Tail Of Distribution Research Articles

Longitudinal predictors of reading and arithmetic at different attainment levels

Reading and arithmetic are distinct academic skills that share similarities in skill acquisition and use. Previous research investigated the cognitive basis of associations and dissociations between reading and arithmetic by using either subtyping or dimensional approaches. In the current study, we aim to bridge the gap between these two approaches by investigating common and distinct predictors of reading and arithmetic at different performance levels with quantile regression models. This allowed us to look more closely at the lower tail of the ability distributions, and to test whether predictions for children with low reading and arithmetic fluency differed from the typical performance range. We analyzed longitudinal data of 357 children speaking English or German. Outcome variables were reading and arithmetic fluency assessed at the end of Grade 1, 2, and 3. Predictors were assessed in Grade 1. Results confirmed nonverbal IQ and working memory as domain-general predictors of reading and arithmetic. The association of reading and arithmetic was mainly explained by nonverbal IQ, phonological awareness, RAN and multi-digit transcoding. Across grades and performance levels, phonological awareness and RAN made a specific contribution to reading. Magnitude processing and multi-digit transcoding were specific predictors of arithmetic. Counting also made a specific prediction to arithmetic in Grade 3, but only in the low performance range. Our findings indicate partly distinct underlying cognitive mechanisms for reading and arithmetic. Shared predictors are involved in retrieval efficiency, language processing and cross-format integration. These results have important implications, as they suggest that most predictors are equally relevant for children with low, typical or even excellent reading and arithmetic fluency.

Going beyond Top EFT

We present a new way to interpret Top Standard Model measurements going beyond the SMEFT framework. Instead of the usual paradigm in Top EFT, where the main effects come from tails in momenta distributions, we propose an interpretation in terms of new physics which only shows up at loop-level. The effects of these new states, which can be lighter than required within the SMEFT, appear as distinctive structures at high momenta, but may be suppressed at the tails of distributions. As an illustration of this phenomena, we present the explicit case of a UV model with a Z\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{Z} $$\\end{document}2 symmetry, including a Dark Matter candidate and a top-partner. This simple UV model reproduces the main features of this class of signatures, particularly a momentum-dependent form factor with more structure than the SMEFT. As the new states can be lighter than in SMEFT, we explore the interplay between the reinterpretation of direct searches for colored states and Dark Matter, and Top measurements, made by ATLAS and CMS in the differential tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} final state. We also compare our method with what one would expect using the SMEFT reinterpretation, finding that using the full loop information provides a better discriminating power.

Identifying Sources of Inter-hospital Variation in Episode Spending for Sepsis Care.

To evaluate inter-hospital variation in 90-day total episode spending for sepsis, estimate the relative contributions of each component of spending, and identify drivers of spending across the distribution of episode spending on sepsis care. Medicare fee-for-service claims for beneficiaries (n=324,694) discharged from acute care hospitals for sepsis, defined by MS-DRG, between October 2014 and September 2018. Multiple linear regression with hospital-level fixed effects was used to identify average hospital differences in 90-day episode spending. Separate multiple linear regression and quantile regression models were used to evaluate drivers of spending across the episode spending distribution. The mean total episode spending among hospitals in the most expensive quartile was $30,500 compared with $23,150 for the least expensive hospitals (P<0.001). Postacute care spending among the most expensive hospitals was almost double that of least expensive hospitals ($7,045 vs. $3,742), accounting for 51% of the total difference in episode spending between the most expensive and least expensive hospitals. Female patients, patients with more comorbidities, urban hospitals, and BPCI-A-participating hospitals were associated with significantly increased episode spending, with the effect increasing at the right tail of the spending distribution. Inter-hospital variation in 90-day episode spending on sepsis care is driven primarily by differences in post-acute care spending.

Downside and Upside Uncertainty Shocks

Abstract An increase in uncertainty is not contractionary per se. What is contractionary is a widening of the left tail of the GDP growth forecast distribution, the downside uncertainty. On the contrary, an increase of the right tail, the upside uncertainty, is mildly expansionary. The reason why uncertainty shocks have been previously found to be contractionary is because movements in downside uncertainty dominate existing empirical measures of uncertainty. The results are obtained using a new econometric approach that combines quantile regressions and structural vector autoregressions (VARs).

Large deviations in statistics of the convex hull of passive and active particles: A theoretical study.

We investigate analytically the distribution tails of the area A and perimeter L of a convex hull for different types of planar random walks. For N noninteracting Brownian motions of duration T we find that the large-L and -A tails behave as P(L)∼e^{-b_{N}L^{2}/DT} and P(A)∼e^{-c_{N}A/DT}, while the small-L and -A tails behave as P(L)∼e^{-d_{N}DT/L^{2}} and P(A)∼e^{-e_{N}DT/A}, where D is the diffusion coefficient. We calculated all of the coefficients (b_{N},c_{N},d_{N},e_{N}) exactly. Strikingly, we find that b_{N} and c_{N} are independent of N for N≥3 and N≥4, respectively. We find that the large-L (A) tails are dominated by a single, most probable realization that attains the desired L (A). The left tails are dominated by the survival probability of the particles inside a circle of appropriate size. For active particles and at long times, we find that large-L and -A tails are given by P(L)∼e^{-TΨ_{N}^{per}(L/T)} and P(A)∼e^{-TΨ_{N}^{area}(sqrt[A]/T)}, respectively. We calculate the rate functions Ψ_{N} exactly and find that they exhibit multiple singularities. We interpret these as DPTs of first order. We extended several of these results to dimensions d>2. Our analytic predictions display excellent agreement with existing results that were obtained from extensive numerical simulations.

Dependence on Tail Copula

In real-world scenarios, we encounter non-exchangeable dependence structures. Our primary focus is on identifying and quantifying non-exchangeability in the tails of joint distributions. The findings and methodologies presented in this study are particularly valuable for modeling bivariate dependence, especially in fields where understanding dependence patterns in the tails is crucial, such as quantitative finance, quantitative risk management, and econometrics. To grasp the intricate relationship between the strength of dependence and various types of margins, we explore three fundamental tail behavior patterns for univariate margins. Capitalizing on the probabilistic features of tail non-exchangeability structures, we introduce graphical techniques and statistical tests designed for analyzing data that may manifest non-exchangeability in the joint tail. The effectiveness of the proposed approaches is illustrated through a simulation study and a practical example.

Turbulent Magnetic Reconnection as an Acceleration Mechanism in Earth’s Magnetotail

Using electric and magnetic fields measured by the Magnetospheric Multiscale (MMS) mission, we construct a test-particle simulation of a turbulent magnetic reconnection region to investigate observed ion acceleration. We identify three types of energized ions: (1) ion jets, (2) Speiser-like energized ions—both of which carry significant energy but do not produce a strong energetic (>80 keV) tail in the ion distribution—and (3) a separate but sizable population of ions that are accelerated to significantly higher energies (>80 keV) by the turbulent fields. The majority of ions that undergo energization by the turbulent fields cross the magnetic null plane multiple times. By preferentially energizing these particles, the turbulence creates a separate population of ions that mostly exits in the dawn direction of the magnetotail and forms a high-energy power-law tail in the ion flux-energy distribution. We also find that the highest acceleration energies are limited by the size of the turbulent region (with respect to ion gyroradii). Since turbulence is widespread in astrophysical plasmas and has no a priori limit on scale size, the MMS observations suggest turbulence may have a significant role in particle acceleration.

Exploring skill distribution tails through stochastic dominance

SummaryLocation choices of differently skilled workers are analyzed in previous work on labor mobility, which proposes a model that suggests thicker tails in the skill distributions of large cities. This paper replicates the empirical findings of this work by using quantile regression and density plots as employed in the existing study, while also suggesting an alternative testing method for thick tails in the form of an initial stochastic dominance test. The test reveals clear evidence of a thicker lower tail, but the results are less clear for the upper tail, which raises some questions on how to best handle extreme upper tails of skill distributions.

Statistical inference for multivariate extremes via a geometric approach

Abstract A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts. However, these results are purely probabilistic, and the geometric approach itself has not been fully exploited for statistical inference. We outline a method for parametric estimation of the limit set shape, which includes a useful non-/semi-parametric estimate as a pre-processing step. More fundamentally, our approach provides a new class of asymptotically motivated statistical models for the tails of multivariate distributions, and such models can accommodate any combination of simultaneous or non-simultaneous extremes through appropriate parametric forms for the limit set shape. Extrapolation further into the tail of the distribution is possible via simulation from the fitted model. A simulation study confirms that our methodology is very competitive with existing approaches and can successfully allow estimation of small probabilities in regions where other methods struggle. We apply the methodology to two environmental datasets, with diagnostics demonstrating a good fit.

General Purpose and Focused Invention, Market Value, and Productivity

We study returns to general purpose and focused invention at the firm level for a panel of manufacturing firms in the U.S. for the period 1976-1995, by studying their relationships with market value and Total Factor Productivity. We construct stocks of patents that lie at the two relevant tails of the distribution of the generality index (Trajtenberg et al., 1997; Henderson et al, 1998) to measure general purpose and focused invention at the firm level. In line with expectations, there is a market value premium to focused invention, and a productivity premium to general purpose invention. Estimates for the value of focus indicate that moving a single patent from the upper tail of the generality distribution to the lower tail would increase market value by .24×q million 1992 dollars on average, where q is Tobin’s q. The firm with the average general patent stock would gain 6.7×q million in market value if all its patents at the highest quartile of the generality distribution were moved to the lowest. In terms of the value of general purposeness, moving all its focused patents to the general category increases Total Factor Productivity by 2.3% to 2.8%, and five-year productivity growth by 3.9% to 5.2%, for the average firm. A potential implication is that corporate basic research is associated with significant long-term benefits in terms of productivity growth.

The finite mixture model for the tails of distribution: Monte Carlo experiment and empirical applications

AbstractThe finite mixture model estimates regression coefficients distinct in each of the different groups of the dataset endogenously determined by this estimator. In what follows the analysis is extended beyond the mean, estimating the model in the tails of the conditional distribution of the dependent variable within each group. While the clustering reduces the overall heterogeneity, since the model is estimated for groups of similar observations, the analysis in the tails uncovers within groups heterogeneity and/or skewness. By integrating the endogenously determined clustering with the quantile regression analysis within each group, enhances the finite mixture models and focuses on the tail behavior of the conditional distribution of the dependent variable. A Monte Carlo experiment and two empirical applications conclude the analysis. In the well‐known birthweight dataset, the finite mixture model identifies and computes the regression coefficients of different groups, each one with its own characteristics, both at the mean and in the tails. In the family expenditure data, the analysis of within and between groups heterogeneity provides interesting economic insights on price elasticities. The analysis in classes proves to be more efficient than the model estimated without clustering. By extending the finite mixture approach to the tails provides a more accurate investigation of the data, introducing a robust tool to unveil sources of within groups heterogeneity and asymmetry otherwise left undetected. It improves efficiency and explanatory power with respect to the standard OLS‐based FMM.

Contrastive Learning Penalized Cross-Entropy with Diversity Contrastive Search Decoding for Diagnostic Report Generation of Reduced Token Repetition

Medical imaging description and disease diagnosis are vitally important yet time-consuming. Automated diagnosis report generation (DRG) from medical imaging description can reduce clinicians’ workload and improve their routine efficiency. To address this natural language generation task, fine-tuning a pre-trained large language model (LLM) is cost-effective and indispensable, and its success has been witnessed in many downstream applications. However, semantic inconsistency of sentence embeddings has been massively observed from undesirable repetitions or unnaturalness in text generation. To address the underlying issue of anisotropic distribution of token representation, in this study, a contrastive learning penalized cross-entropy (CLpCE) objective function is implemented to enhance the semantic consistency and accuracy of token representation by guiding the fine-tuning procedure towards a specific task. Furthermore, to improve the diversity of token generation in text summarization and to prevent sampling from unreliable tail of token distributions, a diversity contrastive search (DCS) decoding method is designed for restricting the report generation derived from a probable candidate set with maintained semantic coherence. Furthermore, a novel metric named the maximum of token repetition ratio (maxTRR) is proposed to estimate the token diversity and to help determine the candidate output. Based on the LLM of a generative pre-trained Transformer 2 (GPT-2) of Chinese version, the proposed CLpCE with DCS (CLpCEwDCS) decoding framework is validated on 30,000 desensitized text samples from the “Medical Imaging Diagnosis Report Generation” track of 2023 Global Artificial Intelligence Technology Innovation Competition. Using four kinds of metrics evaluated from n-gram word matching, semantic relevance, and content similarity as well as the maxTRR metric extensive experiments reveal that the proposed framework effectively maintains semantic coherence and accuracy (BLEU-1, 0.4937; BLEU-2, 0.4107; BLEU-3, 0.3461; BLEU-4, 0.2933; METEOR, 0.2612; ROUGE, 0.5182; CIDER, 1.4339) and improves text generation diversity and naturalness (maxTRR, 0.12). The phenomenon of dull or repetitive text generation is common when fine-tuning pre-trained LLMs for natural language processing applications. This study might shed some light on relieving this issue by developing comprehensive strategies to enhance semantic coherence, accuracy and diversity of sentence embeddings.

A HANK[formula omitted] model of monetary unions

How does a monetary union alter the impact of business cycle shocks at the household level? We develop a Heterogeneous Agent New Keynesian model of two countries (HANK2) and show in closed form that a monetary union shifts the adjustment to a shock horizontally across countries, within the brackets of the union-wide wealth distribution, rather than vertically, that is, across the brackets of the union-wide wealth distribution. Calibrating the model to the euro area reveals that a monetary union alters the impact of shocks most strongly in the tails of the wealth distribution but leaves the middle class almost unaffected.

On Models of Time Series

Recently a number of time series models have been constructed and studied for real valued observations using different marginal distributions by several researchers. Many naturally occurring time series observations show a tendency to follow asymmetric and heavy tailed distributions. A review of literature on some heavy tailed models of time series is done in this paper.

Capital risk, fiscal policy, and the distribution of wealth

We develop a dynamic model economy where self-employed entrepreneurs allocate their net worth to their firm capital and risk-less government bonds, facing borrowing constraints, uninsurable labour endowment and capital depreciation risk. We derive a numerical approximation of the model’s equilibrium and compare it with a benchmark economy with no capital risk. Unlike labour endowment risk, capital risk reduces aggregate capital accumulation and wages and generates a positive risk premium. Low- (high-) net-worth entrepreneurs, whose consumption depends primarily on labour (financial) income, hold higher (lower) capital risk exposure. These patterns exacerbate inequality by increasing the share of financially constrained individuals and fattening the tails of the net worth distribution. Fiscal policy affects these outcomes by redistributing resources and affecting the risk premium. Capital tax cuts benefit more low- or high-net-worth entrepreneurs, depending on whether taxes on bonds or labour income finance them.

Searching the differences through the tails of distributions using an approach based on Mahalanobis distance and percentile bootstrap

One of the main objectives of applied statistics is to determine whether two independent groups differ, and if so, to understand how they do. The Student t-test is the conventional method for doing this; however, it merely depends on a sensitive measure of location and a sampling distribution with some restrictive assumptions. There are some robust alternatives in the literature, but they concentrate on just one reference point over the entire distribution as well. It is often of interest to analyze the differences that occur in the tails of distributions, namely the quantiles. In this study, two independent groups are compared using a method based on a Mahalanobis distance and a percentile bootstrap approach. Two recently proposed and two well-known quantile estimators are used with the proposed method. Results for both theoretical distributions and real data sets are examined. Using the proposed method in conjunction with the Navruz and Özdemir (NO) estimator saved nominal Type-I error in all but five experimental cases out of 61 and it could potentially offer valuable insights into detecting the differences that occurred in the tails of the distributions.

Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits

Abstract We propose methods to estimate and make inferences on conditional quantile processes for models with both nonparametric and (locally or globally) linear components. We derive their asymptotic properties, optimal bandwidths, and uniform confidence bands over quantiles allowing for robust bias correction. Our framework covers the sharp regression discontinuity design, which is used to study the effects of unemployment insurance benefits extensions, focusing on heterogeneity over quantiles and covariates. We show economically strong effects in the tails of the outcome distribution. They reduce the within-group inequality, but can be viewed as enhancing between-group inequality, although they help to bridge the gender gap.

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone. The code is based on the extended Press–Schechter model and is computationally efficient, typically taking a few seconds on a personal laptop for a given set of cosmological parameters. The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope, as well as scanning the theory space with the Markov Chain Monte Carlo method. As an example application, we use the tool to study the cosmological implication of the candidate galaxies presented in Labbé et al. The standard Λ cold dark matter (ΛCDM) model is well consistent with the data if the star formation efficiency can reach ∼0.3 at high redshift. For a low star formation efficiency ϵ ∼ 0.1, the ΛCDM model is disfavored at ∼2σ–3σ confidence level.

Inference for New Environmental Contours Using Extreme Value Analysis

AbstractEnvironmental contours are often used in engineering applications to describe risky combinations of variables according to some definition of an exceedance probability. These contours can be used to both understand multivariate extreme events in environmental processes and mitigate against their effects, e.g. in the design of structures. Such ideas are also useful in other disciplines, with the types of extreme events of interest depending on the context. Despite clear connections with extreme value modelling, much of this methodology has so far not been exploited in the estimation of environmental contours; in this work, we provide a way to unify these areas. We focus on the bivariate case, introducing two new definitions of environmental contours. We develop techniques for their inference which exploit a non-standard radial and angular decomposition of the variables, building on previous work for estimating limit sets. Specifically, we model the upper tails of the radial distribution using a generalised Pareto distribution, with adaptable smoothing of the parameters of this distribution. Our methods work equally well for asymptotically independent and asymptotically dependent variables, so do not require us to distinguish between different joint tail forms. Simulations demonstrate reasonable success of the estimation procedure, and we apply our approach to an air pollution data set, which is of interest in the context of environmental impacts on health.Supplementary materials accompanying this paper appear online.

Direct Evidence of Bitcoin Wash Trading

We use the internal trading records of a major Bitcoin exchange leaked by hackers to detect and characterize wash trading—a type of market manipulation in which a single trader clears the trader’s own limit orders to “cook” transaction records. Our finding provides direct evidence for the widely suspected “fake volume” allegation against cryptocurrency exchanges, which has so far only been backed by indirect estimation. We then use our direct evidence to evaluate various indirect techniques for detecting the presence of wash trades and find measures based on Benford’s law, trade size clustering, lognormal distributions, and structural breaks to be useful, whereas ones based on power law tail distributions to give opposite conclusions. We also provide suggestions to effectively apply various indirect estimation techniques. This paper was accepted by Professor Bruno Biais, finance. Funding: J. Li acknowledges support by the U.S. Department of Homeland Security [Grant 205187] through the Criminal Investigations and Network Analysis Center. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2021.01448 .