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Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of n items from a data universe equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in n. Given the sketch and a query item y, one should be able to approximate its rank in the stream, i.e., the number of stream elements smaller than or equal to y. Most works to date focused on additive εn error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This article investigates multiplicative (1±ε )-error approximations to the rank. Practical motivation for multiplicative error stems from demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values. The most space-efficient algorithms due to prior work store either O(log(ε²n)/ε²) or O(log³ (εn)/ε ) universe items. We present a randomized sketch storing O(log1.5 (εn)/ε ) items that can (1 ± ε )-approximate the rank of each universe item with high constant probability; this space bound is within an O(√log(εn)) factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments. [ABSTRACT FROM AUTHOR]

The propensity of water to remain in a metastable liquid state at temperatures below its equilibrium melting point holds significant potential for cryopreserving biological material such as tissues and organs. The benefits conferred are a direct result of progressively reducing metabolic expenditure due to colder temperatures while simultaneously avoiding the irreversible damage caused by the crystallization of ice. Unfortunately, the freezing of water in bulk systems of clinical relevance is dominated by random heterogeneous nucleation initiated by uncharacterized trace impurities, and the marked unpredictability of this behavior has prevented the implementation of supercooling outside of controlled laboratory settings and in volumes larger than a few milliliters. Here, we develop a statistical model that jointly captures both the inherent stochastic nature of nucleation using conventional Poisson statistics as well as the random variability of heterogeneous nucleation catalysis through bivariate extreme value statistics. Individually, these two classes of models cannot account for both the time-dependent nature of nucleation and the sample-to-sample variability associated with heterogeneous catalysis, and traditional extreme value models have only considered variations of the characteristic nucleation temperature. We conduct a series of constant cooling rate and isothermal nucleation experiments with physiological saline solutions and leverage the statistical model to evaluate the natural variability of kinetic and thermodynamic nucleation parameters. By quantifying freezing probability as a function of temperature, supercooled duration, and system volume while accounting for nucleation site variability, this study also provides a basis for the rational design of stable supercooled biopreservation protocols. [ABSTRACT FROM AUTHOR]

Motivated by the papers of Mladenović and Piterbarg (2006), Krajka (2011), and Pereira and Tan (2017), we study the limit properties for the maxima from non stationary random fields subject to missing observations and obtain the weakly convergence and almost sure convergence results for these maxima. Some examples such as Gaussian random fields, chi-random fields, and Gaussian order statistics fields are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper systematically investigates the dynamic mechanical response and fragment characteristics of sandstone with asymmetrical conjugate fissures subjected to preexisting static stress based on the split Hopkinson pressure bar apparatus. The cross-fissured sandstone exhibits significant variations in mechanical behavior when exposed to higher dynamic strain rates under identical static pre-stress. The cross-fissured sandstone with a higher dynamic strain rate is characterized by a greater coupled strength under the same static pre-stress; for a given dynamic load, the highest coupled strength occurs under the static pre-stress of 60% UCS. The failure mode of the cross-fissured sandstone is predominantly governed by the dynamic strain rate, independent of static pre-stress variations considered in this investigation. At lower dynamic strain rates, the specimens typically exhibit a mixed tensile-shear failure mode, characterized by the dominance of larger fragments in the broken specimens. In contrast, under high dynamic impacts, the sandstone tends to fail in a shear-dominated manner, resulting in smaller fragments with a more uniform size distribution. Furthermore, the study explores how varying dynamic strain rates and static pre-stress influence the fragment characteristics of the cross-fissured sandstone. Higher dynamic strain rates and increased static pre-stress generally lead to smaller mean fragment sizes. This phenomenon is quantitatively described by fitting fragment size distributions using the Generalized Extreme Value (GEV) distribution, revealing a decrease in the location parameter (μ) and an increase in fractal dimension. These metrics indicate that higher dynamic strain rates and static pre-stress result in sandstone specimens breaking into smaller fragments with a more homogeneous size distribution. These findings contribute to a deeper understanding of rock dynamics, with potential implications for engineering applications involving similar geological configuration under dynamic loading conditions. [ABSTRACT FROM AUTHOR]

Aiming at the problems of insufficient ability of artificial COA in the late optimization search period, loss of population diversity, easy to fall into local extreme value, resulting in slow convergence and lack of exploration ability; In this paper, an improved COA algorithm based on chaotic sequence, nonlinear inertia weight, adaptive T-distribution variation strategy and alert updating strategy is proposed to enhance the performance of COA (shorted as TNTWCOA). The algorithm introduces chaotic sequence mechanism to initialize the position. The position distribution of the initial solution is more uniform, the high quality initial solution is generated, the population richness is increased, and the problem of poor quality and uneven initial solution of the Coati Optimization Algorithm is solved. In exploration phase, the nonlinear inertial weight factor is introduced to coordinate the local optimization ability and global search ability of the algorithm. In the exploitation phase, adaptive T-distribution variation is introduced to increase the diversity of individual population under low fitness value and improve the ability of the algorithm to jump out of the local optimal value. At the same time, the alert update mechanism is proposed to improve the alert ability of COA algorithm, so that it can search within the optional range. When Coati is aware of the danger, Coati on the edge of the population will quickly move to the safe area to obtain a better position, while Coati in the middle of the population will randomly move to get closer to other Coatis. IEEE CEC2017 with 29 classic test functions were used to evaluate the convergence speed, convergence accuracy and other indicators of TNTWCOA algorithm. Meanwhile, TNTWCOA was used to verify 4 engineering design optimization problems, such as pressure vessel optimization design and welding beam design. The results of IEEE CEC2017 and engineering design Optimization problems are compared with Improved Coati Optimization Algorithm (ICOA), Coati Optimization Algorithm (COA), Golden Jackal Optimization Algorithm (GJO), Osprey Optimization Algorithm (OOA), Sand Cat Swarm Optimization Algorithm (SCSO), Subtraction-Average-Based Optimizer (SABO). The experimental results show that the improved TNTWCOA algorithm significantly improves the convergence speed and optimization accuracy, and has good robustness. Three‑bar truss design problem, The Gear Train Design Problem, Speed reducer design problem shows a strong solution advantage. The superior optimization ability and engineering practicability of TNTWCOA algorithm are verified. [ABSTRACT FROM AUTHOR]

Causal inference for extreme events has many potential applications in fields such as climate science, medicine, and economics. We study the extremal quantile treatment effect of a binary treatment on a continuous, heavy-tailed outcome. Existing methods are limited to the case where the quantile of interest is within the range of the observations. For applications in risk assessment, however, the most relevant cases relate to extremal quantiles that go beyond the data range. We introduce an estimator of the extremal quantile treatment effect that relies on asymptotic tail approximation, and use a new causal Hill estimator for the extreme value indices of potential outcome distributions. We establish asymptotic normality of the estimators and propose a consistent variance estimator to achieve valid statistical inference. We illustrate the performance of our method in simulation studies, and apply it to a real dataset to estimate the extremal quantile treatment effect of college education on wage. for this article are available online. [ABSTRACT FROM AUTHOR]

Background 1,4-Dioxane (1,4-D) is a byproduct of the synthesis of surfactants, typically found in some cosmetics products such as shampoo, toothpaste, and soap. The presence of 1,4-D in cosmetics products is limited to a certain amount since 1,4-D is classified as a probable human carcinogen. Objective This present study was intended to validate static headspace gas chromatography-mass spectrometry (HS GC-MS) for the determination of 1,4-D in cosmetics products. Methods The condition of HS and GC-MS was optimized to get the best condition for analysis of 1,4-D using 1,4-dioxane-d8 (1,4-D-d8) as internal standard (IS). The developed method was validated by evaluating the key performance characteristics, including specificity, linearity, limit of detection (LoD), limit of quantification (LoQ), accuracy, and precision. Results The results showed that HS GC-MS was specific since the peaks of the selected ion monitoring (SIM) mode could be separated and confirmed at m/z 88 and m/z 96 for 1,4-D and 1,4-D-d8, respectively. The method was linear over the concentration range of 0.1287–1.2875 µg/mL, with R2 > 0.999 and RSD residuals <2.0. A collaborative study was conducted on this method, with 10 participating laboratories from four countries. The outcome of this study was found to be accurate and precise, as evidenced by the excellent recoveries ranging from 94.6% to 102.1%, and with good reproducibility with RSD values ranging from 0.2 to 1.1%. The collaborative studies exhibited that all data reported by 10 participating laboratories in four countries were inliers without any extreme values observed either in mean or RSD values Conclusions HS GC-MS is found to be fit and suitable for the determination of trace level of 1,4-D in cosmetics products. Highlights The HS GC-MS method could be proposed as a standard method for quantitative analysis of 1,4-D in cosmetics products since the collaborative studies indicated that the developed method meet the requirement in "Guidelines for Collaborative Study Procedures to Validate Characteristics of a Method of Analysis." [ABSTRACT FROM AUTHOR]

A statistical study was made of the summer extreme temperatures over peninsular Spain in the last forty years. Records from 158 observatories regularly distributed over Iberia with no missing data were available for the common period from 1981 to 2020. For this purpose, a hierarchical spatio-temporal model with a Gaussian copula and a generalized extreme value parametrization of the extreme events was used. The temporal trend in maximum extreme temperatures was studied making use of both a stationary model and a nonstationary one that takes into account the influence of anthropogenic climate change on extreme temperatures using the global mean temperature as a function of time for the study period. The results led to a better fit of the nonstationary model, with there being a 3.5-fold greater increase in the 20-year return level of the extreme temperatures than in that corresponding to the global mean temperature. [ABSTRACT FROM AUTHOR]

Reliable crash data are not usually available in low- and middle-income countries (LMICs). In these regions, surrogate safety measures (SSMs) can be used as effective tools for quantifying road safety. Traffic conflicts are the most-used SSMs, primarily defined based on temporal or spatial proximity between vehicles. Time-to-collision (TTC), a conflict indicator and its derivatives, are commonly used to define conflicts based on 1D interactions may not be suitable for nonlane-based traffic where vehicular interactions are 2D (longitudinal and lateral). This study aims to propose a methodology to define conflicts considering 2D vehicle interactions. Traffic video data were recorded at four unsignalized T-intersections, identified as black spots on divided highways in India. A bivariate extreme value approach was used to define conflict in 2D vehicular interaction using TTC and lateral gap. The results show that incorporating lateral and longitudinal conflict indicators into the bivariate extreme value models can significantly improve conflict-based risk assessment. The proposed approach can be used to define safety-critical events required in vehicle warning systems for nonlane-based traffic. [ABSTRACT FROM AUTHOR]

The study investigates the crash risk of powered two-wheelers (PTWs) involved in multiple conflict types, with different vehicle classes constituting a mixed traffic stream. This study uses the extreme value theory to estimate the crash risk after establishing the conflict thresholds for potential rear-end and side-swipe conflicts by accounting for interacting vehicle types. The study considers four vehicle pairs involving PTWs: PTW-PTW, PTW-MThW (motorized three-wheeler), PTW-Car, and PTW-Bus. The study found that the conflict thresholds corresponding to rear-end and side-swipe types increase with the interacting vehicle size. The crash risk is lowest for the PTW-PTW pair (0.315%) in rear-end conflicts, whereas the risk is the highest for the PTW-MThW pair (3.7%) in side-swipe conflicts. The crash risk corresponding to the PTW interacting with other vehicle types is higher than that of the PTW-PTW pair. Hence, the implementation of exclusive PTW lanes could be an effective risk mitigation strategy for PTW-dominant mixed traffic environments. [ABSTRACT FROM AUTHOR]

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]

Bivariate extreme value distributions can be used to model dependence of observations from random variables in extreme levels. There is no finite dimensional parametric family for these distributions, but they can be characterized by a certain one-dimensional function which is known as Pickands dependence function. In many applications the general approach is to estimate the dependence function with a non-parametric method and then conduct further analysis based on the estimate. Although this approach is flexible in the sense that it does not impose any special structure on the dependence function, its main drawback is that the estimate is not available in a closed form. This paper provides some theoretical results which can be used to find a closed form approximation for an exact or an estimate of a twice differentiable dependence function and its derivatives. We demonstrate the methodology by calculating approximations for symmetric and asymmetric logistic dependence functions and their second derivatives. We show that the theory can be even applied to approximating a non-parametric estimate of dependence function using a convex optimization algorithm. Other discussed applications include a procedure for testing whether an estimate of dependence function can be assumed to be symmetric and estimation of the concordance measures of a bivariate extreme value distribution. Finally, an Australian annual maximum temperature dataset is used to illustrate how the theory can be used to build semi-infinite and compact predictions regions. [ABSTRACT FROM AUTHOR]

The optimization of the initial design or the development of repair and replacement strategies for pipes within the water distribution network (WDN) during its operational phase relies on the utilization of crisp values. Some input variables such as nodes demand, pipe's roughness coefficient and reservoir water level have the uncertain nature. Alterations in input parameter values during the operational period, attributed to uncertainty, induce shifts in the behavior and performance of the WDN compared to scenarios with crisp input parameters. Recognizing and analyzing these variations are imperative for making informed decisions to address their ramifications and mitigate problems within the water distribution network. This research analyzes the uncertainty surrounding WDN node pressures, post-implementation of optimal instructions for pipe repair and replacement. The input parameters considered for this analysis include the uncertainty associated with the pipe's roughness coefficient and the nodes demand within the network. To achieve this objective, a combined approach utilizing both a simulation model (EPANET) and the fuzzy α-cut methodology is employed. Triangular fuzzy membership functions (MF) are chosen for both the input and output variables in the analysis. The extreme value combinations of the two uncertain input variables, at each level of uncertainty, are formulated into four distinct scenarios, serving as the input fuzzy set for the simulation model. Among the research scenarios, the second scenario, characterized by the combination of the minimum pipe's roughness coefficient and the maximum demand, is designated as the critical scenario. The findings indicate that in the critical scenario, under the highest level of uncertainty, the WDN reliability index diminishes significantly, ranging from approximately 30–40%. This decrease is primarily attributed to the inadequate supply of required pressure to most nodes within the network. At lower levels of uncertainty, the reliability index of the network surpasses 75%, indicating a relatively acceptable performance. Specifically, in the first and fourth scenarios, the network reliability index consistently exceeds 72%. Notably, in the third scenario, the network reliability index remains consistently above 90% across all uncertainty levels. [ABSTRACT FROM AUTHOR]

The Indus River, a lifeline for Pakistan, holds paramount significance for its geography, history, and economy. This research delves into a comprehensive analysis of the river's behavior by introducing a novel statistical framework. Combining the Gumbel Type 2 distribution and the Rayleigh distribution, a new generalized Gumbel Type 2 (GG2) distribution is derived, and used for modeling the data about the river's outflow at the Tarbela Dam during 2020–2021. Our study contributes to the understanding of the complex dynamics of the Indus River. The GG2 distribution, designed for extreme value events, adept at modeling positive-valued variables, were combined to model the complexed characteristics of the river's flow. Parameters are estimated using both classical and Bayesian methods, enhancing the accuracy and reliability of our findings. The Bayse estimators are not in the closed form expression, hence the Tierney-Kadane approximation technique is used. Through simulation study and analysis, the data set of overflows of the river Indus over Tarbela Dam, the Bayes estimators demonstrate superior performance in minimizing risk compared to classical estimators. It is shown graphically that that our proposed distribution performs better than its competitor distributions. The results not only deepen our understanding of the river's behavior but also offer insights crucial for infrastructure planning, flood control, and resource allocation. [ABSTRACT FROM AUTHOR]

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The present study focuses on understanding the behavior of motorized 2-wheeler (MTW) riders at urban unsignalized intersections in India. In the Indian context, over 60% of road crash fatalities are attributed to vulnerable road users, with MTWs serving as the predominant contributors, accounting for 44% of total fatalities. Notably, unsignalized intersections have emerged as critical sites for accidents involving vulnerable road users. Postencroachment time is used to assess traffic conflicts of MTW users. Furthermore, the study employs the exceedance property of extreme value theory to calculate crash probabilities. Tobit and grouped random parameters Tobit regression models are developed to model crash probabilities, incorporating variables such as traffic volume, traffic composition, gap acceptance time, intersection characteristics, and intersection conflict area at 4 urban unsignalized intersections in Surat, India. MTW riders have the lowest gap acceptance time among vehicles in the traffic stream. Cars and other heavy vehicles readily accept gaps when MTWs are in the conflicting stream at unsignalized intersections, which increases traffic conflicts. MTWs have the highest crash rates in the traffic stream. Among the developed models, the grouped random parameters Tobit regression captures the spatial unobserved heterogeneity of the study sites and outperforms the simple Tobit regression model. The results also indicate that MTW riders are exposed to a higher risk of crashes while turning at unsignalized intersections. The presence of a central traffic island has varied implications; it raises crash rates at 3-legged intersections but lowers them at 4-legged intersections for 2-wheelers. The study concludes that MTW crash rates are influenced by traffic and intersectional factors. Increased gap acceptance time correlates with lower crash rates. Countermeasure selections require detailed investigations, because it was observed that the presence of central traffic islands has varied effects on crash rates at 3-legged and 4-legged unsignalized intersections. [ABSTRACT FROM AUTHOR]

In this study, we propose the application of the GARCH‐EVT‐Copula model in estimating liquidity‐adjusted value‐at‐risk (L‐VaR) of energy stocks while modeling nonlinear dependence between return and bid‐ask spread. Using the L‐VaR framework of Bangia et al. (1998), we present a more parsimonious model that effectively captures non‐zero skewness, excess kurtosis, and volatility clustering of both return and spread distributions of energy stocks. Moreover, to measure the nonlinear dependence between return and spread series, we use multiple copulas: Clayton, Gumbel, Frank, Normal, and Student‐t. Based on the statistical backtesting and economic loss functions, our results suggest that the GARCH‐EVT‐Clayton copula is superior and most consistent in forecasting L‐VaR compared with other competing models. This finding has several implications for investors, market makers, and daily traders who appreciate the importance of liquidity in market risk computation. [ABSTRACT FROM AUTHOR]

This paper contributes to the understanding of sovereign credit default swap (CDS) markets by examining the response of CDS spreads to macroeconomic factors and exploring extreme value dependence and its relation to economic cycles. The study focuses on four emerging countries in the Asia–Pacific sovereign CDS markets from 2009 to 2023 and utilises a dynamic quantile autoregressive distributed lag (QARDL) approach to account for statistical stylized facts. The findings reveal significant relationships between economic growth, inflation, volatility index (VIX), interest rates and real effective exchange rate on CDS spreads, with varying effects across quantiles and countries. Additionally, the study explores the impact of economic expansion and contraction on CDS spreads, highlighting the significant negative effects of the expansion in certain countries and the positive impacts of contraction phases. These findings provide valuable insights for policymakers in risk management and policy decision-making, emphasizing the need for policies that promote sustainable growth; manage market risks during volatile periods and consider the implications of interest rates, exchange rates and economic phases on financial stability. The empirical model used is evaluated for dynamic stability, and policy implications are discussed in light of the research outcomes. [ABSTRACT FROM AUTHOR]

Media multitasking is widespread, yet its relationship with creativity remains unclear. This study employs a combination of measures, including the media multitasking questionnaire, alternative uses task (AUT) for divergent thinking, Chinese compound remote association task (CCRAT) for convergent thinking, and a creative problem-solving task, to examine the relationship between media multitasking and creativity. Extreme values grouping [one standard deviation above or below the mean of the media multitasking index (MMI)], median value grouping, and regression analysis were used to explore the relationship between media multitasking and creativity. The results revealed the following findings: (1) across the three analysis methods, there was no significant relationship between media multitasking and performance on the AUT task. However, within the range of one standard deviation above or below the mean of the MMI, media multitasking showed a significant positive correlation with fluency, flexibility, and total scores on the AUT task. (2) Media multitasking significantly predicted the accuracy of responses on the CCRAT task positively. (3) Media multitasking significantly predicted lower scores on the applicability of creative problemsolving tasks. [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]

Human activities, climate change, and land-use alterations accelerated soil erosion in recent decades and imposed significant threats to soil fertility and stability worldwide. Understanding and quantifying the spatiotemporal variation of soil erosion risks is crucial for adopting the best management practices for surface soils conservation. Here, we present a novel high-resolution (30 m) soil erosion framework based on the G2 erosion model by integrating satellite and reanalysis datasets and Machine Learning (ML) models to assess soil erosion risks and hazards spatiotemporally. The proposed method reflects the impacts of climate change in 1 h time resolutions and land use in 30 m scales on soil erosion risks for almost 4 decades (between 1985 and 2017). The soil erosion hazardous maps were generated/evaluated using Extreme Value Analysis (EVA), utilizing long-term annual soil erosion estimations/projections to aid policymakers in developing management strategies to protect lands against extreme erosion. The proposed framework is evaluated in the Sultanate of Oman, which lacks soil erosion estimation/assessment studies due to data scarcity. Results indicate that soil erosion has increasing perilous trends in high altitudes of the Sultanate of Oman that may cause substantial risks to soil health and stability. [ABSTRACT FROM AUTHOR]

Study Design. Prospective cohort study. Objective. Investigate load-induced effects in lumbar intervertebral discs (IVDs) and differences between low back pain (LBP) patients and controls. Summary of Background Data. T2-map values, obtained from quantitative MRI sequences, reflect IVD tissue composition and integrity. Feasibility studies with T2-mapping indicate different load-induced effects in entire IVDs and posterior IVD parts between LBP patients and controls. Larger studies are required to confirm these findings and increase the understanding of specific characteristics distinguishing IVD changes in LBP patients compared with controls. Materials and Methods. Lumbar IVDs of 178 patients (mean age: 43.8 yr; range: 20-60 yr) with >3 months of LBP and 74 controls (mean age: 40.3 yr; range: 20-60 yr) were imaged with T2-map sequence in a 3T scanner in supine position without axial load, immediately followed by a repeated examination, using the same sequence, with axial load. On both examinations, mean T2-map values were obtained from entire IVDs and from central/posterior IVD parts on the three midsagittal slices in 855 patient IVDs and 366 control IVDs. Load-induced effect was compared with Fold-change ratio and adjusted for IVD-degeneration grade. Results. Loading induced an increase in T2-map values in both patients and controls. Excluding most extreme values, the ranges varied between -15% and +35% in patients and -11% and +36% in controls (first to 99th percentile). Compared with controls, the T2-map value increase in patients was 2% smaller in entire IVDs (Fold-change: 0.98, P= 0.031), and for central and posterior IVD parts 3% (Fold-change: 0.98, P=0.005), respectively, 2% (Foldchange: 0.9, P= 0.015) smaller. Conclusions. This quantitative study confirmed diverse load-induced behaviors between LBP patients and controls, suggesting deviant biomechanical characteristics between IVDs in patients and controls not only attributed to the global grade of degeneration. These findings are an important step in the continuous work of identifying specific IVD phenotypes for LBP patients. [ABSTRACT FROM AUTHOR]

Tunneling in sandy dolomite strata often faces hazards such as collapse, water inrush, and water-sand inrush, seriously threatening the safety of tunnel construction. There are currently limited studies on the mechanical behaviors of sandy dolomite tunnels. In view of this, an analytical solution for tunneling in sandy dolomite strata is derived in this study, and then parametric analysis is performed to analyze the mechanical response of rock mass in sandy dolomite tunnels. The results demonstrate five tunnel sidewall stress scenarios according to the different lateral pressure coefficients (λ). Varying λ values impact stress distribution and tunnel stability, with extreme values posing risks of instability. Tunnel safety is greatly reduced when rock stress approaches the plastic limit. At different internal friction angles, cohesion, and initial rock stresses, radial stress decreases gradually as the radius increases. The stress values under different conditions tend to be similar, while the effects of internal friction angle, cohesion, and initial rock stress on stress in the elastic zone decrease with increasing distance from the center of the tunnel. Under different internal friction angles and cohesion, the plastic zone radius increases with increasing distance from the excavation surface, and a larger internal friction angle and cohesion lead to an increase in stress. The stress and cohesion of a rock mass significantly affect the plastic zone radius, and an increase in tunnel excavation radius also leads to an increase in the radius of plastic zone. These findings provide a reference and insight for similar geotechnical engineering practices in the future. [ABSTRACT FROM AUTHOR]

Traditional method of determining closure and initiation stress of fractured rocks by analyzing the stress-strain curve has problems such as strong subjectivity and large errors. This study utilized the rock closure stress values and onset stress values determined by three traditional methods, namely, axial strain method, fracture volume method and empirical value taking method, as the base database. The Student t distribution theory was used to obtain a confidence interval based on its overall distribution of values and to achieve a combination of the advantages of multiple methods. Within confidence interval, the Monte Carlo stochastic simulation was used to determine the convergence interval of the second stage to further improve the accuracy. Finally, mean value of the randomly sampled values after reaching the convergence stage was taken as the probability value of rock closure and crack initiation stress. The results showed that the 3 traditional methods for calculating rock closure and initiation stresses are significantly different. In contrast, the proposed method biases more towards multi-numerical distribution intervals and also considers the preference effects of different calculation methods. In addition, this method does not show any extreme values that deviate from the confidence intervals, and it has strong accuracy and stability compared to other methods. [ABSTRACT FROM AUTHOR]

This paper proposes a learning-based model for the resource-constrained edge nodes in the blockchain-enabled Internet of Medical Things (IoMT) systems to realize efficient querying. Three layers are designed in the new model: data evaluation layer, data storage layer and data distribution layer. The data evaluation layer extracts the features from medical data and evaluates their values based on the Extreme Learning Machine (ELM) method. Then, in the data storage layer, according to the value of medical data, a novelty data structure called Merkle–Huffman tree (M-H tree) is established. Compared with the Merkle tree, high-value data (frequently accessed data) in M-H tree is saved closer to the root node and can be found faster. In the data distribution layer, the sharding-based blockchain model is adopted to increase the storage scalability of the IoMT system. Finally, the experimental results show that the new learning-based model can effectively improve the query speed of the blockchain-enabled medical system by about 3.5% and free up large amounts of storage space on IoMT devices. [ABSTRACT FROM AUTHOR]

The risk of revenue instability is a concern for any nonprofit. Existing research leads to the well-known strategy of equalizing revenues across sources to reduce revenue volatility. This study offers several expansions to this strategy. First, rather than focusing solely on deviations from mean revenue, I incorporate extreme revenue loss, or downside risk, as it threatens organizational survival and occurs more frequently than expected. Second, while revenue equalization is indifferent to the type of revenue source, I incorporate portfolio diversification that seeks a negative correlation between sources to avoid simultaneous losses. Using 2008 to 2012 financial data, results of fixed-effects regression suggest that portfolio diversification can reduce revenue volatility and downside risk. Moreover, the relationships between financial flexibility, growth potential, and revenue risk are more nuanced compared to existing research focused solely on deviation risk. The results can help nonprofits consider incorporating downside risk in revenue portfolio management to enhance financial security. [ABSTRACT FROM AUTHOR]

The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two accelerated mixed types of stable distributions are obtained as the extreme limit laws of random sampling competing risks under linear and power normalizations, respectively. The theoretical findings are well illustrated by typical examples and numerical studies. The developed methodology and models provide new insights into modeling complex data across numerous fields. [ABSTRACT FROM AUTHOR]

Spatial information about plant health and productivity are essential when assessing the progress towards Sustainable Development Goals such as life on land and zero hunger. Plant health and productivity are strongly linked to a plant's phenological progress. Remote sensing, and since the launch of Sentinel-1 (S1), specifically, radar-based frameworks have been studied for the purpose of monitoring phenological development. This study produces insights into how crop phenology shapes S1 signatures of PolSAR features and InSAR coherence of wheat, canola, sugar beet. and potato across multiple years and orbits. Hereby, differently smoothed time series and a base line of growing degree days are stacked to estimate the patterns of occurrence of extreme values and break points. These patterns are then linked to in situ observations of phenological developments. The comparison of patterns across multiple orbits and years reveals that a single optimized fit hampers the tracking capacities of an entire season monitoring framework, as does the sole reliance on extreme values. VV and VH backscatter intensities outperform all other features, but certain combinations of phenological stage and crop type are better covered by a complementary set of PolSAR features and coherence. With regard to PolSAR features, alpha and entropy can be replaced by the cross-polarization ratio for tracking certain stages. Moreover, a range of moderate incidence angles is better suited for monitoring crop phenology. Also, wheat and canola are favored by a late afternoon overpass. In sum, this study provides insights into phenological developments at the landscape level that can be of further use when investigating spatial and temporal variations within the landscape. [ABSTRACT FROM AUTHOR]

Time series of traffic flows, extracted from mobile phone origin–destination data, are employed for monitoring people crowding and mobility in areas subject to flooding risk. By applying a vector autoregressive model with exogenous covariates combined with dynamic harmonic regression to such time series, we detected the presence of many extreme events in the residuals, which exhibit heavy-tailed distribution. For this reason, we propose a time series clustering procedure based on tail dependence which is suitable for data characterized by a spatial dimension, since objects' geographical proximity is taken into account. The final aim is to obtain clusters of areas characterized by the common tendency to the manifestation of extreme events, that in this case study are represented by extremely high incoming traffic flows. The proposed method is applied to the Mandolossa, a strongly urbanized area located on the western outskirts of Brescia (northern Italy) which is subject to frequent flooding. [ABSTRACT FROM AUTHOR]

Classical estimators fail to be efficient in practical scenarios when data is riddled with extreme values known as outliers. Robust estimation strategies are insensitive to outliers and may be used in such cases. The current work is focused on developing a novel robust estimation strategy using Huber M-estimation. A new chain-product type estimator for population mean has been suggested utilizing data on two auxiliary variables. A numerical comparison has been carried out between the proposed robust estimator and the corresponding classical estimator using real and simulated data containing outliers. Recommendations have been made for its practical use based on the encouraging results. [ABSTRACT FROM AUTHOR]

The combine harvester equipped with attitude-adjustment functionality significantly enhances its adaptability to complex terrain but often struggles to maintain the reliability of its mechanisms. Therefore, investigating the dynamic load characteristics of the attitude-adjustment mechanism becomes imperative. This article employed the DEM–FMBD (Discrete Element Method–Flexible Multibody Dynamics) bidirectional coupling simulation method to establish a multibody dynamic model of a tracked combine harvester. The study delved into the interaction mechanism and dynamic stress response characteristics between the tracked chassis and the complex terrain under various height adjustments, lateral adjustment angles, longitudinal adjustment angles, and different field-ridge crossing methods. Finally, the accuracy of the coupled simulation model was validated through a constructed stress detection system. The research findings revealed that the displacement and tilt angle deviation of the hydraulic cylinders utilized to execute the chassis adjustment actions in the constructed coupled simulation model was less than 5%, and the deviation between the simulation results and the actual maximum dynamic stress under multiple working conditions ranged from 7% to 15%. This verification confirmed the effectiveness of the DEM–FMBD coupled simulation method. Under different adjustment conditions, the maximum stress position was consistently distributed in the same area of the left-front and left-rear rotating arms. The primary and secondary effects of the various parts of the adjustment mechanism on the overall reliability of the chassis were as follows: left front > right front > left rear > right rear. By implementing the middle height with the adjustment strategy, the dynamic stress extreme value of the adjustment mechanism can be effectively reduced by 21.98%, thereby enhancing the structural stability of the chassis. [ABSTRACT FROM AUTHOR]

The paper presents the reconstruction of sea levels in the North Sea and Baltic Sea using Kalman filter approach. Based on the statistical characteristics of one year of daily maps of sea level from the Geesthacht COAstal model SysTem (GCOAST) and daily data at tide gauges along the coastline of two basins, the method can reconstruct effectively and accurately the multidecadal sea level anomalies. The high accuracy reconstruction data were then used to investigate the interannual variability in both basins and to estimate the difference between outflows and inflows (net flux) through the Danish Straits. The highest mean, standard deviation, and extreme values of sea level anomalies appear in winter and are well reproduced in different regions, such as the German Bight, the Southern North Sea, the Bothnian Bay, the Gulfs of Finland and Riga. The sea level variability is highly correlated with the mean sea level pressure and the zonal wind, particularly in the German Bight and in the winter months. The contributions of river runoff and net precipitation on the net flux are significant in the spring. The local wind has a greater influence on the net flux than the remote drivers. [ABSTRACT FROM AUTHOR]

While weighting methods are popular for comparing the effects of multi-level treatment in observational studies, their performance can be unstable in the presence of extreme values of the generalized propensity score (GPS). Matching methods are more resistant to GPS outliers but bear the risk of GPS model misspecification. In this article, we propose a double score matching (DSM) estimator of the pairwise average treatment effect (ATE) based on the GPS and the generalized prognostic score (GPGS) evaluated at one treatment level at a time. The de-biased DSM estimator not only maintains the advantage of matching methods but also alleviates the model dependence problem due to its double robustness: it consistently estimates the true pairwise ATE if either the GPS or the GPGS is correctly specified. [ABSTRACT FROM AUTHOR]

This study delves into the application of Shannon entropy to analyze the long-term variability in climate data, specifically focusing on precipitation and temperature. By employing data from 1901 to 2010 across 377 catchments worldwide, we investigated the dynamics of climate variables using the generalized extreme value (GEV) distribution and Shannon entropy measures. The methodology hinged on the robust bootstrap technique to accommodate the inherent uncertainties in climatic data, enhancing the reliability of our entropy estimates. Our analysis revealed significant trends in entropy values, suggesting variations in the unpredictability and complexity of climate behavior over the past century. These trends were critically assessed using non-parametric tests to discern the underlying patterns and potential shifts in climate extremes. The results underscore the profound implications of entropy trends in understanding climate variability and aiding the prediction of future climatic conditions. This research not only confirms the utility of Shannon entropy in climatological studies but also highlights its potential in enhancing our understanding of complex and chaotic climate systems. The study's findings are vital for developing adaptive strategies in response to the evolving nature of climate extremes, thus contributing to more informed decision-making in environmental management and policy formulation. [ABSTRACT FROM AUTHOR]

We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big -jump principle. The principle states that in the presence of stochastic processes with power tails statistics, if at a certain time a physical quantity takes on a value much larger than its typical value, this large fluctuation is realized through a single macroscopic jump that exceeds the typical scale of the process by several orders of magnitude. In particular, our estimation focuses on the asymptotic behavior of the tail of the probability distribution of maxima, a fundamental quantity in a wide class of stochastic models used in chemistry to estimate reaction thresholds, in climatology for earthquake risk assessment, in finance for portfolio management, and in ecology for the collective behavior of species. We determine the analytical form of the probability distribution of rare events in the extreme value statistics of three jump processes with power tails: Lévy flights, Lévy walks, and the Lévy–Lorentz gas. For the Lévy flights, we re-obtain through the big-jump approach recent analytical results, extending their validity. For the Lévy–Lorentz gas, we show that the topology of the disordered lattice along which the walker moves induces memory effects in its dynamics, which influences the extreme value statistics. Our results are confirmed by extensive numerical simulations. [ABSTRACT FROM AUTHOR]

IoT applications have greatly improved the convenience of our lives, generating large amounts of IoT data. How to efficiently use these data to feed IoT applications has become a significant research problem, and many studies have used machine learning methods for advanced IoT data analytics. However, the prediction models of these studies generally suffer from the problem of easy overfitting, and insufficient work done on the analysis and selection of features. In terms of prediction models, this paper proposes a second-order hybrid fusion weight–median (W–M) algorithm, which first ensures the sensitivity of the data by weighted average fusion and then reduces the impact of extreme values on the data by median fusion. In terms of feature analysis and selection, this study constructed feature crosses by studying time and weather factors and proposes a second-order feature selection, recursive feature elimination-cross validation-Pearson correlation coefficient (RFECV-PCC) algorithm, which combines the RFECV method and Pearson correlation coefficient for feature selections. Experiments were conducted to evaluate the prediction results using root mean square logarithmic error (RMSLE) and comparison of the simulation results of the dataset, which the real-time data measurement showed that the W–M algorithm has the strongest RMSLE generalization ability, further improving the prediction accuracy after feature selection by the RFECV-PCC algorithm. [ABSTRACT FROM AUTHOR]

The increase in greenhouse gases in the atmosphere has worsened global warming, and marked changes have been observed in meteorological and climatic events, especially since the early 2000s. Trend analysis studies are important for determining changes in meteorological and climatic events over time. This study investigated the trends of maximum precipitation and minimum temperature in the Aegean Region and Eastern Anatolia Region of Türkiye by conducting an innovative trend analysis (ITA), the Mann–Kendall (MK) test, and linear regression analysis (LRA). As a method, ITA has been used together with traditional methods in the last decade, and its advantages have been demonstrated in comparative trend studies. An important contribution of ITA is that it can categorize datasets according to their size (low, medium, and high). The classification technique of the ITA method includes dividing the sorted dataset into three equal parts and separately examining the trends of low, medium, and high data values. This approach is reasonable for datasets with low skewness (or normally distributed series). However, the normal distribution acceptance of ITA data classification is insufficient for trend analysis of data series with extreme values. Therefore, we propose a modified data classification method to rationally examine skewed datasets with the use of quartiles. Our study was performed for the trend analysis of maximum rainfall and minimum temperature data in two regions located in the west and east of Türkiye showing different climatic characteristics. In the first part of the study in which the numerical trend analysis of ITA was evaluated, the MK and LRA methods showed similar results, whereas the ITA detected trends at a greater number of stations owing to its sensitivity feature in detecting trends. In the second part, which included data classification in trend analysis, the equal split data classification used in the ITA and the modified data classification proposed in the study were compared. The comparative results of the trend analysis of the maximum rainfall and minimum temperature data showed the superiority of the proposed data classification in examining the trend of extreme values, especially for maximum rainfall data with relatively high skewness. [ABSTRACT FROM AUTHOR]

Climate models are indispensable tools for decision-making, yet their efficacy in characterizing climatic conditions in regions of complex topography, such as Central-Western Argentina (CWA), remains challenging. Therefore, the main objective of this study was to evaluate mean and extreme values of temperature and precipitation simulations from a set of CMIP6 climate models in CWA. The mean values were compared against CRU TS 4.05 for the period 1950–2014; and the extreme values against ERA5 for the temperature and ERA5, CPC, and CHIRPS for the precipitation during 1981–2010. To evaluate the mean values, we considered several statistical metrics that accounted for the representation of the annual cycle, the long-term trends, and the spatial patterns, followed by a selection of the climate models that best represent the region. Subsequently, we analyzed 20 climate extreme indices using Taylor Diagrams and box-and-whiskers plots. The CMIP6 models tended to exhibit a wet bias over CWA, with temperature simulations warmer (colder) than observations over the Andes (Lowlands). Moreover, most models adequately captured the increase in temperature, as well as the increase in precipitation in the lowlands and its decrease in the Andes. From the set of 24 precipitation and 12 temperature simulations, we evaluated the performance for the representation of climate extremes, finding that most models had difficulties with the quantification of indices based on percentiles. This climate information can be valuable to obtain more accurate climate projections for CWA and to aid decision-making in a region with significant wine production and high reliance on water resources. [ABSTRACT FROM AUTHOR]

In the increasingly intricate electromagnetic environment, the radar receiver may simultaneously encounter multiple intentional or unintentional jamming signals, which results in temporal and spectral overlap of received signals and forms a composite jamming signal. The nature and extent of interference contained in the received signal are often unknown, while they significantly affect the accuracy of radar detection. AnOpen‐Set Compound Jamming Signal Recognition Framework based on Multi‐Task Multi‐Label (MTML‐OCJR) is proposed. Based on the time–frequency characteristic of compound jamming signals, the proposed framework employs multi‐label classification to identify components of compound jamming signals while incorporating an unknown signal detection task into the classification process. Time–frequency image reconstruction combined with extreme value model estimation is used to detect unknown types of jamming signals, enabling simultaneous signal recognition and anomaly detection. The obtained results show that the proposed approach has superior recognition performance for composite jamming signals in closed‐set environments and high anomaly detection ability for unknown signals in open‐set environments. This method has the potential to significantly enhance the effectiveness and reliability of jamming systems in battlefield scenarios. [ABSTRACT FROM AUTHOR]

First-generation college students (FGCS) experience high rates of attrition compared to continuing generation college students. FGCS frequently identify with several other historically marginalized identities on college campuses. The development of a sense of belonging on-campus is one of the main drivers of retention. The current study examines how sense of belonging on-campus develops during the first-year of college for different FGCS and how attitudes about on-campus relationships evolve over time. Thirteen participants were interviewed at three time points during their first year of college. Grounded theory analysis revealed four themes: 1) higher education provides a cultural learning environment; 2) multiple factors create challenges to relationship building; 3) extreme value differences create hard limits around friendships; and 4) within group friendships provide social and psychological value. Findings extend the current literature on the importance of social belonging for retention of diverse FGCS and highlight the importance of intersectionality in this work. [ABSTRACT FROM AUTHOR]

Translation of ensemble predictions into high-precipitation warnings is assessed using user-oriented metrics. Short-range probabilistic forecasts are derived from an operational ensemble prediction system using neighbourhood postprocessing and conversion into categorical predictions by decision threshold optimization. Forecast skill is modelled for two different types of users. We investigate the balance between false alarms and missed events and the implications of the scales at which forecast information is communicated. We propose an ensemble-based deterministic forecasting procedure that can be optimized with respect to spatial scale and a frequency ratio between false alarms and missed events. Results show that ensemble predictions objectively outperform the corresponding deterministic control forecasts at low precipitation intensities when an optimal probability threshold is used. The optimal threshold depends on the choice of forecast performance metric, and the superiority of the ensemble prediction over the deterministic control is more apparent at higher precipitation intensities. Thresholds estimated from a short forecast archive are robust with respect to forecast range and season and can be extrapolated for extreme values to estimate severe-weather guidance. Numerical weather forecast value is found to be limited: the highest usable precipitation intensities have return periods of a few years only, with resolution limited to several tens of kilometres. Implied precipitation warnings fall short of common skill requirements for high-impact weather, confirming the importance of human expertise, nowcasting information, and the potential of machine learning approaches. The verification methodology presented here provides a benchmark for high-precipitation forecasts, based on metrics that are relatively easy to compute and explain to non-experts. [ABSTRACT FROM AUTHOR]

The wind pressure caused by the high-speed passage of intercity railway trains applies a significant load on the platform screen doors, to ensure the safe of the platform screen doors and achieve reasonable design and construction goals, it is necessary to explore the distribution law and mechanism of wind pressure load on the platform screen doors first. Using Fluent software, RNG k-ε turbulence model was selected, and the control equations were discretized by finite volume method, the second-order upwind scheme and center difference scheme were used to solve the convective and diffusive fluxes, the influence of wind pressure load on platform screen doors caused by intercity train passing through stations was studied. The research results indicates: When a train passes through a station at high speed, the increase in the ross-section area of the enclosed area allows the compressed air to dissipate faster, thereby reducing the wind pressure load on the platform screen doors and minimizing the extreme values of the wind pressure load on the doors; Before the train arrives at the platform screen door, the slight change in the retreat distance between the platform screen door and the platform edge has little effect on the extreme wind pressure load of the platform screen door; After the train arrives at the platform screen door, the airflow changes and distribution in the enclosed area become more severe and complex, the increase in cross-section area makes the wind pressure load of the platform screen door more significantly affected by the change in the retreat distance of the platform screen door; The increase in train passing speed will lead to an increase in the extreme wind pressure load on the platform screen doors; During the process of the train passing through the station, the maximum load at each point of the platform screen door decreases overall along the direction of the train's travel, however, as the speed of the train passing through the station increases, the minimum load (suction) near the end of the platform screen door in the direction of the train's travel tends to increase, and this phenomenon becomes more pronounced as the speed increases. [ABSTRACT FROM AUTHOR]

Flood frequency analysis at large scales, essential for the development of flood risk maps, is hindered by the scarcity of gauge flow data. Suitable methods are thus required to predict flooding in ungauged basins, a notoriously complex problem in hydrology. We develop a Bayesian hierarchical model (BHM) based on the generalized extreme value (GEV) and the generalized Pareto distribution for regional flood frequency analysis at high resolution across a large part of North America. Our model leverages annual maximum flow data from ≈20,000 gauged stations and a dataset of 130 static catchment-specific covariates to predict extreme flows at all catchments over the continent as well as their associated statistical uncertainty. Additionally, a modification is made to the data layer of the BHM to include peaks over threshold flow data when available, which improves the precision of the discharge level estimates. We validated the model using a hold-out approach and found that its predictive power is very good for the GEV distribution location and scale parameters and improvable for the shape parameter, which is notoriously hard to estimate. The resulting discharge return levels yield a satisfying agreement when compared with the available design peak discharge from various government sources. The assessment of the covariates' contributions to the model is also informative with regard to the most relevant underlying factors influencing flood-inducing peak flows. According to the developed aggregate importance score, the key covariates in our model are temperature-related bioindicators, the catchment drainage area and the geographical location. [ABSTRACT FROM AUTHOR]

This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression. [ABSTRACT FROM AUTHOR]

Volatility forecasting from high‐frequency data plays a crucial role in many financial fields, such as risk management, option pricing, and portfolio management. Many existing statistical models could better describe and forecast the characteristics of volatility, whereas they do not simultaneously account for the long‐term memory of volatility, the nonlinear characteristics of high‐frequency data, and technical index information during the modeling phase. The purpose of this paper is to use the prediction advantage of deep learning long short‐term memory (LSTM) model to predict the volatility fusing three classes of information, that is, high frequency realized volatility (H), technical indicators (I), and the parameters of generalized autoregression conditional heteroskedasticity(GARCH), heterogeneous autoregressive (HAR), and c, resulting in a novel LSTM‐HIT model to forecast realized volatility. We employ the extreme value theory (EVT) of a semiparametric method to estimate the quantile of standardized return and construct the LSTM‐HIT‐EVT model to forecast the value at risk (VaR). Empirical results show that the LSTM‐HIT model provides the most accurate volatility forecast among the various considered models and that the LSTM‐HIT‐EVT model yields forecasts more accurate than other VaR models. [ABSTRACT FROM AUTHOR]

Drought research is needed to understand the complex nature of drought phenomena and to develop effective management and mitigation strategies accordingly. This study presents a comprehensive regional frequency analysis (RFA) of 12-month meteorological droughts in the Kızılırmak Basin of Turkey using the L-moments approach. For this purpose, monthly precipitation data from 1960 to 2020 obtained from 22 meteorological stations in the basin are used. In the drought analysis, the Standard Precipitation Index (SPI), Z-Score Index (ZSI), China-Z Index (CZI) and Modified China-Z Index (MCZI), which are widely used precipitation-based indices in the literature, are employed. Here, the main objectives of this study are (i) to determine homogeneous regions based on drought, (ii) to identify the best-fit regional frequency distributions, (iii) to estimate the maximum drought intensities for return periods ranging from 5 to 1000 years, and (iv) to obtain drought maps for the selected return periods. The homogeneity test results show that the basin consists of a single homogeneous region according to the drought indices considered here. The best-fit regional frequency distributions for the selected drought indices are identified using L-moment ratio diagrams and ZDIST goodness-of-fit tests. According to the results, the best-fit regional distributions are the Pearson-Type 3 (PE3) for the SPI and ZSI, generalized extreme value (GEV) for the CZI, and generalized logistic distribution (GLO) for the MCZI. The drought maps obtained here can be utilized as a useful tool for estimating the probability of drought at any location across the basin, even without enough data for hydrological research. [ABSTRACT FROM AUTHOR]

The Weibull tail‐coefficient (WTC) plays a crucial role in extreme value statistics when dealing with Weibull‐type tails. Several distributions, such as normal, Gamma, Weibull, and logistic distributions, exhibit this type of tail behavior. The WTC, denoted by θ$$ \theta $$, is a parameter in a right‐tail function of the form F‾(x):=1−F(x)=:e−H(x)$$ \overline{F}(x):&#x0003D; 1-F(x)&#x0003D;: {\mathrm{e}}&#x0005E;{-H(x)} $$, where H(x)=−ln(1−F(x))$$ H(x)&#x0003D;-\ln \left(1-F(x)\right) $$ represents a regularly varying cumulative hazard function with an index of regular variation equal to 1/ θ,θ∈ℝ+$$ \theta, \theta \in {\mathrm{\mathbb{R}}}&#x0005E;{&#x0002B;} $$. The commonly used WTC‐estimators in literature are often defined as functions of the log‐excesses, making them closely related to estimators of the extreme value index (EVI) for Pareto‐type tails. For a positive EVI, the classical estimator is the Hill estimator. Generalized means have been successfully employed in estimating the EVI, leading to reduction of bias and of root mean square error for appropriate threshold values. In this study, we propose and investigate new classes of WTC‐estimators based on power p$$ p $$ of the log‐excesses within a second‐order framework. The performance of these new estimators is evaluated through a large‐scale Monte Carlo simulation study, comparing them with existing WTC‐estimators available in the literature. [ABSTRACT FROM AUTHOR]