Tail Of Distribution Research Articles

Alternative statistical interpretation for the apparent plateaus in the duration distributions of gamma-ray bursts

The existence of a plateau in the short-duration tail of the observed distribution of cosmological long-soft gamma ray bursts (LGRBs) is posited to be the first direct evidence of collapsars. A similar plateau in the short-duration tail of the observed duration distribution of short-hard gamma ray bursts (SGRBs) has been suggested as evidence of compact binary mergers. We present an equally plausible alternative interpretation for this evidence, based on a purely statistical approach. Specifically, we show that the observed plateau in the short-duration tail of the duration distribution of LGRBs can naturally occur in the statistical distributions of strictly positive physical quantities, exacerbated by the effects of mixing with the duration distribution of SGRBs, observational selection effects, and data aggregation (e.g., binning) methodologies. The observed plateau in the short-duration tail of the observed distributions of SGRBs may likewise result from a combination of sample incompleteness and inhomogeneous binning of data. We further confirm the impact of these factors on the observation of a plateau in the duration distributions of GRBs through extensive numerical Monte Carlo simulations. This analysis corroborates and strengthens a purely statistical and sample-incompleteness interpretation of the observed plateau in the duration distribution of LGRBs and SGRBs, without invoking the physics of collapsars or jet-propagation through the stellar envelope.

Heavy tail distribution and Deuterium excess for drought assessment case of Djelfa- watershed (Algeria)

Heavy tail distribution and Deuterium excess for drought assessment case of Djelfa- watershed (Algeria)

Dynamic linkages in agricultural and energy markets: A quantile impulse response approach

AbstractThis article investigates the dynamic linkages between agricultural and energy markets, with a focus on an econometric analysis of multivariate stochastic dynamics based on the joint distribution of state variables. The analysis relies on a quantile approach followed by the evaluation of a copula. Applied to nonlinear price dynamics, the approach is flexible and supports a general evaluation of impulse response functions representing how prices adjust over time and across markets in response to a given shock. The analysis allows for arbitrary distribution functions; it captures own‐price and cross‐price dynamics that can depend on the nature of shocks; and it also allows current changes to affect all moments of the future price distributions. The usefulness of the approach is illustrated in an econometric investigation of dynamic linkages in US corn, ethanol, and crude oil markets. We show how price adjustments can vary across quantiles, reflecting different speeds of adjustments depending on market conditions. We find evidence of nonlinear dynamics specific to the tails of the price distributions. We uncover evidence of positive contemporaneous codependence, especially tail dependence. We show how price shocks affect mean, variance, skewness as well as kurtosis of future price distributions. These results stress the importance of going beyond a standard mean‐variance analysis. They also shed new light on the deep linkages existing in the food‐fuel nexus.

Investigation on the joint travel behavior in bike sharing systems during the COVID-19 pandemic: Insights from New York City

As the COVID-19 pandemic worsened, many people saw bikes as one of the safest means of transportation in the hard-hit cities. All the bike sharing utilization patterns during the pandemic are worthy of careful attention. However, there is still a lack of comprehensive understanding of niche but notable cycling behaviors, such as multi-person round trip (MPRT), defined as two or more cyclists intentionally riding together then returning bikes to the original docking station. This study extends the relevant literature by firstly proposing a MPRT identification framework based on individual bike sharing trip records, with consideration of interpersonal relationships between co-travelers, as well as the specificity of round trips against one-way trips. Taking New York City as a case study, this study examines the changes over space and time of MPRT frequencies from 2019 (i.e. pre-pandemic period) to 2020 (i.e. pandemic period), and the reasons for it. Notably, special consideration of the aforementioned analysis is paid to the influence of the real-time situation of COVID-19 in terms of cases, deaths, hospitalizations, and tests. Results reveal that (1) the MPRT frequencies obey a long tail distribution, both prior to and during the COVID-19 outbreak; (2) the group size, temporal patterns and co-traveler community are profoundly affected by the COVID-19 outbreak; (3) four indicators related to COVID-19 show different influences on co-travelers over time; (4) bike sharing availability and personal economic situation are closely related with MPRT frequencies. These findings can help develop more targeted strategies for improving the operation of a bike sharing system to meet the possible diversified demands of cyclists during the future pandemics.

Genetic control of root morphology in response to nitrogen across rapeseed diversity.

Rapeseed (Brassica napus L.) is an oil-containing crop of great economic value but with considerable nitrogen requirement. Breeding root systems that efficiently absorb nitrogen from the soil could be a driver to ensure genetic gains for more sustainable rapeseed production. The aim of this study is to identify genomic regions that regulate root morphology in response to nitrate availability. The natural variability offered by 300 inbred lines was screened at two experimental locations. Seedlings grew hydroponically with low or elevated nitrate levels. Fifteen traits related to biomass production and root morphology were measured. On average across the panel, a low nitrate level increased the root-to-shoot biomass ratio and the lateral root length. A large phenotypic variation was observed, along with important heritability values and genotypic effects, but low genotype-by-nitrogen interactions. Genome-wide association study and bulk segregant analysis were used to identify loci regulating phenotypic traits. The first approach nominated 319 SNPs that were combined into 80 QTLs. Three QTLs identified on the A07 and C07 chromosomes were stable across nitrate levels and/or experimental locations. The second approach involved genotyping two groups of individuals from an experimental F2 population created by crossing two accessions with contrasting lateral root lengths. These individuals were found in the tails of the phenotypic distribution. Co-localized QTLs found in both mapping approaches covered a chromosomal region on the A06 chromosome. The QTL regions contained some genes putatively involved in root organogenesis and represent selection targets for redesigning the root morphology of rapeseed.

Tale About Inflation Tails

We study probabilities of extreme inflation events in the Unites States and the euro area. Using a state-space model that incorporates information from a large set of professional forecasters, we generate the term structure of inflation forecasts as well as probabilities of future inflation for any range of inflation outcomes in closed form at any horizon. Since the onset of the COVID-19 pandemic, inflation expectations increased materially amid heightened uncertainty about future inflation. Likelihood of significant departures of inflation targets in the longer term reached about 15 percent in the middle of 2022, increasing from near zero levels in 2020. Such an increase in the right tail of the probability distribution over future inflation outcomes drives an increase in inflation expectations and inflation risk premiums. Several popular external uncertainty measures are associated with variation in tail probabilities.

Ion kinetic effects on the formation of intense laser-driven shock waves

The ion kinetic effect on the formation of intense laser-driven collisional shock waves is investigated via hybrid fluid-particle-in-cell simulations. It is found that the ion heat flux dominates the shock formation, which is considerably larger than the electron heat flux in the shock region. The rise of the temperature due to the laser energy deposition drives a heatwave into the overdense plasma, creating an electron–ion energy exchange zone between the critical surface and heat wave front. The heated ions, which are generated at the electron–ion energy exchange zone via the friction force, are found to travel to the high-density region and cause a tail distribution gain. Despite the small quantity, the heated tail ions contribute most of the ion heat flux during the shock formation. Additionally, as the electron heat flux decreases, the population of the heated tail ions is reduced, leading to a fall in the ion heat flux. This results in the delay or even suppression of the shock formation, because the ions are in a non-equilibrium state in the vicinity of the shock region, the ratio of the downstream ion temperature to the upstream ion temperature tends to a modestly decrease in comparison to the theory. The study provides a clear picture of the formation process of laser-driven shock waves.

A Flexible EM-Like Clustering Algorithm for Noisy Data.

Though very popular, it is well known that the Expectation-Maximisation (EM) algorithm for the Gaussian mixture model performs poorly for non-Gaussian distributions or in the presence of outliers or noise. In this paper, we propose a Flexible EM-like Clustering Algorithm (FEMCA): a new clustering algorithm following an EM procedure is designed. It is based on both estimations of cluster centers and covariances. In addition, using a semi-parametric paradigm, the method estimates an unknown scale parameter per data point. This allows the algorithm to accommodate heavier tail distributions, noise, and outliers without significantly losing efficiency in various classical scenarios. We first present the general underlying model for independent, but not necessarily identically distributed, samples of elliptical distributions. We then derive and analyze the proposed algorithm in this context, showing in particular important distribution-free properties of the underlying data distributions. The algorithm convergence and accuracy properties are analyzed by considering the first synthetic data. Finally, we show that FEMCA outperforms other classical unsupervised methods of the literature, such as k-means, EM for Gaussian mixture models, and its recent modifications or spectral clustering when applied to real data sets as MNIST, NORB, and 20newsgroups.

Transformation of Various Measures of Financial Risks with their Limitation on Outcomes Associated with Losses

In assessing the risk of investing in various financial assets, risk management focuses on the analysis of the worst possible losses (the right tail of the loss distribution). At the same time, most often, when speaking about losses, it is assumed that losses can, in principle, take on negative values (which corresponds to receiving positive profits). However, there are many theoretical studies suggesting that losses take only positive values. Many risk managers use only a portion of the sample of data that corresponds to positive losses when assessing the relevant risk measures using the statistical method or the Monte Carlo method. The purpose of this paper is to study the transformation of risk estimates of various levels of catastrophicity with such a change in the space of elementary events, and hence the law of loss distribution. The paper uses methods of analysis of financial risks of various levels of catastrophicity, including methods developed in the author’s previous papers. As a result of the study, it turned out that with such a transformation of the random value of losses, all the most important estimates are significantly transformed with the help of risk measures of various catastrophicity. The author concludes that the theoretical conclusions of the work will also contribute to a more conscious understanding of the theoretical results and the results of practical risk assessments, depending on the basis on which this assessment was made: allowing losses to accept negative values or focusing only on their positive values.

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 which combines quantile regressions and structural VARs.

Storm gust prediction with the integration of machine learning algorithms and WRF model variables for the Northeast United States

Abstract Wind gusts are often associated with severe hazards and can cause structural and environmental damages, making gust prediction a crucial element of weather forecasting services. In this study, we explored the utilization of machine learning (ML) algorithms integrated with numerical weather prediction outputs from the Weather Research and Forecasting model (WRF), to align the estimation of wind gust potential with observed gusts. We have used two ML algorithms, namely Random Forest (RF), and Extreme Gradient Boosting (XGB), along with two statistical techniques: Generalized Linear Models with identity link function (GLM-Identity) and log link function (GLM-Log), to predict storm wind gusts for the NE USA. We used 61 simulated extratropical and tropical storms that occurred between 2005 and 2020, to develop and validate the ML and statistical models. To assess the ML model performance, we compared our results with post-processed gust potential from WRF. Our findings showed that ML models, especially XGB, performed significantly better than statistical models and WRF-UPP, and were able to better align predicted with observed gusts across all storms. The ML models faced challenges capturing the upper tail of the gust distribution, and the learning curves suggested that XGB was more effective than RF in generating better predictions with fewer storms.

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.

Pharmaceutical Considerations and Metabolic Fate of Parenteral Lipid Nanoparticle Dosage Forms

The physical stability of parenteral dispersions for delivery of drugs to patients is of particular clinical importance, given their general overall superior bioavailability compared to other routes of administration. Although official pharmacopeial methods for lipid injectable emulsions have been established for triglyceride oil-in-water dispersions (i.e., “mini-emulsions”) through USP Chapter <729>, no pharmaceopeial guidance exists for lipid nanoparticle (LNP)-based “micro-emulsions”. At present, there are several LNP-based drugs approved for clinical use, including mRNA vaccines. Moreover, the increased interest in using mRNA as a platform technology for an array of potential therapeutic drug candidates increases the importance of developing appropriate methods to ensure their physical stability, safety and efficacy. For all dispersions and by various detection mechanisms (e.g., electrical, mechanical, mathematical), the fusion or growth of droplets/particles in the large-diameter tails of the particle size distribution (PSD) signals the onset of instability. Consequently, the measurement for LNP dispersions will require the use of a modified optical detection design in order to extend the lower particle detection limit into the “relative” large-diameter tail of the PSD for both light extinction and light-scattering methods based on single-particle optical sensing techniques. Fortunately, the technology is currently available and capable of providing the requisite quantitative analysis.

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.