Tail Of Distribution Research Articles

Large effects and the infinitesimal model

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring’s genetic trait component and the average of their two parents’ genetic trait components is Normally distributed and independent of the parents’ values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent α<2, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a “stable distribution”, for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.

What controls the tail behaviour of flood series: rainfall or runoff generation?

Abstract. Many observed time series of precipitation and streamflow show heavy-tail behaviour. For heavy-tailed distributions, the occurrence of extreme events has a higher probability than for distributions with an exponentially receding tail. If we neglect heavy-tail behaviour we might underestimate the magnitude of rarely observed, high-impact events. Robust estimation of upper-tail behaviour is often hindered by the limited length of observational records. Using long time series and a better understanding of the relevant process controls can help with achieving more robust tail estimations. Here, a simulation-based approach is used to analyse the effect of precipitation and runoff generation characteristics on the upper tail of flood peak distributions. Long, synthetic precipitation time series with different tail behaviour are produced by a stochastic weather generator. These are used to force a conceptual rainfall–runoff model. In addition, catchment characteristics linked to a threshold process in the runoff generation are varied between model runs. We characterize the upper-tail behaviour of the simulated precipitation and discharge time series with the shape parameter of the generalized extreme value (GEV) distribution. Our analysis shows that runoff generation can strongly modulate the tail behaviour of flood peak distributions. In particular, threshold processes in the runoff generation lead to heavier tails. Beyond a certain return period, the influence of catchment processes decreases and the tail of the rainfall distribution asymptotically governs the tail of the flood peak distribution. Beyond which return period this is the case depends on the catchment storage in relation to the mean annual rainfall amount.

Comprehensive Impurity Profiling of mRNA: Evaluating Current Technologies and Advanced Analytical Techniques.

In vitro transcription (IVT) of mRNA is a versatile platform for a broad range of biotechnological applications. Its rapid, scalable, and cost-effective production makes it a compelling choice for the development of mRNA-based cancer therapies and vaccines against infectious diseases. The impurities generated during mRNA production can potentially impact the safety and efficacy of mRNA therapeutics, but their structural complexity has not been investigated in detail yet. This study pioneers a comprehensive profiling of IVT mRNA impurities, integrating current technologies with innovative analytical tools. We have developed highly reproducible, efficient, and stability-indicating ion-pair reversed-phase liquid chromatography and capillary gel electrophoresis methods to determine the purity of mRNA from different suppliers. Furthermore, we introduced the applicability of microcapillary electrophoresis for high-throughput (<1.5 min analysis time per sample) mRNA impurity profiling. Our findings revealed that impurities are mainly attributed to mRNA variants with different poly(A) tail lengths due to aborted additions or partial hydrolysis and the presence of double-stranded mRNA (dsRNA) byproducts, particularly the dsRNA 3'-loop back form. We also implemented mass photometry and native mass spectrometry for the characterization of mRNA and its related product impurities. Mass photometry enabled the determination of the number of nucleotides of different mRNAs with high accuracy as well as the detection of their size variants [i.e., aggregates and partial and/or total absence of the poly(A) tail], thus providing valuable information on mRNA identity and integrity. In addition, native mass spectrometry provided insights into mRNA intact mass, heterogeneity, and important sequence features such as poly(A) tail length and distribution. This study highlights the existing bottlenecks and opportunities for improvement in the analytical characterization of IVT mRNA, thus contributing to the refinement and streamlining of mRNA production, paving the way for continued advancements in biotechnological applications.

The extreme upper tail of Japan’s citation distribution reveals its research success

A number of indications, such as the number of Nobel Prize winners, show Japan to be a scientifically advanced country. However, standard bibliometric indicators place Japan as a scientifically developing country. The present study is based on the conjecture that Japan is an extreme case of a general pattern in highly industrialized countries. In these countries, scientific publications come from two types of studies: some pursue the advancement of science and produce highly cited publications, while others pursue incremental progress and their publications have a very low probability of being highly cited. Although these two categories of papers cannot be easily identified and separated, the scientific level of Japan can be tested by studying the extreme upper tail of the citation distribution of all scientific articles. In contrast to standard bibliometric indicators, which are calculated from the total number of papers or from sets of papers in which the two categories of papers are mixed, in the extreme upper tail, only papers that are addressed to the advance of science will be present. Based on the extreme upper tail, Japan belongs to the group of scientifically advanced countries and is significantly different from countries with a low scientific level. The number of Clarivate Citation laureates also supports our hypothesis that some citation-based metrics do not reveal the high scientific level of Japan. Our findings suggest that Japan is an extreme case of inaccuracy of some citation metrics; the same drawback might affect other countries, although to a lesser degree.

Identification-robust methods for comparing inequality with an application to regional disparities

We propose Fieller-type methods for inference on generalized entropy inequality indices in the context of the two-sample problem which covers testing the statistical significance of the difference in indices, and the construction of a confidence set for this difference. In addition to irregularities arising from thick distributional tails, standard inference procedures are prone to identification problems because of the ratio transformation that defines the considered indices. Simulation results show that our proposed method outperforms existing counterparts including simulation-based permutation methods and results are robust to different assumptions about the shape of the null distributions. Improvements are most notable for indices that put more weight on the right tail of the distribution and for sample sizes that match macroeconomic type inequality analysis. While irregularities arising from the right tail have long been documented, we find that left tail irregularities are equally important in explaining the failure of standard inference methods. We apply our proposed method to analyze income per-capita inequality across U.S. states and non-OECD countries. Empirical results illustrate how Fieller-based confidence sets can: (i) differ consequentially from available ones leading to conflicts in test decisions, and (ii) reveal prohibitive estimation uncertainty in the form of unbounded outcomes which serve as proper warning against flawed interpretations of statistical tests.

Heterogeneity, climate change, and crop yield distributions: Solvency implications for publicly subsidized crop insurance programs

AbstractClimate change continues to fuel concern about the future cost of publicly subsidized crop insurance programs in developed nations. These changes in climate are expected to alter the upper and lower tails of crop yield distributions differently. This may best be captured by modeling the climate–yield relationship heterogeneously across different parts of the yield distribution. To this end, we consider a mixture model with the parameters expressed as nonparametric functions (to capture any nonlinearities) of weather variables estimated by machine learning methods (neural net). By doing so, we are able to identify possibly heterogeneous effects of climate change on each component, the mixing probabilities, and thus all moments of the yield distribution. We find changing climate alters, quite significantly, the entire shape of the yield distribution. The overall probability of the lower tail tends to increase as temperatures rise, to the point where some yield distributions become positively skewed. Across a range of climate change scenarios, premium rates for fixed guarantees are expected to rise 20–66% relative to no climate change by 2040. However, if we allow the yield guarantees to also fall because of additional losses from climate change, premium rates (albeit not comparable given yield guarantees are different) increase notably less (6–14%), suggesting less solvency issues than first thought.

A new method for long-term safety analysis of marine structures

This paper proposes to utilise a new adaptive kernel density estimation (KDE) method based on a linear diffusion process for fitting the significant wave height data in order to calculate the sea state parameter distribution tails more accurately, particularly the higher, more extreme values. The accuracy of the proposed method has been demonstrated based on fittings to two measured ocean wave datasets. This proposed method has subsequently been utilised for deriving accurate 50-year and 500-year environmental contour lines. The advantages of using a more reliable contour line derived from using the proposed new method for long-term safety analysis of marine structures have been substantiated.

Spatial earnings inequality

Earnings inequality in Germany has increased dramatically. Measuring inequality locally at the level of cities annually since 1985, we find that behind this development is the rapidly worsening inequality in the largest cities, driven by increasing earnings polarisation. In the cross-section, local earnings inequality rises substantially in city size, and this city-size inequality penalty has increased steadily since 1985, reaching an elasticity of .2 in 2010. Inequality decompositions reveal that overall earnings inequality is almost fully explained by the within-locations component, which in turn is driven by the largest cities. The worsening inequality in the largest cities is amplified by their greater population weight. Examining the local earnings distributions directly reveals that this is due to increasing earnings polarisation that is strongest in the largest places. Both upper and lower distributional tails become heavier over time, and are the heaviest in the largest cities. We establish these results using a large and spatially representative administrative data set, and address the top-coding problem in these data using a parametric distribution approach that outperforms standard imputations.

Linear multifractional stable motion for modeling of fluid-filled regions in retinal optical coherence tomography images

Fluid appears in several retinal disorders can be visualized by optical coherence tomography (OCT) images. Since manual survey of OCT images is challenging, automatic fluid detection is desirable. This paper develops a generalized multifractal framework to model the local scale-invariant property of retinal OCT signals and accordingly proposes a simple methodology for automatic localization of fluid-filled regions. The proposed framework comprises both local self-similarity and heavy tailed distribution of OCT signals by generalization of fractional Levy stable motion (fLsm) to the Riemann-Liouville multifractional Levy stable motion (RL-mLsm). In order to measure the multifractality appears in RL-mLsm, the scaling properties of Levy flights and stochastic differential equations (SDEs) are used to develop a fractional momentbased algorithm namely, multi-fractional Levy fluctuation analysis (MLFA) algorithm. Here, we apply MLFA to model OCT images. Modeling results indicate the significant difference between the multifractal bandwidth in non-fluid and fluid regions. In addition, by utilizing various surrogate series of the signals, we discover the source of multifractality of OCT signals. As an application of the proposed multifractal modeling, we propose a new method, based on simple clustering of estimated local scaling exponent of modeled OCT signals, to localize fluid regions in OCT images. The localization method is validated, and the experimental results reveal the superiority of proposed method. Overall, the proposed multifractal framework has full advantages on excellent improvement of fluid localization, which promises the proposed model is suitable for effective description of self-similar nature of normal and abnormal OCT images independent of capturing device.

Probabilistic seismic collapse risk assessment of non-engineered masonry buildings in Malawi

This study presents the most recent development of a nationwide earthquake risk model for non-engineered masonry buildings in Malawi. Due to its location within the East African Rift, Malawi experienced several moderate earthquakes that caused seismic damage and loss. Recently, a new probabilistic seismic hazard model has been developed by considering fault-based seismic sources, in addition to conventional areal sources. The most recent 2018 national census data provide accurate exposure information for Malawian people and their assets at detailed spatial resolutions. To develop seismic fragility functions that are applicable to Malawian housing stocks, building surveys and experimental tests of local construction materials have been conducted. By integrating these new developments of seismic hazard, exposure, and vulnerability modules, a quantitative seismic building collapse risk model for Malawi is developed on a national scale. For the rapid computation of seismic risk curves at individual locations, an efficient statistical approach for approximating the upper tail distribution of a seismic hazard curve is implemented. Using this technique, a seismic risk curve for a single location can be obtained in a few seconds, thereby, this can be easily expanded to the whole country with reasonable computational times. The results from this new quantitative assessment tool for seismic impact will provide a sound basis for risk-based disaster mitigation policies in Malawi.

Analyzing the Impact of Carbon Risk on Firms’ Creditworthiness in the Context of Rising Interest Rates

Carbon risk, a type of climate risk, is expected to have a crucial impact, especially on high-carbon-emitting, “polluting” firms as opposed to less carbon-intensive, “clean” ones. With a rising number of actions and policies being continuously proposed to mitigate these concerns and an increasing number of investors demanding more climate adaptation initiatives, this transition risk will certainly need to be incorporated into a firm’s credit risk assessment. In this paper, we explore the impact of the carbon risk factor, constructed as the daily median difference in default protection between polluting and clean European firms, on firm creditworthiness using quantile regressions on the tail distribution of credit default swap spreads for different maturities between 2020 and 2023. In particular, the recent European interest rate hikes lead to unexpected conclusions about when the carbon risk factor affects firm creditworthiness and how rapidly the net-zero economy transition must occur. Contrary to the previous literature, we find that investors are expecting the transition to occur in the medium-to-long term.

Renyi entropy based design of heavy tailed distribution for return of financial assets

It is well-known that returns of financial assets exhibit heavy tail property and there has been no distribution which can reliably capture this characteristic so far. To contribute to the solution of this problem, we derive a new heavy tail distribution using the maximum entropy principle for Renyi entropy under the absolute moment constraints. Our newly derived distribution with two shape parameters forms a family of distributions. They are smooth, scaleable, symmetric and may be heavy tailed if their shape parameter attains the appropriate value. As a result, parameters of this distribution can be estimated by maximum likelihood estimation technique. The ability of the derived distribution to model the heavy tail property of financial assets is verified on a range of financial instruments. The results we obtained show that it can be a better option for modeling the returns of financial assets compared to other well-known heavy tailed distributions.

Asymptotic properties of [formula omitted]th spacings based on records

In this work, the mth spacings based on record values obtained from continuous distributions are discussed. We first present distributional results for such spacings, and then, by making use of classification of distribution tails, derive asymptotic results for the mth record spacings. We also obtain strong limit results for them and illustrate our theoretical results by examples. Finally, we support our findings by data obtained from simulation experiments.

AIRI: Predicting Retention Indices and Their Uncertainties Using Artificial Intelligence.

The Kováts retention index (RI) is a quantity measured using gas chromatography and is commonly used in the identification of chemical structures. Creating libraries of observed RI values is a laborious task, so we explore the use of a deep neural network for predicting RI values from structure for standard semipolar columns. This network generated predictions with a mean absolute error of 15.1 and, in a quantification of the tail of the error distribution, a 95th percentile absolute error of 46.5. Because of the Artificial Intelligence Retention Indices (AIRI) network's accuracy, it was used to predict RI values for the NIST EI-MS spectral libraries. These RI values are used to improve chemical identification methods and the quality of the library. Estimating uncertainty is an important practical need when using prediction models. To quantify the uncertainty of our network for each individual prediction, we used the outputs of an ensemble of 8 networks to calculate a predicted standard deviation for each RI value prediction. This predicted standard deviation was corrected to follow the error between the observed and predicted RI values. The Z scores using these predicted standard deviations had a standard deviation of 1.52 and a 95th percentile absolute Z score corresponding to a mean RI value of 42.6.

A Lifshitz-Slyozov type model for adipocyte size dynamics: limit from Becker-Döring system and numerical simulation.

Biological data show that the size distribution of adipose cells follows a bimodal distribution. In this work, we introduce a Lifshitz-Slyozov type model, based on a transport partial differential equation, for the dynamics of the size distribution of adipose cells. We prove a new convergence result from the related Becker-Döring model, a system composed of several ordinary differential equations, toward mild solutions of the Lifshitz-Slyozov model using distribution tail techniques. Then, this result allows us to propose a new advective-diffusive model, the second-order diffusive Lifshitz-Slyozov model, which is expected to better fit the experimental data. Numerical simulations of the solutions to the diffusive Lifshitz-Slyozov model are performed using a well-balanced scheme and compared to solutions to the transport model. Those simulations show that both bimodal and unimodal profiles can be reached asymptotically depending on several parameters. We put in evidence that the asymptotic profile for the second-order system does not depend on initial conditions, unlike for the transport Lifshitz-Slyozov model.

Distinct anthropogenic greenhouse gas and aerosol induced marine heatwaves

In the era of escalating climate change, understanding human impacts on marine heatwaves (MHWs) becomes essential. This study harnesses climate model historical and single forcing simulations to delve into the individual roles of anthropogenic greenhouse gases (GHGs) and aerosols in shaping the characteristics of global MHWs over the past several decades. The results suggest that GHG variations lead to longer-lasting, more frequent, and intense MHWs. In contrast, anthropogenic aerosols markedly curb the intensity and growth of MHWs. Further analysis of the sea surface temperature (SST) probability distribution reveals that anthropogenic GHGs and aerosols have opposing effects on the tails of the SST probability distribution, causing the tails to expand and contract, respectively. Climate extremes such as MHWs are accordingly promoted and reduced. Our study underscores the significant impacts of anthropogenic GHGs and aerosols on MHWs, which go far beyond the customary concept that these anthropogenic forcings modulate climate extremes by shifting global SST probabilities via modifying the mean-state SST.

Global Downscaled Projections for Climate Impacts Research (GDPCIR): preserving quantile trends for modeling future climate impacts

Abstract. Global climate models (GCMs) are important tools for understanding the climate system and how it is projected to evolve under scenario-driven emissions pathways. Their output is widely used in climate impacts research for modeling the current and future effects of climate change. However, climate model output remains coarse in relation to the high-resolution climate data needed for climate impacts studies, and it also exhibits biases relative to observational data. Treatment of the distribution tails is a key challenge in existing bias-adjusted and downscaled climate datasets available at a global scale; many of these datasets used quantile mapping techniques that were known to dampen or amplify trends in the tails. In this study, we apply the Quantile Delta Mapping (QDM) method (Cannon et al., 2015) for bias adjustment. After bias adjustment, we apply a new spatial downscaling method called Quantile-Preserving Localized-Analog Downscaling (QPLAD), which is designed to preserve trends in the distribution tails. Both methods are integrated into a transparent and reproducible software pipeline, which we apply to global, daily GCM surface variable outputs (maximum and minimum temperature and total precipitation) from the Coupled Model Intercomparison Project Phase 6 (CMIP6) experiments (O'Neill et al., 2016) for the historical experiment and four future emissions scenarios ranging from aggressive mitigation to no mitigation, namely SSP1–2.6, SSP2–4.5, SSP3–7.0, and SSP5–8.5 (Riahi et al., 2017). We use the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 (Hersbach et al., 2020) temperature and precipitation reanalysis as the reference dataset over the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report (AR6) reference period of 1995–2014. We produce bias-adjusted and downscaled data over the historical period (1950–2014) and the future emissions pathways (2015–2100) for 25 GCMs in total. The output dataset is the Global Downscaled Projections for Climate Impacts Research (GDPCIR), a global, daily, 0.25∘ horizontal-resolution product which is publicly available and hosted on Microsoft AI for Earth's Planetary Computer (https://planetarycomputer.microsoft.com/dataset/group/cil-gdpcir/, last access: 23 October 2023).

Investigating the Impact of Consumption Distribution on CRRA Estimation: Quantile-CCAPM-Based Approach

Abstract Using quantile maximization decision theory, this paper considers a quantile-based Euler equation that states that the asset price is a function of the quantiles of the payoff, consumption growth, the stochastic discount factor, risk aversion, and the distribution of the consumption growth rate. We use a more general distribution assumption (log-elliptical distributions) than the log-normality of the consumption growth rate assumed in the literature. The simulation results show that: (1) the higher the downside risk aversion, the lower the constant relative risk aversion; (2) the heavier the tails of the Student-t distribution, the higher the risk aversion for each level of downside risk aversion; and (3) the curve of the relationship between risk aversion and downside risk aversion shifts upward when the normality assumption is dropped, and the magnitude of this shift is high even for high degrees of freedom of the Student-t distribution. Our results suggest that using normally distributed errors to model stock returns and consumption growth rates could lead to an underestimation of the risk aversion coefficient.

Multiple power-law tails in the density and column-density distribution in contracting star-forming clumps

ABSTRACT We present a numerical study of the evolution of power-law tails (PLTs) in the (column-)density distributions (N-PDF, ρ-PDF) in contracting star-forming clumps in primordial gas, without and with some initial rotational and/or turbulent support. In all considered runs multiple PLTs emerge shortly after the formation of the first protostar. The first PLT (PLT 1) in the ρ-PDF is a stable feature with slope q1 ≃ −1.3 which corresponds – under the condition of preserved spherical symmetry – to the outer envelope of the protostellar object with density profile ρ ∝ l−2 in the classical Larson–Penston collapse model, where l is the radius. The second PLT (PLT 2) in the ρ-PDF is stable in the pure-infall runs but fluctuates significantly in the runs with initial support against gravity as dozens of protostars form and their mutual tidal forces change the density structure. Its mean slope, 〈q2〉 ≃ −2, corresponds to a density profile of ρ ∝ l−3/2 which describes a core in free fall in the classical Larson–Penston collapse model or an attractor solution at scales with dominating protostellar gravity. PLT 1 and PLT 2 in the N-PDFs are generally consistent with the observational data of Galactic low-mass star-forming regions from Herschel data. In the runs with initial support against gravity a third PLT (PLT 3) in the ρ-PDFs appears simultaneously with or after the emergence of PLT 2. It is very shallow, with mean slope of 〈q3〉 ≃ −1, and is associated with the formation of thin protostellar accretion discs.

Robust adaptive analysis of extreme dynamic responses of wave energy converters

In the current study, a new adaptive binned kernel density estimation method has been introduced. In the proposed new method, Fourier transforms have been utilized to accomplish the convolution rather than performing the convolution by hand. By utilizing the fast Fourier transform, direct and inverse Fourier transforms have been found in a relatively short amount of time when implementing the new method. Upon analyzing the computed results, it has been observed that the newly proposed adaptive binned kernel density estimation distribution curve exhibits a high level of smoothness in the tail region. Furthermore, it demonstrates a strong alignment with the histogram derived from the recorded ocean wave dataset obtained at the NDBC station 46053. These are the major advantages of the proposed new method comparing with other existing methods such as the parametric method, the ordinary KDE method, and Abramson's adaptive KDE method. The specific research gap identified in the field is that none of the existing methods can predict the sea state parameter probability distribution tails both accurately and efficiently, and the proposed new method has successfully addressed this research gap. Upon careful examination of the calculation results, it becomes evident that the projected 50-year extreme power-take-off heaving force value, derived using the newly proposed method, is 1989300N. This value significantly surpasses (by more than 9.5%) the forecasted value of 1816200N obtained through the application of the Rosenblatt-I-SORM contour method. The findings of this study suggest that the newly proposed adaptive binned kernel density estimation method exhibits robustness and demonstrates accurate forecasting capabilities for the 50-year extreme dynamic responses of wave energy converters.