approaches tend to have higher variance compared to the other approaches considered. The results suggest that there is no one-size-fits-all option for extreme value estimation of shortterm snow accumulations, but highlights the potential value from integrating multiple extreme value estimation approaches. [ABSTRACT FROM AUTHOR]

Modeling of extreme events is important in many scientific fields, including environmental and civil engineering, and impacts and risk assessments. Among available methods, statistical models that allow estimating extremes' frequency and intensity are regularly used in procedures to anticipate potential changes in extreme events. Extreme value theory provides a theoretical basis for statistical estimation of extreme events using frequency analysis. The challenge in modeling is knowing when to use the block maxima method or the peaks-over-threshold (POT) method. Each has its drawbacks. POT describes the main characteristics of the observed extreme series; the threshold selection is always challenging and might affect the accuracy of the simulated results and the credibility of changes in extreme values. To encompass this challenge, mixture models offer more flexibility to represent samples with nonhomogeneous data. This study presents the gamma generalized Pareto (GGP) mixture model for estimating risk occurrence of hydroclimatic extremes. The model was developed in its general form, whereas the observed hydrometeorological extreme events depend on multidimensional covariates. A maximum likelihood algorithm is proposed to estimate the parameters with a constraint on the shape parameter of the generalized Pareto (GP) distribution. A Monte Carlo (MC) simulation compared the proposed model with the classical POT approach, with a fixed threshold, and the annual maximum series of streamflow. The approach was applied using a daily hydrological data set from an observed station located in the Saint John River at Fort Kent (01AD002), New Brunswick, Canada. The results show a flexibility to model extremes for dependent or nonstationary time series and adequately describes the central part of the observed frequencies, as well as the tails. [ABSTRACT FROM AUTHOR]

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This study applied the theory of statistical analysis, Extreme Value Theory (EVT), with dengue fever cases reported between 2010 and 2019 from the Department of Disease Control Bureau of Epidemiology, Ministry of Health, Nakhon Sawan region. From the results of this study, it showed that the highest monthly recurrence values of dengue fever for Nakhon Sawan province in every 5, 10, and 20 years were 43.1725, 54.6569, and 68.1125 per 100,000 populations, respectively. [ABSTRACT FROM AUTHOR]

Marathons are one of the ultimate challenges of human endeavor. In this paper, we apply extreme value statistics to predict fastest marathon times achievable for ten marathons around the world and for both men and women. We concentrate on the theoretical minimum time for each gender at each venue, irrespective of who runs there. Thus, we measure the potential of each marathon, not the actual performance of the runners. • Predictions of fastest marathon times achievable for ten marathons given; • The first manuscript applying extreme value statistics for a range of marathons. • Predictions are given for both genders. [ABSTRACT FROM AUTHOR]

Extreme precipitation events can lead to disastrous floods, which are the most significant natural hazards in the Mediterranean regions. Therefore, a proper characterization of these events is crucial. Extreme events defined as annual maxima can be modeled with the generalized extreme value (GEV) distribution. Owing to spatial heterogeneity, the distribution of extremes is non-stationary in space. To take non-stationarity into account, the parameters of the GEV distribution can be viewed as functions of covariates that convey spatial information. Such functions may be implemented as a generalized linear model (GLM) or with a more flexible non-parametric non-linear model such as an artificial neural network (ANN). In this work, we evaluate several statistical models that combine the GEV distribution with a GLM or with an ANN for a spatial interpolation of the GEV parameters. Key issues are the proper selection of the complexity level of the ANN (i.e., the number of hidden units) and the proper selection of spatial covariates. Three sites are included in our study: a region in the French Mediterranean, the Cap Bon area in northeast Tunisia, and the Merguellil catchment in central Tunisia. The comparative analysis aim at assessing the genericity of state-of-the-art approaches to interpolate the distribution of extreme precipitation events. [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]

The maximum electromagnetic field formed in the electrically large enclosures for a given input power has always been the focus of electromagnetic compatibility issues such as radiation sensitivity and shielding effectiveness. To model the maximums in a simple manner, the electrically large enclosure can be regarded as a reverberation chamber (RC), thus the generalized extreme value (GEV) theory based framework is used for both undermoded and overmoded frequencies. Since the mechanical stirrer is not easy to be installed like that for RC, frequency stirring and mechanical stirring related configurations are discussed, and the corresponding results have confirmed the validity of frequency stirring with the estimate of the parameters in GEV distribution. As for the maximum field, a comparison has been made between GEV distribution and IEC 61000-4-21, and the corresponding results have also highlighted that the maximum field can be assessed by frequency stirring configuration, and by GEV distribution with a desired confidence. [ABSTRACT FROM AUTHOR]

The spatiotemporal characteristics of mean and maximum dry spells (DSs) in Croatia were analysed through general climatology and the return values associated with different return periods. An analysis was performed across seven regions with different precipitation regimes comprising data from 131 meteorological stations for 1961–2015. Daily precipitation limits of 1, 5, and 10 mm were used to define dry days, and DSs were defined as consecutive series of dry days. Generalized extreme value (GEV) and generalized Pareto (GP) distributions were applied to the DS annual maxima (AM) and the peak over threshold (POT) series, respectively. The respective distribution parameter methodology and interpretation combined both frequentist and Bayesian approaches. The regional mean DS lengths clearly indicated a dominance of DS durations in easternmost Croatia during the cold season (mainly winter) and in the southern Adriatic during the warm season (mainly summer). Elsewhere, combined climatic influences were reflected, with the shortest DSs found in the highlands. This spatial pattern was more pronounced for DS5 and DS10, whereas differences in DS1 durations were not evident. Spatial DS distribution return values associated with various return periods obtained by the GEV and GP distributions followed the general DS climatology. The visual inspection of an appropriate threshold for GP‐POT modelling, using the GP parameter stability graphs and L‐moment ratio diagrams, indicated that the 75th percentile value was best for all three DS categories. Although the estimates obtained by the two methods could not be directly compared, the GP model generally found longer DS return values than those obtained by the GEV, particularly in the regions with long DS. This study provides a climatological basis for drought parameters and drought risk assessment in Croatia. Moreover, the results are relevant for adjacent regions, complementing and enriching the current DS characteristics knowledge in southeastern Europe. [ABSTRACT FROM AUTHOR]

The generalized extreme value (GEV) distribution is the only possible limiting distribution of properly normalized maxima of a sequence of independent and identically distributed random variables. As such, it has been widely applied to approximate the distribution of maxima over blocks. In these applications, GEV properties such as finite lower endpoint when the shape parameter ξ$$ \xi $$ is positive or the loss of moments due to the magnitude of ξ$$ \xi $$ are inherited by the finite‐sample maxima distribution. The extent to which these properties are realistic for the data at hand has been widely ignored. Motivated by these overlooked consequences in a regression setting, we here make three contributions. First, we propose a blended GEV (bGEV) distribution, which smoothly combines the left tail of a Gumbel distribution (GEV with ξ=0$$ \xi =0 $$) with the right tail of a Fréchet distribution (GEV with ξ>0$$ \xi >0 $$). Our resulting distribution has, therefore, unbounded support. Second, we proposed a principled method called property‐preserving penalized complexity (P3$$ {}^3 $$C) prior to decide on the existence of the GEV distribution first and second moments a priori. Third, we propose a reparametrization of the GEV distribution that provides a more natural interpretation of the (possibly covariate‐dependent) model parameters, which in turn helps define meaningful priors. We implement the bGEV distribution with the new parameterization and the P3$$ {}^3 $$C prior approach in the R‐INLA package to make it readily available to users. We illustrate our methods with a simulation study that reveals that the GEV and bGEV distributions are comparable when estimating the right tail under large‐sample settings. Moreover, some small‐sample settings show that the bGEV fit slightly outperforms the GEV fit. Finally, we conclude with an application to NO2$$ {}_2 $$ pollution levels in California that illustrates the suitability of the new parameterization and the P3$$ {}^3 $$C prior approach in the Bayesian framework. [ABSTRACT FROM AUTHOR]

This work used the measured data during the whole test period to study the law of temperature change in the steel rail beams, and the distribution characteristics of the sunshine temperature field, in straddle-type monorail tourist transportation systems, employing a field-test and a numerical simulation. The curve form of the temperature gradient was determined by a comparative analysis of the existing domestic and foreign norms. Finally, the generalized extreme value distribution model was used to predict the extreme value of the representative value of the temperature difference, and the value of the temperature base, for different return periods, and the complete temperature gradient model were determined. Results: During the whole test period, the maximum vertical positive temperature difference of the steel box girder was 15.21 °C, and the negative temperature difference was −5.07 °C. In addition, the effect of the ambient temperature, considering solar radiation, was found to be an important factor affecting the distribution of the vertical temperature difference. The analysis determined that the positive and negative temperature difference curves in the unpaved steel box girder were multi-segment polylines and linear straight lines, respectively. The extreme value predicts that the representative temperature differences between T1 and T2 of the 450 mm beam during the 50-year return period were 17.2 °C and 4.58 °C, respectively, and T1 and T2 under the 100-year return period were 17.38 °C and 4.62 °C, respectively. [ABSTRACT FROM AUTHOR]

The objective of the present study was to examine and predict the annual maximum temperature in the northeast of Thailand by using data from 25 stations and employing spatial extreme modeling which is based on max-stable process (MSP) using schlatter's method. We analyzed extreme temperature data using the MSP using latitude, longitude, and altitude variables. Our result showed that the maximum temperature has an increasing trend. The return level estimates of the study areas from both the local generalized extreme value (GEV) model and MSP models show that the Nong Khai, Maha Sarakham, and Khon Kaen stations had higher return levels than the other stations for every return period, whereas Pak Chong Agromet had the lowest return levels. Furthermore, the results showed that MSP modeling is more suitable than point-wise GEV distribution. We realize that the spatial extreme modeling based on MSP provides more precise and robust return levels as well as some indices of the maximum temperatures for both the observation stations and the locations with no observed data. The results of this study are consistent with those of some previous studies. The increasing trend in return levels could affect agriculture and the surrounding environment in northeast Thailand. Spatial extreme modeling can be beneficial in the impact management and vulnerability assessment under extreme event scenarios caused by climate change. [ABSTRACT FROM AUTHOR]

This study aims to overcome the problem of dimensionality, accurate estimation, and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) uncertainty intervals in high frequency data. A Bayesian bootstrapping and backtest density forecasts, which are based on a weighted threshold and quantile of a continuously ranked probability score, are developed. Developed backtesting procedures revealed that an estimated Seasonal autoregressive integrated moving average-generalized autoregressive score-generalized extreme value distribution (SARIMA–GAS–GEVD) with a skewed student-t distribution had the best prediction performance in forecasting and bootstrapping VaR and ES. Extension of this non-stationary distribution in literature is quite complicated since it requires specifications not only on how the usual Bayesian parameters change over time but also those with bulk distribution components. This implies that the combination of a stochastic econometric model with extreme value theory (EVT) procedures provides a robust basis necessary for the statistical backtesting and bootstrapping density predictions for VaR and ES. [ABSTRACT FROM AUTHOR]

Many failure and fracture studies of reactor pressure vessel material 20MnMoNi55 steel are performed in cryogenic conditions to study the scattered failure distribution property of the material in the lower self of ductile to brittle transition region. The experimental failure values of the RPV material are fitted with generalized extreme value (GEV) distribution and Weibull distribution through the commercial Statistical package R-i368 4.05 to study the nature of the distribution of fracture toughness in the lower self of ductile To brittle transition region. The nature of the distribution of fracture toughness of the RPV material 20MnMoNi55 steel is investigated from those experimental results. It is observed stochastically that the GEV distribution provides a better fit to the experimental failure data than the established Weibull distribution at least in the brittle portion of the DBT region of the tested material. This investigation is also supported by the two goodness of fit tests (Anderson–Darling test and Kolmogorov–Smirnov). Kolmogorov—Smirnov test results qualify Weibull distribution but indicated GEV as a better-fitted distribution of the experimental results. While Weibull distribution failed to qualify Anderson Darling test but GEV distribution qualifies the test. Therefore, GEV distribution can be thought, as a better option than Weibull distribution to capture the failure distribution for the RPV material in the lower self of the DBT region. [ABSTRACT FROM AUTHOR]

Extreme high still water levels (EHSWLs) are calculated at four tide stations located along North San Francisco Bay for a range of return periods. The observed hourly still water level varying from 7 years to 122 years measurement durations and predicted tide data for the tide stations are used in the study. The conventional annual block maxima (ABM), r-largest order statistics (r-LOS), peak over threshold (POT), and convolution (joint probability) methods are used to calculate the return levels. The return level estimates by the four methods are critically compared, and the merits and limitations of the methods are investigated. Various other research questions such as the effect of the probability distribution and block size on the return level estimates, the accuracy of return level estimates with limited annual maximums, the effect of the data resolution on the return level estimates with the convolution method are investigated. The analyses show that using a limited annual maximum affects the return level estimates most. The error can go up to 0.37 m in the 100-year return level at the San Francisco station. The direct extreme value analysis (EVA) methods produce very similar results, whereas the convolution method results in significantly (0.16 m) higher return levels. The monthly and daily block sizes in the block maxima method estimate very close return levels to annual block size. The differences produced due to the probability distributions alternative to generalized extreme value (GEV) are within or very close to the 95% confidence margin of error (MOE) of ABM-GEV estimates. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui 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.)

Pressure fluctuation is commonly used to characterize the dynamic of fluidized bed, and bubble movements resulting in pressure fluctuations will seriously affect the stable operation of fluidized bed. This paper presents an extreme value statistical analysis model that uses generalized extreme value (GEV) distribution to analyze the pressure fluctuation time series, predict its future fluctuation state, and further provide risk warning for fluidized bed operation. The pressure fluctuation time-series for four mainly fluidization behaviors (single bubble, multiple bubble, exploding bubble and transport conditions) in an actual experiment were analyzed by the proposed method. The results show that the error rate of the proposed method in this paper is controlled within±10%, and the average error rate is controlled within −1.7%–3.7%. By analyzing the risk margin of the extreme pressure fluctuations of each flow regime, the risk margin of exploding bubble is the largest, and more stringent measures should be taken to ensure the stable operation of the fluidized bed in this flow state. In summary, the risk warning of the fluidized bed can be detected in the joint efforts of the confidence interval and the risk margin of the pressure fluctuation return level of each flow regime. [ABSTRACT FROM AUTHOR]

Spatial extremes are common for climate data as the observations are usually referenced by geographic locations and dependent when they are nearby. An important goal of extremes modeling is to estimate the T-year return level. Among the methods suitable for modeling spatial extremes, perhaps the simplest and fastest approach is the spatial generalized extreme value (GEV) distribution and the spatial generalized Pareto distribution (GPD) that assume marginal independence and only account for dependence through the parameters. Despite the simplicity, simulations have shown that return level estimation using the spatial GEV and spatial GPD still provides satisfactory results compared to max-stable processes, which are asymptotically justified models capable of representing spatial dependence among extremes. However, the linear functions used to model the spatially varying coefficients are restrictive and may be violated. We propose a flexible and fast approach based on the spatial GEV and spatial GPD by introducing fused lasso and fused ridge penalty for parameter regularization. This enables improved return level estimation for large spatial extremes compared to the existing methods. Supplemental files for this article are available online. [ABSTRACT FROM AUTHOR]

Reliable assessment of high quantiles, namely quantile with relatively low exceedance probability, based on available sample is of interest in hydrology, meteorology, finance and many other fields. Interval estimation of extreme quantities in real-world mechanisms is essential, but it is challenging due to complexities in underlying data-generating processes, small sample sizes, data are not normal, failure of the standard statistical assumptions etc. leading to huge stochastic uncertainties. A composite quantile function estimator aligned using tail of generalized extreme value distribution is employed to construct bootstrap confidence intervals for high-order quantiles. The proposed semi-parametric estimator is shown to be asymptotically unbiased and consistent. The utility of the proposed estimator in comparison with traditional nonparametric and parametric bootstrap in terms of coverage probability for small size and case study application to real-world precipitation datasets has been illustrated. Limitations posed in computations and scope for future work is highlighted. [ABSTRACT FROM AUTHOR]

The block maxima approach is an important method in univariate extreme value analysis. While assuming that block maxima are independent results in straightforward analysis, the resulting inferences maybe invalid when a series of block maxima exhibits dependence. We propose a model, based on a first‐order Markov assumption, that incorporates dependence between successive block maxima through the use of a bivariate logistic dependence structure while maintaining generalized extreme value (GEV) marginal distributions. Modeling dependence in this manner allows us to better estimate extreme quantiles when block maxima exhibit short‐ranged dependence. We demonstrate via a simulation study that our first‐order Markov GEV model performs well when successive block maxima are dependent, while still being reasonably robust when maxima are independent. We apply our method to two polar annual minimum air temperature data sets that exhibit short‐ranged dependence structures, and find that the proposed model yields modified estimates of high quantiles. [ABSTRACT FROM AUTHOR]

We consider forecasting functional time series of extreme values within a generalized extreme value distribution (GEV). The GEV distribution can be characterized using the three parameters (location, scale, and shape). As a result, the forecasts of the GEV density can be accomplished by forecasting these three latent parameters. Depending on the underlying data structure, some of the three parameters can either be modeled as scalars or functions. We provide two forecasting algorithms to model and forecast these parameters. To assess the forecast uncertainty, we apply a sieve bootstrap method to construct pointwise and simultaneous prediction intervals of the forecasted extreme values. Illustrated by a daily maximum temperature dataset, we demonstrate the advantages of modeling these parameters as functions. Further, the finite-sample performance of our methods is quantified using several Monte Carlo simulated data under a range of scenarios. [ABSTRACT FROM AUTHOR]

Sea level rise can bring disastrous outcomes to people living in coastal regions by increasing flood risk or inducing stronger storm surges. We study long‐term linear trends in monthly maximum sea levels by applying extreme value methods. The monthly maximum sea levels are extracted from multiple tide gauges around the coastal regions of the world over a period of as long as 169 years. Due to instrument changes, location changes, earthquakes, land reclamation, dredging, etc., the sea level data could contain inhomogeneous shifts in their means, which can substantially impact trend estimates if ignored. To rigorously quantify the long‐term linear trends and return levels for the monthly maximum sea level data, we use a genetic algorithm to estimate the number and times of changepoints in the data. As strong periodicity and temporal correlation are pertinent to the data, bootstrap techniques are used to obtain more realistic confidence intervals to the estimated trends and return levels. We find that the consideration of changepoints changed the estimated linear trends of 89 tide gauges (approximately 30% of tide gauges considered) by more than 20cmcentury‐1. Our results are summarized in maps with estimated extreme sea level trends and 50‐year return levels. [ABSTRACT FROM AUTHOR]

This article compares the performances of three fitting methods (SLmom, S1NCM, and S3NCM) to account for temporal characteristics of Annual Maximum Precipitations (AMPs) on daily and sub‐daily time scales using scaling General Extreme Value (GEV) distribution at a local site. Based on simple scaling properties of AMPs, the temporal downscaling model (called Scaling‐GEV) with parameter estimation methods are used to estimate sub‐daily AMPs from observed daily data. The feasibility and accuracy of the suggested method were assessed using rainfall data available from Dorval in Quebec (Canada) and Seoul (South Korea) for the period 1961–1990. Presence of simple scaling properties of AMPs for two stations has shown that it is feasible to use the temporal downscaling method for describing the linkage between AMPs of different time scales. Numerical and graphical analyses revealed that the Scaling‐GEV distribution by the Three‐Non central moments (NCM) method (S3NCM) provides the most accurate estimates compared to observed data amongst three fitting methods. In addition, this study suggested a modified bootstrap technique to determine confidence intervals (CIs) CIs of extreme rainfall series using the simple scaling properties of extreme rainfalls and only daily AMPs. Although the CIs were constructed by only daily AMPs and the simple scaling properties, the observed sub‐daily AMPs are generally within the 95% CI estimated. [ABSTRACT FROM AUTHOR]

This study aims to overcome the problem of dimensionality, accurate estimation, and forecasting Value-at-Risk (VaR) and Expected Shortfall (ES) uncertainty intervals in high frequency data. A Bayesian bootstrapping and backtest density forecasts, which are based on a weighted threshold and quantile of a continuously ranked probability score, are developed. Developed backtesting procedures revealed that an estimated Seasonal autoregressive integrated moving average-generalized autoregressive score-generalized extreme value distribution (SARIMA–GAS–GEVD) with a skewed student-t distribution had the best prediction performance in forecasting and bootstrapping VaR and ES. Extension of this non-stationary distribution in literature is quite complicated since it requires specifications not only on how the usual Bayesian parameters change over time but also those with bulk distribution components. This implies that the combination of a stochastic econometric model with extreme value theory (EVT) procedures provides a robust basis necessary for the statistical backtesting and bootstrapping density predictions for VaR and ES.

In order to cope with traffic accidents efficiently, the maximum number of traffic accidents, deaths and serious injuries that can occur during the day should be presented quantitatively. In order to examine the characteristics of traffic accidents in different regions, it was divided into the Seoul metropolitan area, Chungcheong area, Gyeongbuk area, Honam area, and Gyeongnam area and was suitable for the generalized extreme value distribution (GEV). The parameters of the GEV distribution were estimated by the L-moments, and the Anderson-Darling test and the Cramer-von Mises test confirmed the suitability of the distribution. According to the analysis, the maximum number of traffic accidents that can occur once every 50 years is 401 in the Seoul metropolitan area, 168 in the South Gyeongsang region, 455 in the North Gyeongsang region, 136 in the Chungcheong region and 205 in the South Jeolla region. Compared to the Seoul metropolitan area, which has a large population and car registration, the number of traffic accidents is relatively high due to the large area, mountainous areas, and logistics movement caused by the industrial complex. [ABSTRACT FROM AUTHOR]

A major winter storm brought up to 42 inches of snow in parts of the Mid-Atlantic and Northeast states for January 22–24, 2016. The blizzard of January 2016 impacted about 102.8 million people, claiming at least 55 lives and $500 million to $3 billion in economic losses. This article studies two important aspects of extreme snowfall events: 1. trends in annual maxima and threshold exceedances and 2. return levels for extreme snowfall. Applying extreme value methods to the extreme snow data in the New York City area, we quantify linear trends in extreme snowfall and assess how severe the 2016 blizzard is in terms of return levels. To find a more realistic standard error for the extreme value methods, we extend Smith's method to adapt to both spatial and temporal correlations in the snow data. Our results show increasing, but insignificant trends in the annual maximum snowfall series. However, we find that the 87.5th percentile snowfall has significantly increased by 0.564 inches per decade, suggesting that, while the maximum snowfall is not significantly increasing, there have been increases in the snowfall among the larger storms. We also find that the 2016 blizzard is indeed an extreme snow event equivalent to about a 40-year return level in the New York City area. The extreme value methods used in this study are thoroughly illustrated for general readers. Data and modularized programming codes are to be available online to aid practitioners in using extreme value methods in applications. [ABSTRACT FROM AUTHOR]

We investigate the challenges to be faced by quality practitioners to implement a control chart for individuals aimed at monitoring the stability of maximum/minimum realizations of profile quality features. We consider the situation where only a limited amount of inspections can be scheduled, which is typical of the most recent manufacturing applications for the production of small lots of customized products or processes characterized by frequent changeovers. A quantitative study on simulated profiles described by functional data modelled as random Gaussian fields is provided. Finally, we discuss how the proposed control chart can be implemented in a canning process. [ABSTRACT FROM AUTHOR]

• A new change-point model for the r -largest order statistics is proposed. • The proposed model can be used for any application that involves an extreme time series with a structural break. • A Bayesian adaptation for the estimation of the optimal number of order statistics is proposed. • Simulations and real data sets shows the good performance of this new model. • The application in three examples verifies the performance of the new model is better than that the usual model. This study makes a new contribution to extreme value theory by proposing a change-point model of the distribution of the r -larger order statistics. In some situations, using only the maxima of grouped data results in a small sample size that may require a larger dataset. In this sense, using the joint distribution of the r -largest order statistics provides more information and, consequently, better estimators. We perform a comprehensive simulation to show the advantage of this method over other competitive models that approach the change-point model in extremes. Finally, the proposed model is fitted to river quota data (environmental data) and NASDAQ daily returns data (financial data) to demonstrate its potential for practical application. [ABSTRACT FROM AUTHOR]

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University 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 extreme value theory (EVT) is used to assess the risk of extreme events caused by natural calamities or untoward circumstances in the social and economic sectors. The theory can be used to study the frequency of rare events and to build up a predictive model so that one can attempt to forecast the frequency of such future extreme events such as a financial collapse and the amount of damage from such a collapse. Even though many statistical techniques have been used to analyze the manner in which the Federal Reserve determines the level of the Federal Fund Rates, no known study has used EVT to analyze and predict the extreme fund rates. In this study, the US Federal Funds Rate, one of the most publicized and important economic indicators in the financial world, from 1954–2019 has been analyzed. The contributions of this study are: (1) to provide an appropriate model for the normalized Federal Funds Rate data; (2) to compare several estimation techniques in estimating parameters for two possible models; (3) to predict the maximum economic return rate from a Federal Funds Rate in the future by using the concept of the return period; and (4) to investigate the bias of estimated parameters applying a simulation study. Simulated data and real financial data are used for the study, and the outcome satisfies the efficiency of its application. [ABSTRACT FROM AUTHOR]