Extreme Distribution Research Articles

On the Existence of Extreme Coherent Distributions with No Atoms

The paper is devoted to the study of extremal points of C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document}, the family of all bivariate coherent distributions on [0,1]2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$[0,1]^2$$\\end{document}. It is well-known that the set C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document} is convex and weak∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {weak}^*$$\\end{document} compact, and all extreme points of C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {C}}$$\\end{document} must be supported on sets of Lebesgue measure zero. Conversely, examples of extreme coherent measures with a finite or countably infinite number of atoms have been successfully constructed in the literature. The main purpose of this article is to bridge the natural gap between those two results: We provide an example of extreme coherent distribution with an uncountable support and with no atoms. Our argument is based on classical tools and ideas from dynamical systems theory. This unexpected connection can be regarded as an independent contribution of the paper.

On the Generating Mechanisms of Daily Precipitation in the Conterminous United States: Climatology, Trends, and Associated Marginal and Extreme Distributions

On the Generating Mechanisms of Daily Precipitation in the Conterminous United States: Climatology, Trends, and Associated Marginal and Extreme Distributions

Study on the Annual Extreme Distribution of Wave Load of River-to-Sea Ships

Abstract According to the wave scatter diagram of the river-to-sea specific route waters, the applicability of the method about predicting the annual extreme wave bending moment in DNV Note 30.6 to river-to-sea ships is discussed, by using the Wave loads Calculation System (WALCS), and a method applicable to the river-to-sea ships to determine the annual extreme wave bending moment is proposed: considering the ship type and wave scatter diagram, the sea state corresponding to the annual extreme wave bending moment is to be determined by comparing the results of short-term prediction of wave loads, and based on the short-term Rayleigh distribution prediction results, the annual extreme distribution of wave bending moment, which is obeying the Gumbel distribution, is to be determined using sequence statistical method.

Extrapolation Framework and Characteristic Analysis of Load Spectrum for Agriculture General Power Machinery

As a crucial step in food production, tillage and land preparation play a pivotal role in achieving sustainable crop production and improving the soil environment. However, accurate assessment of the load that agricultural machinery implements during the operation process has always been a vexing problem that needs urgent solutions. In this paper, an extrapolation and reconstruction framework for the time-domain load is constructed based on the probability-weighted moments (PWM) estimation and the peaks-over-threshold function, and the load spectrum is obtained for agriculture general power machinery. Firstly, the load acquisition system was developed, the traction resistance and output torque of the tractor were measured, and the collected load signals were preprocessed. Next, the mean excess function and PWM estimation are introduced to select the optimal threshold and generalized Pareto distribution (GPD) fitting parameters and the extreme load distribution that exceeds the threshold range is fitted. The extreme points in the original data are replaced by generating new extreme points that follow the GPD distribution, and the extrapolation of the load spectrum is achieved. Finally, the real extrapolated load spectrum was validated based on statistical characteristics and rainflow counting analysis, and the correlation coefficient between the fitting data and the extreme load samples was greater than 0.99. It can retain the load sequence characteristics of the original load to a great extent, truly reflecting the load state during the operation of agricultural machinery. Meanwhile, the characteristics of the load spectrum can be accurately obtained, such as extreme, mean, and amplitude values, and the real load during deep loosening and rotary tillage are accurately described. The values provide more authentic and reliable data support for the subsequent selection of optimal operating parameters, reliability design of the power transmission system, and the life assessment of the agricultural implements.

Convection-permitting climate model representation of severe convective wind gusts and future changes in southeastern Australia

Abstract. Previous research has suggested that the frequency and intensity of surface hazards associated with thunderstorms and convection, such as severe convective winds (SCWs), could potentially change in a future climate due to global warming. However, because of the small spatial scales associated with SCWs, they are unresolved in global climate models, and future climate projections are uncertain. Here, we evaluate the representation of SCW events in a convection-permitting climate model (Bureau of Meteorology Atmospheric Regional Projections for Australia, BARPAC-M) run over southeastern Australia for the months of December–February. We also assess changes in SCW event frequency in a projected future climate for the year 2050 and compare this with an approach based on identifying large-scale environments favourable for SCWs from a regional parent model (BARPA-R). This is done for three different types of SCW events that have been identified in this region, based on clustering of the large-scale environment. Results show that BARPAC-M representation of the extreme daily maximum wind gust distribution is improved relative to the gust distribution simulated by the regional parent model. This is due to the high spatial resolution of BARPAC-M output, as well as partly resolving strong and short-lived gusts associated with convection. However, BARPAC-M significantly overestimates the frequency of simulated SCW events, particularly in environments having steep low-level temperature lapse rates. A future decrease in SCW frequency under conditions with steep lapse rates is projected by BARPAC-M, along with less frequent favourable large-scale environments. In contrast, an increase in SCW frequency is projected under conditions of high surface moisture, with more frequent favourable large-scale environments. Therefore, overall changes in SCWs for this region remain uncertain, due to different responses between event types, combined with historical model biases.

Extreme Wave-Induced Pressure Distribution and Wave Forces on Tandem Pile Groups: An Experimental Study

As the foundation of marine infrastructure, pile groups are subjected to extreme wave loads. Existing research primarily focuses on regular waves and wave forces. There is limited research on the pressure distribution of pile bodies under extreme waves. This paper describes a wave flume experiment where waves of a self-proposed extreme wave type were generated. The experiment considers three water depths (25/35/45 cm), three wave-pushing velocities (20/30/40 cm/s), and two clear distances (D, 2D). A total of 216 measuring points equipped with digital pressure sensors captured the vertical and circumferential pressure distribution and wave positive force. The results show that (1) the vertical and circumferential pressure distribution patterns of each component pile and the single pile are similar in various loading scenarios and clear distances. (2) The measuring point pressure, pressure after circumferential integration, and wave positive force are positively correlated with wave-pushing velocity. (3) The wave pressure is positively correlated with the water depth, while the pressure after circumferential integration is negatively correlated with the water depth. (4) When the clear distance is D, the wave positive force coefficient of each component pile is less than 1.0.

Continuity of Gaussian extreme distributions

Distribution continuity is established for extremes of Gaussian processes with bounded sample paths and positive variance or continuous sample paths over compact domain, and for multiparameter Brownian sheets. These results provide probabilistic support for global inference on unknown functions.

Identifying loci in mobility networks with applications in New Zealand work commutes: a statistical test for identifying extreme stationary distribution values in Markov transition matrices

Human mobility describes physical patterns of movement of people within a spatial system. Many of these patterns, including daily commuting, are cyclic and quantifiable. These patterns capture physical phenomena tied to processes studied in urban planning, epidemiology, and other social, behavioral, and economic sciences. This paper advances human mobility research by proposing a statistical method for identifying locations that individual move to and through at a rate proportionally higher than other locations, using commuting data for the country of New Zealand as a case study. We term these locations mobility loci and they capture a global property of communities in which people commute. The method makes use of a directed-graph representation where vertices correspond to locations, and traffic between locations correspond to edge weights. Following a normalization, the graph can be regarded as a Markov chain whose stationary distribution can be calculated. The proposed permutation procedure is then applied to determine which stationary distribution values are larger than what would be expected, given the structure of the directed graph and traffic between locations. The results of this method are evaluated, including a comparison to what is already known about commuting patterns in the area as well as a comparison with similar features.

On the rank of two-dimensional simplicial distributions

Simplicial distributions provide a framework for studying quantum contextuality, a generalization of Bell’s non-locality. Understanding extremal simplicial distributions is of fundamental importance with applications to quantum computing. We introduce a rank formula for twisted simplicial distributions defined for 2-dimensional measurement spaces and provide a systematic approach for describing extremal distributions.

Modelling climate change-induced nonstationarity in rainfall extremes: A comprehensive approach for hydrological analysis

Climate change and global warming have induced a dynamic shift in extreme rainfall patterns, leading to nonstationary behaviour. This alteration in behaviour challenges conventional hydrologic design, which assumes stationarity and can yield misleading outcomes. This study aims to address nonstationarity by modelling distribution parameters with covariates. Utilizing a 70-year (1951–2020) high-resolution India Meteorological Department (IMD) gridded dataset, extreme annual rainfall across diverse Indian cities was extracted and modelled. Previous research and goodness-of-fit tests favour the Generalized Extreme Value (GEV) distribution for modelling extremes. This study incorporates indices like Nino3.4, dipole mode index, global and local temperature, CO2, and time to characterize nonstationarity in extreme annual rainfall, leveraging climate cycles and global warming. Performance assessment employs the Akaike information criterion, Bayesian information criterion and Likelihood ratio test, while quantile reliability is evaluated through confidence intervals (CIs). Findings reveal widespread nonstationary trends in most grid points, translating to wider CIs in estimated quantiles for chosen non-exceedance probability and covariates in fitted models. Generally, nonstationary conditions are associated with broader confidence bands in return levels, highlighting nonstationary model weaknesses compared to stationary models. However, the results showed that the rainfall extremes follow a nonstationary pattern. Hence, there is a strong need to develop nonstationary models of low uncertainty.

The surrogate model for short-term extreme response prediction based on ANN and Kriging algorithm

Numerical simulation is a common method for calculating the short-term extreme response of floating offshore wind turbines (FOWTs). However, it requires significant computational resources. This study presents a dynamic response database for a 5MW semi-submersible FOWT under complex environmental conditions, including wind speed, effective wave height, and wave spectral peak period, using a numerical model. The peak over threshold (POT) method can be used to obtain the parametric database of short-term extreme responses, which includes the short-term extreme response distribution parameters for four responses: float surge, mooring tension, outward bending moment at the leaf root surface (OoPBM) and tower base pitching moment (TBPM). And the parameter database is applied to train models such as the Genetic Algorithm optimization Back Propagation neural network (GA-BP) and Kriging algorithm models. The research indicates that a correlation can be established between environmental conditions and short-term extreme response parameters using two algorithms. The accuracy of surrogate model prediction for some parameters can be improved by grouping the data based on wind speed and training separately. Additionally, selecting the appropriate surrogate model for each parameter separately can improve the accuracy of short-term extreme response prediction.

Spatiotemporal of Particulate Matter (PM2.5) and Ozone (O3) in Eastern Northeast Brazil

ABSTRACT This research examines particulate matter with a diameter of 2.5 micrometers (PM2.5) and ozone (O3) variation across the climatic mesoregions of Alagoas. Mean PM2.5 and O3 concentrations across three mesoregions were as follows: East (5.91; 44.22 μg.m−3), Hinterland (6.90; 44.18 μg.m−3), and Arid (7.03; 44.23 μg.m−3). Spatial and temporal variations were observed, with PM2.5 concentrations highest in the northwest (NW) and O3 concentrations in the east (E), influenced by local sources, weather, and transportation. Differences between rainy and dry years were noted, attributed to biomass burning and dust particle transport. This study establishes a baseline for understanding air quality, lacking monitoring stations, aiding policymaking. It provides insights into PM2.5 and O3 dynamics, with PM2.5 concentrations highest in the NW and lower O3 concentrations in the E. Temporal variations emphasize the need for dynamic monitoring. Positive correlations between PM2.5 and O3 highlight complex relationships. Practical implications include proactive policymaking and the necessity for monitoring stations. Rigorous statistical methodologies inform model selection, enhancing environmental data understanding. Despite changes in land use, studies on extreme probability distributions are limited, emphasizing the need for robust methodologies for environmental data analysis to address air pollution challenges effectively in Alagoas.

Mammalian Life History: Weaning and Tooth Emergence in a Seasonal World.

The young of toothed mammals must have teeth to reach feeding independence. How tooth eruption integrates with gestation, birth and weaning is examined in a life-history perspective for 71 species of placental mammals. Questions developed from high-quality primate data are then addressed in the total sample. Rather than correlation, comparisons focus on equivalence, sequence, the relation to absolutes (six months, one year), the distribution of error and adaptive extremes. These mammals differ widely at birth, from no teeth to all deciduous teeth emerging, but commonalities appear when infants transit to independent feeding. Weaning follows completion of the deciduous dentition, closest in time to emergence of the first permanent molars and well before second molars emerge. Another layer of meaning appears when developmental age is counted from conception because the total time to produce young feeding independently comes up against seasonal boundaries that are costly to cross for reproductive fitness. Mammals of a vast range of sizes and taxa, from squirrel monkey to moose, hold conception-to-first molars in just under one year. Integrating tooth emergence into life history gives insight into living mammals and builds a framework for interpreting the fossil record.

Heat extremes linearly shift with global warming, with frequency doubling per decade since 1979

Abstract Heat extremes have been increasing both in frequency and in intensity in most land regions of the world, and this increase has been attributed to human activities. In the last decade, many outstanding and record shattering heat extremes have occurred worldwide, triggering fears of a nonlinear behaviour or an “acceleration” in the development of heat conditions, considering the warming level when the event occurred. Here we show that the evolution of yearly temperature maxima, with return periods above 10 years, consistently shifts with global temperatures and does not significantly depart from this behaviour in recent years or decades when considered globally or at the scale of continents. This result is obtained by using a classical statistical event attribution technique, where the assumption that the distribution of block-maxima extremes linearly shifts with global warming is tested across years and world land regions. However, the pace of frequency change is large, with the probability of heat extremes exponentially rising and nearly doubling every decade since 1979, particularly when considering events with a return period of about 10 to 50 years in 2000. This makes the climate of a decade ago unrepresentative of today’s climate. Our results overall mean that we do not expect events like the recent outstanding extremes to undergo nonlinear changes, despite fast changes. They also show that assumptions underlying attribution techniques used in many recent studies are consistent with recent temperature trends.

Revisiting the Tertiary-induced Binary Black Hole Mergers: The Role of Superthermal Wide Tertiary Eccentricity Distributions

Recent studies show that the eccentricity distribution of wide binaries (semimajor axis ≳103 au) observed by Gaia tends to favor large eccentricities more strongly than the canonical thermal distribution (P(e) ∝ e)—such distributions are termed “superthermal.” Motivated by this observation, we revisit the formation channel of black hole (BH) binary mergers in triple stellar systems and study the impact of superthermal eccentricity distributions in the outer binaries. We explore the persistence of the highly eccentric outer orbits after each component in a stellar triple has undergone mass loss due to supernova explosions. We find that the outer eccentricity distribution can remain significantly superthermal for modestly hierarchical BH triples satisfying a in/a out ≳ 0.005 (where a in and a out are the semimajor axes of the inner and outer orbits), and are otherwise shaped by mass-loss induced kicks and dynamical instability. We then study the impact of these different outer eccentricity distributions of the remaining BH triples on mergers via the tertiary-induced channel. Of interest, we find that mergers can sometimes be produced even when the initial stellar orbits are near alignment (not subject to the von-Zeipel–Lidov–Kozai effect; ZLK effect) as long as the system is sufficiently hierarchical. On the other hand, although the impact of the octupole-order ZLK effect is much greater when the outer binary is more eccentric, we find that the merger fraction only changes modestly for extreme outer eccentricity distributions because the largest eccentricities tend to lead to dynamical instability.

Comparative analysis of federated learning algorithms under extreme non-IID conditions for computer vision

Data heterogeneity presents enormous challenges for Federated Learning (FL) where data is characterized by non-independent and identically distributed (non-IID) patterns across participating clients. Although a prominent issue, there is a lack of comprehensive studies regarding the efficacy of FL algorithms under different configurations of hyperparameters and models. Three state-of-the-art algorithms were chosen to be the focus of this paper FedAvg, FedProx, and SCAFFOLD. Experiments of the paper study varying degrees of data imbalance and number of local training steps to see their effects on model training results. The algorithms and hyperparameters were evaluated using ResNet50, AlexNet, and DenseNet121 on the CIFAR-10 dataset. Experimental results reveal that FedAvg and SCAFFOLD generally outperform FedProx, except for the latter excelling in the scenario of extreme non-IID data distributions in combination with minimal local training. It was also observed that models with complex architectures like ResNet50 are more susceptible to data imbalances, while simpler models such as AlexNet prove to be more robust. This study provides valuable insights to how different configurations of hyperparameters affect FL in non-IID scenarios, contributing to future development of more efficient and robust FL algorithms.

Extremal invariant distributions of infinite Brownian particle systems with rank dependent drifts

Extremal invariant distributions of infinite Brownian particle systems with rank dependent drifts

Assessment of random dynamic behavior for EMUs high-speed train based on Monte Carlo simulation

A novel statistical method was developed to obtain a dynamic response with irregular line excitations and independent uncertain parameters. The proposed approach combines a three-dimensional vehicle-track coupling dynamics model and uncertainty parameters. Moreover, a new method is used to treat the dynamic indices: derailment coefficient, vertical/lateral wheel/rail force, vertical/lateral car body acceleration, and wheel reduction ratio. The model is validated by comparing simulations (deterministic) results with field measurements, which provide excellent agreement with limited data. According to the findings, the results reveal that the high vibration effect arises when the uncertainty parameter in the dynamic system exists. The total fit effects, the consistency of the vehicle safety, and the tail fit effects are determined for selecting the best method. Therefore, regarding the approach, the lognormal and extreme maximum distribution values may be the appropriate assumed distribution for dynamic safety under limited data.

Past and future joint return period of precipitation extremes over South Asia and Southeast Asia

Climate change is one of the major reasons for the increased intensity and frequency of precipitation extremes in tropical regions. This will have a significant impact on underdeveloped countries in South Asia and Southeast Asia. Therefore, this study analyzes changes in spatiotemporal patterns and the joint behavior of precipitation extremes across South Asian and Southeast Asian countries for the historical period (1975 to 2014) and future periods (2021–2060 (F1) and 2061–2100 (F2)). This study develops bias-corrected precipitation data and ranks General Circulation Models (GCMs) using the Empirical Quantile Mapping method and TOPSIS method, respectively. A multi-model ensemble of precipitation extremes is created using the top five GCMs. The Mann Kendall test is used to analyze trends in precipitation extremes. Joint probabilistic analysis is also conducted for different combinations of ETCCDI precipitation-based indices using Archimedes and Elliptical copulas. The results of the trend analysis indicate significant positive trends for R20mm (19.26%), R95pTOT (18.40%), Rx5Day (11.53%), and CWD (10.46%), while CDD (5.07%) shows a significant negative trend across the study area during historical period (1975–2014). The results of R20mm, R95pTOT, and Rx5Day under SSP585 shows almost 19 to 39% of area comes under significant positive trend during the F1 period. This becomes more evident in F2, with trends under SSP585 rising between 32% and 61%. The high-emissions scenario SSP585 reveals an increase in these positive trends compared to SSP126 in both the future periods (F1 and F2). These results indicating a noticeable rise in extreme precipitation events. The analysis of changes in the joint return period of precipitation extremes indicates that the South Peninsular India, North East India, West Central India and Central Northeast India, as well as most parts of Southeast Asian countries, will experience very heavy intensify precipitations in the future. In addition, persistent co-occurrence of dry and wet conditions will be observed in Pakistan, North West India, and Central Northeast India. This study provides useful information on the distribution of precipitation extremes in different regions of the study area.

A novel link fabrication attack detection method for low-latency SDN networks

The application of Software-defined Networking (SDN) in low-latency scenarios, such as 6G, has received immense attention. Notably, our research reveals that SDN remains susceptible to link fabrication attacks (LFA) in low-latency environments, where existing detection methods fail to effectively detect LFA. To address this issue, we propose a novel detection method called Correlated Link Verification (CLV). CLV is composed of three phases. Firstly, we introduce a data processing method to mitigate measurement error and enhance robustness. Secondly, we present a multipath transmission simulation method to convert the measured performance disparity between correlated links into statistical features. Thirdly, we propose a dynamic threshold calculation method, which utilizes the statistical features to determine thresholds based on extreme value theory and probability distribution fitting. Finally, CLV identifies the fabricated link within correlated links based on the thresholds and current statistical features. Extensive experiments have been conducted to validate the feasibility, effectiveness, scalability and robustness of CLV. The experimental results demonstrate that CLV can effectively detect LFA in low-latency SDN networks.