Tail Of Distribution Research Articles

Future Changes in Regional Tropical Cyclone Wind, Precipitation, and Flooding Using Event‐Based Downscaling

AbstractUnderstanding changes in the hazard component of climate risk is important to inform societal resilience planning in a changing climate. Here, we examine local changes in wind speed, rainfall, and flooding related to tropical cyclones (TCs) and compare them across statistical and dynamical modeling approaches. Our focus region is the Delaware River Basin, located in the northeastern United States. We pair event‐based downscaling with large ensemble climate model information to capture the details of extreme TC wind, rain, and flooding, and their likelihood, in a changing climate. We identify local TCs in the Community Earth System Model 2 Large Ensemble (CESM2‐LENS). We find fewer TCs in the future, but these future storms have higher wind speeds and are wetter. We also find that TCs produce heavier 3‐day precipitation distributions than all other summertime weather events, with TCs constituting a larger percentage of the upper tail of the full precipitation distribution. With this information, we identify a small collection of 200‐year return events and compare the resulting TC rain and wind across dynamical and statistical downscaling methods. We find that dynamical downscaling produces peak rain rates far higher than CESM or the statistical downscaling method. It can also produce quite different future changes in precipitation totals for the small set of events considered here. This leads to vastly different flood responses. Overall, our results highlight the need to interpret future changes of event‐based simulations in the context of downscaling method limitations.

Frequency beating and damping of breathing oscillations of a harmonically trapped one-dimensional quasicondensate

We study the breathing (monopole) oscillations and their damping in a harmonically trapped one-dimensional (1D) Bose gas in the quasicondensate regime using a finite-temperature classical field approach. By characterising the oscillations via the dynamics of the density profile's rms width over long time, we find that the rms width displays beating of two distinct frequencies. This means that 1D Bose gas oscillates not at a single breathing mode frequency, as found in previous studies, but as a superposition of two distinct breathing modes, one oscillating at frequency close to $\simeq\!\sqrt{3}\omega$ and the other at $\simeq\!2\omega$, where $\omega$ is the trap frequency. The breathing mode at $\sim\!\sqrt{3}\omega$ dominates the beating at lower temperatures, deep in the quasicondensate regime, and can be attributed to the oscillations of the bulk of the density distribution comprised of particles populating low-energy, highly-occupied states. The breathing mode at $\simeq\!2\omega$, on the other hand, dominates the beating at higher temperatures, close to the nearly ideal, degenerate Bose gas regime, and is attributed to the oscillations of the tails of the density distribution comprised of thermal particles in higher energy states. The two breathing modes have distinct damping rates, with the damping rate of the bulk component being approximately four times larger than that of the tails component.

Who is doing better? Exploring the effect of COVID-19 on students’ academic performance across the test score distribution

ABSTRACT Previous studies have found a negative effect on average student performance on standardised tests following the Covid-19 crisis. However, the effects might differ depending on the student’s position in the achievement distribution. Understanding distributional effects allows us to determine how to better direct resources to students most affected. Using a quantile treatment effects model, we estimate the effects of Covid-19 on academic performance of students in the Colombian standardised high school exit examination. Our estimates show a U-shaped pattern: the negative effect is smaller for students located at the tails of the test score distribution.

CHASING THE TAIL: A GENERALIZED PARETO DISTRIBUTION APPROACH TO ESTIMATING WEALTH INEQUALITY

AbstractSince the work reported in Vermeulen (Review of Income and Wealth, 64(2), 357–387; 2018), a literature has developed using the simple Pareto distribution along with “rich list” information to improve estimates of the upper tail of the wealth distribution measured in surveys. Because the construction of such external data is typically opaque and subject to error, it may be best not to depend exclusively on this approach. This paper develops an alternative approach, using the generalized Pareto distribution (GPD), extending an estimation strategy developed by Castillo and Hadi (Journal of the American Statistical Association, 92(440), 1609–1620; 1997) in a novel way to survey data. The extension allows for addressing imperfections in the effective coverage of the upper tail of the wealth distribution, as well as allowing the imposition of an external measure of aggregate wealth as a constraint. The paper implements the method on Austrian survey data that has weak coverage of wealthy households. The results indicate that even with a range of plausible adjustments for data imperfections, relying only on the survey data to project the upper tail is insufficient to yield implied wealth aggregates in the range implied by aggregate figures. Imposing the implied aggregate as a constraint is necessary. The approach may be particularly useful in comparing survey‐based inequality measures across and within countries and over time, as well as in constructing distributional financial accounts.

A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data

The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution.

Precise large deviations for sums of dependent random variables with subexponential distribution

. In this article, we study the precise large deviations for sums of non identically distributed random variables { X i , i ≥ 1 } with distribution functions { F i , i ≥ 1 } that are widely upper orthant dependent (WUOD, in short) and ϕ-mixing. Moreover, the random variables are dependent, according to some copulas. We assume that the average of the right tails of distribution functions F i is equivalent to the subexponential distribution F.

Guaranteed minimum withdrawal benefits with high-water mark fee structure.

The Guaranteed Minimum Withdrawal Benefit (GMWB), an adjunct incorporated within variable annuities, commits to reimbursing the entire initial investment regardless of the performance of the underlying funds. While extensive research exists in financial and actuarial literature regarding the modeling and valuation techniques of GMWBs, much of it is founded on a static fee structure. Our study introduces an innovative fee structure based on the high-water mark (HWM) principle and a regime-switch jump-diffusion model for the pricing of GMWBs, employing numerical solutions through the Monte Carlo method for solving the stochastic differential equation (SDE). Furthermore, a companion piece of research addresses the risk management of GMWBs within the same analytical framework as the pricing component, an aspect that has received limited attention in the existing literature. In assessing the necessary capital reserves for unforeseen losses, our methodology involves the computation of two risk metrics associated with the tail distribution of net liability from the insurer's perspective, Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE). Comprehensive numerical results and sensitivity analyses are also provided.

Supercoiled DNA percentage: A key in-process control of linear DNA template for mRNA drug substance manufacturing

The development of messenger RNA (mRNA) vaccines and therapeutics necessitates the production of high quality in-vitro-transcribed mRNA drug substance with specific critical quality attributes (CQAs), which are closely tied to the uniformity of linear DNA template. The supercoiled plasmid DNA is the precursor to the linear DNA template, and the supercoiled DNA percentage is commonly regarded as a key in-process control (IPC) during the manufacturing of linear DNA template. In this study, we investigate the influence of supercoiled DNA percentage on key mRNA CQAs, including purity, capping efficiency, double-stranded RNA (dsRNA), and distribution of polyA tail. Our findings reveal a significant impact of supercoiled DNA percentage on mRNA purity, and in vitro transcription yield. Notably, we observe that the impact on mRNA purity can be mitigated through Oligo-dT chromatography, alleviating the tight range of DNA supercoiled percentage to some extent. Overall, this study provides valuable insights into IPC strategies for DNA template CMC (Chemistry, Manufacturing, and Controls) and process development for mRNA drug substance.

Study on spatial distribution, regional differences and dynamic evolution of rural financial risk in China.

Based on panel data from 2009 to 2021, covering 30 provinces in China, we have been constructed the Rural Financial Risk Index using the objective entropy weighting method to study rural financial risk in China systematically from the perspective of spatial distribution. Specifically, we discuss the spatial distribution, regional differences and dynamic evolution of rural financial risk across Chinese four different regions divided into the Northeast, East, Central and West. It's found that Local government debt and Land transfer income are the two primary determinants influencing the level of rural financial risk in China. Furthermore, we conclude the ranking value of rural financial risk across four regions that the central exhibits the highest level, followed by the West, the East, and finally the Northeast, where the reasons for such ranking results as follows. Firstly, although the highest level of risk among provinces in the West is equivalent to that in the Central, there exists a smaller minimum rural financial risk in the former compared to the latter. Then, it should be noted that there's a low-low agglomeration of rural financial risk in the Northeast, while it demonstrates a high-high agglomeration in the Central according to the Moran Index test analysis. Again, there's a declining trend in rural financial risk disparity within the region and an upward trend is observed when comparing different regions (except the East vs West), especially increase largely between the Northeast and Central in past two years after analyzing the decomposition of Dagum Gini coefficient. Moreover, we study the absolute differences and dynamic evolution in different four regions through three-dimensional diagram of kernel density estimation, and it's found that the change of rural financial risk in four regions moved to the right as a whole, while the tail distribution remains inconspicuous. The absolute difference is diminishing in the Northeast, and the two-level differentiation characteristics tend to weaken as a whole in the Central, with a disordered wave peak height observed in both the East and West. Finally, the article presents pertinent policy implications but limitations according to the research findings.

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.

Effect of nonlinearity of discrete Langevin model on behavior of extremes in generated time series

In this work we analyze the influence of nonlinearity on the behavior of extremal values of time series generated by two discrete Langevin models: fixing the diffusion function in the first (M1), the probability distribution function in the second (M2). The extremes were generated by applying the run theory. A mathematical relationship was found between nonlinearity of models and means and distributions of run lengths and inter-extreme times as well as with the clustering of extremes. Furthermore, the Allan factor curves of the extremes suggest that the sequences of extremes are fractal for timescales up to the mean inter-extreme time. Our main findings are that the variation of the nonlinearity parameter in model M1 (leading to the increase of the distribution tail length) can cause a significant variation of the extreme characteristics and an increase of the clustering while the variation of the nonlinearity parameter in model M2 (with fixed distribution) has a little effect on extremes.

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.

The Changing Nature of Pollution, Income, and Environmental Inequality in the United States

This paper uses tax records linked to administrative Census data and high-resolution measures of air pollution exposure (PM2.5) to study the evolution of the Black-White pollution exposure gap since 1984. We decompose changes in the racial exposure gap into (i) rank-preserving compression of the pollution distribution and (ii) changes stemming from a reordering of Black and White households within the pollution distribution. We find a narrowing of the racial exposure gap that is overwhelmingly driven by rank-preserving changes rather than positional changes. Recently, however, the relative positions of Black and White households in the upper tail of the pollution distribution have converged.

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.

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.