Tail Of Distribution Research Articles

Contact pressure explains half of the abdominal aortic aneurysms wall thickness inter-study variability.

The stochastic rupture risk assessment of an abdominal aortic aneurysm (AAA) critically depends on sufficient data set size that would allow for the proper distribution estimate. However, in most published cases, the data sets comprise no more than 100 samples, which is deemed insufficient to describe the tails of AAA wall thickness distribution correctly. In this study, we propose a stochastic Bayesian model to merge thickness data from various groups. The thickness data adapted from the literature were supplemented by additional data from 81 patients. The wall thickness was measured at two different contact pressures for 34 cases, which allowed us to estimate the radial stiffness. Herein, the proposed stochastic model is formulated to predict the undeformed wall thickness. Furthermore, the model is able to handle data published solely as summary statistics. After accounting for the different contact pressures, the differences in the medians reported by individual groups decreased by 45%. Combined data can be fitted with a lognormal distribution with parameters μ = 0.85 and σ = 0.32 which can be further used in stochastic analyses.

A comprehensive analysis of the tail-dependent structure of wind loads and its engineering applications

Wind load field characteristics on the roof surface of low-rise buildings based on field measurements have crucial engineering guidance value. In the background, tail-dependence structure from measured wind loads can assist in modeling the joint tail distribution of multivariate wind loads. In this study, the non-parameter estimation method, multi-copula function model and multivariate peak over threshold model are applied to estimate its precise value. The upper tail dependence coefficient's value is around 0.20 when the quantile for p(y) = 0.75. When p(y) = 0.95, the Gumbel copula overestimates the tail-dependence value slightly. Additionally, the lower tail-dependence values estimated by the Clayton copula are around 0.19 at 0.25 quantile. For extreme tail-dependence coefficients, little difference exists in the estimated results by the non-parameter estimation method and the peak over threshold model, in which its value varies from 0.80 to 0.90. Under roof pitch = 5°, its value exhibits some dispersion at different locations. An area weight function is applied to estimate the extreme tail-dependence value between critical regions. Then, the expectation function of tail dependence reaches the peak value in p(x) = 0.50, p(y) = 0.50 and it has different gradients for different variables and tail regions. Additionally, the lower tail dependence structure is significantly stronger than the upper tail dependence for wind loads with negative skewness. For application in wind engineering, potential applications in risk analysis for roof structures, extreme value estimation for local region block wind load, and wind load forecast for unmonitored locations are proposed.

A multivariate statistical framework for mixed storm types in compound flood analysis

Abstract. In coastal regions, compound flooding can arise from a combination of different drivers, such as storm surges, high tides, excess river discharge, and rainfall. Compound flood potential is often assessed by quantifying the dependence and joint probabilities of flood drivers using multivariate models. However, most of these studies assume that all extreme events originate from a single population. This assumption may not be valid for regions where flooding can arise from different generation processes, e.g., tropical cyclones (TCs) and extratropical cyclones (ETCs). Here we present a flexible copula-based statistical framework to assess compound flood potential from multiple flood drivers while explicitly accounting for different storm types. The proposed framework is applied to Gloucester City, New Jersey, and St. Petersburg, Florida, as case studies. Our results highlight the importance of characterizing the contributions from TCs and non-TCs separately to avoid potential underestimation of the compound flood potential. In both study regions, TCs modulate the tails of the joint distributions (events with higher return periods), while non-TC events have a strong effect on events with low to moderate joint return periods. We show that relying solely on TCs may be inadequate when estimating compound flood risk in coastal catchments that are also exposed to other storm types. We also assess the impact of non-classified storms that are not linked to either TCs or ETCs in the region (such as locally generated convective rainfall events and remotely forced storm surges). The presented study utilizes historical data and analyzes two populations, but the framework is flexible and can be extended to account for additional storm types (e.g., storms with certain tracks or other characteristics) or can be used with model output data including hindcasts or future projections.

Global emergence of regional heatwave hotspots outpaces climate model simulations

Multiple recent record-shattering weather events raise questions about the adequacy of climate models to effectively predict and prepare for unprecedented climate impacts on human life, infrastructure, and ecosystems. Here, we show that extreme heat in several regions globally is increasing significantly and faster in magnitude than what state-of-the-art climate models have predicted under present warming even after accounting for their regional summer background warming. Across all global land area, models underestimate positive trends exceeding 0.5 °C per decade in widening of the upper tail of extreme surface temperature distributions by a factor of four compared to reanalysis data and exhibit a lower fraction of significantly increasing trends overall. To a lesser degree, models also underestimate observed strong trends of contraction of the upper tails in some areas, while moderate trends are well reproduced in a global perspective. Our results highlight the need to better understand and model the drivers of extreme heat and to rapidly mitigate greenhouse gas emissions to avoid further harm from unexpected weather events.

Comparing prediction efficiency in the BTW and Manna sandpiles

The state-of-the-art in the theory of self-organized criticality reveals that a certain inactivity precedes extreme events, which are located on the tail of the event probability distribution with respect to their sizes. The existence of the inactivity allows for the prediction of these events in advance. In this work, we explore the predictability of the Bak–Tang–Wiesenfeld (BTW) and Manna models on the square lattice as a function of the lattice length. For both models, we use an algorithm that forecasts the occurrence of large events after a fall in activity. The efficiency of the prediction can be universally described in terms of the event size divided by an appropriate power-law function of the lattice length. The power-law exponents are projected to be 2.75 and 3 for the Manna and BTW models respectively. The scaling with the exponent 2.75 is known for collapsing of the entire size-frequency relationship in the Manna model. However, the correspondence between events on different lattices in the BTW model requires a variety of exponents where 3 is the largest. This indicates that in thermodynamic limit, prediction does exist in the Manna but not in the BTW model, at least based on inactivity. The difference in the universality classes may underline the difference in the prediction.

Investigation of on-pitch SGD structure induced Vth distribution tails downshift in 3D NAND flash memory

Investigation of on-pitch SGD structure induced Vth distribution tails downshift in 3D NAND flash memory

Learning extreme expected shortfall and conditional tail moments with neural networks. Application to cryptocurrency data

We propose a neural networks method to estimate extreme Expected Shortfall, and even more generally, extreme conditional tail moments as functions of confidence levels, in heavy-tailed settings. The convergence rate of the uniform error between the log-conditional tail moment and its neural network approximation is established leveraging extreme-value theory (in particular the high-order condition on the distribution tails) and using critically two activation functions (eLU and ReLU) for neural networks. The finite sample performance of the neural network estimator is compared to bias-reduced extreme-value competitors using synthetic heavy-tailed data. The experiments reveal that our method largely outperforms others. In addition, the selection of the anchor point appears to be much easier and stabler than for other methods. Finally, the neural network estimator is tested on real data related to extreme loss returns in cryptocurrencies: here again, the accuracy obtained by cross-validation is excellent, and is much better compared with competitors.

Unequal Learning Loss: How the COVID-19 Pandemic Influenced the Academic Growth of Learners at the Tails of the Achievement Distribution

The COVID-19 pandemic resulted in substantial unfinished learning for U.S. students, but to differing degrees for various subgroups. Students of color, from low-income families, or who attended high-poverty schools experienced greater unfinished learning. In this study, we examined the degree of unfinished learning for students who went into the pandemic scoring in the top or bottom 10% of achievement in math or reading. Our results show that students who scored at or below the 10th percentile grew less during the pandemic than their similarly scoring, pre-COVID peers and, as of the end of the 2021–2022 school year, had yet to rebound toward pre-COVID levels of growth or achievement. Conversely, students who scored at or above the 90th percentile largely grew at rates closer to their pre-COVID peers. These students were harmed less academically and have recovered more quickly than their peers scoring at or below the 10th percentile.

Markov Chains in the Domain of Attraction of Brownian Motion in Cones

We consider a multidimensional Markov chain X converging to a multidimensional Brownian motion. We construct a positive harmonic function for X killed on exiting the cone. We show that its asymptotic behaviour is similar to that of the harmonic function of Brownian motion. We use the harmonic function to study the asymptotic behaviour of the tail distribution of the exit time τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} of X from a cone.

Estimation and Inference for Extreme Continuous Treatment Effects*

This paper studies estimation and inference for the treatment effect in deep tails of the potential outcome distributions corresponding to a continuously valued treatment, namely the extreme continuous treatment effect. We consider two measures for the tail characteristics: the quantile function and the tail mean function defined as the conditional mean beyond a quantile level. Then, for a quantile level close to 1, we define the extreme quantile treatment effect (EQTE) and extreme average treatment effect (EATE), which are, respectively, the ratios of the quantile and tail mean at different treatment statuses. We propose estimators for the EQTE and EATE based on tail approximations from the extreme value theory. Our limiting theory is for the EQTE and EATE processes indexed by a set of quantile levels and pairs of different treatment statuses. It facilitates uniform inference for the EQTE and EATE over multiple tail levels and multiple treatment effects. Simulations suggest that our method works well in finite samples, and an empirical study illustrates its practical merits.

Stress Field and Crack Pattern Interpretation by Deep Learning in a 2D Solid

ABSTRACTA nonlinear variational auto‐encoder (NLVAE) is developed to reconstruct the plane strain stress field in a solid with embedded cracks subjected to uniaxial tension, uniaxial compression, and shear loading paths. Latent features are sampled from a skew‐normal distribution, which allows encoding marked variations of the features of the stress field across the load steps. The NLVAE is trained and tested based upon stress maps generated with the finite element method (FEM) with cohesive zone elements (CZEs). The NLVAE successfully captures stress concentrations that develop across the loading steps as a result of crack propagation, especially when enhanced disentanglement is emphasized during training. Some latent variables consistently emerge as significant across various microstructure descriptors and loading paths. Correlations observed between the evolution of fabric descriptors and that of their significant stress latent features indicate that the NLVAE can capture important microstructure transitions during the loading process. Crack connectivity, crack eccentricity, and the distribution of zones of highly connected opened cracks versus zones with no cracks are the fabric descriptors that best explain the sequences of latent features that are the most important for the reconstruction of the stress field. Notably, the distributional shape, tail behavior, and symmetry of microstructure descriptor distributions have more influence on the stress field than basic measures of central tendency and spread.

Effect of recycled molybdenum tailings on mechanical properties of ultra-high-performance concrete

This paper presents experimental studies on mechanical properties and micro-structures of ultra-high performance concrete (UHPC) made of recycled molybdenum tailings. The particle size distribution and chemical compositions of recycled molybdenum tailings were analysed at first. Then, compressive and flexural tests were conducted on UHPC in which different volume fractions of recycled molybdenum tailings were used to replace silica sand. The effects of recycled molybdenum tailings replacement ratio on the compressive and flexural strengths were determined through comparisons. Besides, X-ray diffraction tests and backscattered electron tests were carried out to analyse the effect of molybdenum tailings on the micro-structure of UHPC. Based on test data, an optimal replacement ratio of molybdenum tailings was determined which could significantly reduce the cost of UHPC but maintain the mechanical properties in compression. A molybdenum tailings replacement ratio of 30% was recommended to maximise the economic effect and to reduce the carbon emission.

Proton irradiation effect mechanism of backside illuminated CMOS image sensors applied to FGS

A study of the mechanism of proton irradiation effects in the in-orbit operation of the backside illuminated CMOS image sensor (BSI CIS) used for imaging by the Fine Guidance Sensor (FGS) is presented in this paper. According to the proton irradiation environment of the Halo L2 orbit where FGS is located and the duration of in orbit operation, proton irradiation experiments were conducted on the BSI CIS, the core imaging device of FGS. Results show that proton irradiation is expected to cause a significant increase in the dark current of the BSI CIS of the FGS after four years of its in orbit, with the peak of the dark signal distribution shift to the right and an exponential trailing of the tail of the dark signal distribution when the proton fluence reached 6.71 × 1010p/cm2. This is the result of a combination of ionization defects and displacement damage defects. In addition, we also report about the device gain, which is of particular interest in space astronomical exploration. We performed a more detailed single pixel gain test of the device gain and found that the degradation of the gain appears to be correlated with the intensity of the ionization defects. The results of this study can provide theoretical basis for the radiation hardening by design of FGS to some extent.

Modeling of Reversed Fréchet Distribution under Linear Normalizing

Extreme value theory (EVT) is becoming increasingly important as a suitable model of extreme events to represent phenomena in various fields of applications where extreme values may appear and have detrimental effects. In EVT, the Reversed Fréchet (RF) distribution is a special case of the Reversed generalized extreme value distribution (RGEVD) for modeling extreme data under linear normalizing. The purpose of this paper is divided into four objectives: Firstly, we discuss the practical aspects of the two methods that belong to the domain attraction of RF distribution. The second objective is to use RF distribution to model the behavior of two extreme air pollutants. The third objective is based on a diagnostics plot and hypothesis testing used to evaluate an appropriate shape of the tail distribution. Lastly, for the fourth objective, we attempt to obtain the return level period (RLP) that is expected to be exceeded. Maximum likelihood estimation (MLE) is derived and used to estimate the parameters of RF distribution. The results show that applications are significant for modeling by RF distribution in all cases of two air pollutants. Software that was used in all computations and graphics is the R statistical program with packages fExtreme and ismev.

Foundational Aspects for Incorporating Dependencies in Copula-Based Bayesian Networks Using Structured Expert Judgments, Exemplified by the Ice Sheet-Sea Level Rise Elicitation.

The work presented here marks a further advance in expert uncertainty quantification. In a recent probabilistic evaluation of ice sheet process contributions to sea level rise, tail dependence was elicited and propagated through an uncertainty analysis for the first time. The elicited correlations and tail dependencies concerned pairings of three processes: Accumulation, Discharge and Run-off, which operate on major ice sheets in the West and East Antarctic and in Greenland. The elicitation enumerated dependencies between these processes under selected global temperature change scenarios over different future time horizons. These expert judgments allowed us to populate a Paired Copula Bayesian network model to obtain the estimated contributions of these ice sheets for future sea level rise. Including positive central tendency dependence and tail dependence increases the fatness of the upper tails of projected sea level rise distributions, an amplification important for designing and evaluating possible mitigation strategies. Detailing and jointly computing distributional dependencies and tail dependencies can be crucial components of good practice for assessing the influence of uncertainties on extreme values when modelling stochastic multifactorial processes.

Distributions and Correlation Properties of Offshore Wind Speeds and Wind Speed Increments

We determine distributions and correlation properties of offshore wind speeds and wind speed increments by analyzing wind data sampled with a resolution of one second for 20 months at different heights above sea level in the North Sea. Distributions of horizontal wind speeds can be fitted to Weibull distributions with shape and scale parameters varying weakly with the vertical height separation. Kullback–Leibler divergences between distributions at different heights change with the squared logarithm of the height ratio. Cross-correlations between time derivatives of wind speeds are long-term anticorrelated, and the even parts of their correlation functions satisfy sum rules. Distributions of horizontal wind speed increments change from a tent-like shape to a Gaussian with rising increment lag. A surprising peak occurs in the left tail of the increment distributions for lags in a range 10-200km\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10-200\\,{km}$$\\end{document} after applying the Taylor’s hypothesis locally to transform time lags into distances. The peak is decisive in order to obtain an expected and observed linear scaling of third-order structure functions with distance. This suggests that it is an intrinsic feature of atmospheric turbulence.

Energy transition, institutional quality, and financial development in Africa

This study examines the influence of institutional quality and financial sector size on driving renewable energy (RE) development using a sample of 31 African countries. We first employ a nonparametric trending panel data model that allows us to capture the gradual process of RE transition. The estimated common trend function reveals a steady increase in the share of RE from 2002 to 2019. Although fossil fuels dominate the energy structure in some African countries, a shift toward low-carbon sources is emerging, becoming increasingly significant in the energy mix. In the next step, we apply recent panel quantile regression techniques to model the heterogeneous and asymmetric relationships between RE and its main determinants. We find that institutional quality has a prominent influence on advancing the low-carbon transition, with significant positive effects across almost all conditional quantiles of the RE distribution. However, financial sector size seems to be important only for countries with a lower share of RE. Our results also confirm the asymmetric impact of income growth, which is negative in the lower quantiles but positive in the upper tail of the conditional distribution. From a policy perspective, governance factors, including the quality of policy formulation and implementation, have a critical role in promoting clean energy initiatives in Africa.

Quantile dependence: A generalization of upper and lower tail dependence

A popular measure of association is the tail dependence coefficient, which measures the strength of dependence in the tail of a bivariate distribution. In this paper, we introduce the concept of quantile dependence, which extends the idea of tail dependence and can be used to measure the dependence of specific quantiles of two random variables in a particular area of the distribution's domain. We analyze the characteristics of the proposed quantile dependence coefficient and provide various examples to demonstrate our findings.

Evaluating Extremes in Climatology with Average Value-at-Risk Measure: Example of Precipitation Data from Upper Vistula Region in Poland

Abstract The ability to predict changes in the right tail of daily precipitation distributions over short time periods, as well as the probability of clustering extreme values, is critical for current risk management. In the present study, we apply the well-established metric average value-at-risk (AVaR) for the first time within the field of climatology. We also investigate the evolution of the return level (RL) and the extremal index (EI), which we refer to as risk measures. In the case of precipitation processes, a rise in the first two and a reduction in the third may result in increased hazards. These methods were applied to the new data on the daily sum of precipitation from the region of Upper Vistula in Poland from 1951 to 2020 to analyze the dynamics of changes across time. We found that AVaR and RL have the smallest values for the middle of the analyzed period (years 1971–2010), while EI has a maximal value around 1963–92. Both the beginning and the end of the investigated period are characterized by more extreme and clustered precipitation events. Furthermore, this paper includes some recommendations for the tools used to compute the measures.

Citation distributions and research evaluations: The impossibility of formulating a universal indicator

Abstract Purpose To analyze the diversity of citation distributions to publications in different research topics to investigate the accuracy of size-independent, rank-based indicators. The top percentile-based indicators are the most common indicators of this type, and the evaluations of Japan are the most evident misjudgments. Design/methodology/approach The distributions of citations to publications from countries and journals in several research topics were analyzed along with the corresponding global publications using histograms with logarithmic binning, double rank plots, and normal probability plots of log-transformed numbers of citations. Findings Size-independent, top percentile-based indicators are accurate when the global ranks of local publications fit a power law, but deviations in the least cited papers are frequent in countries and occur in all journals with high impact factors. In these cases, a single indicator is misleading. Comparisons of the proportions of uncited papers are the best way to predict these deviations. Research limitations This study is fundamentally analytical, and its results describe mathematical facts that are self-evident. Practical implications Respectable institutions, such as the OECD, the European Commission, and the U.S. National Science Board, produce research country rankings and individual evaluations using size-independent percentile indicators that are misleading in many countries. These misleading evaluations should be discontinued because they can cause confusion among research policymakers and lead to incorrect research policies. Originality/value Studies linking the lower tail of citation distribution, including uncited papers, to percentile research indicators have not been performed previously. The present results demonstrate that studies of this type are necessary to find reliable procedures for research assessments.