Tail Of Distribution Research Articles

Detection of colored noise correlation time with Josephson junctions

It is shown that the effect of an exponentially correlated noisy source on the escape times of a Josephson junction depends upon the noise correlation time. A careful analysis reveals that two effects are preeminent: the increase of the stability (as measured by the average escape time from the metastable state) and the increase of the extreme events in the tails of the escape time distribution. The changes occur if the noise correlation exceeds the characteristic time of the Josephson junction. As the superconducting device is very fast, with a characteristic time easily below the nanosecond, the device is responsive even to very short noise correlation. We speculate that it is thus possible to estimate in situ noise correlation with a superconducting Josephson junction through the measurements of the escapes, without a high-frequency sampling of the noise. Moreover, as the superconducting circuit can be cooled as much as necessary, the device offers the further advantage to be intrinsically very quiet.

Do Not Cut Off Your Tail: A Mega-Analysis of Responses to Auditory Perturbation Experiments.

The practice of removing "following" responses from speech perturbation analyses is increasingly common, despite no clear evidence as to whether these responses represent a unique response type. This study aimed to determine if the distribution of responses to auditory perturbation paradigms represents a bimodal distribution, consisting of two distinct response types, or a unimodal distribution. This mega-analysis pooled data from 22 previous studies to examine the distribution and magnitude of responses to auditory perturbations across four tasks: adaptive pitch, adaptive formant, reflexive pitch, and reflexive formant. Data included at least 150 unique participants for each task, with studies comprising younger adult, older adult, and Parkinson's disease populations. A Silverman's unimodality test followed by a smoothed bootstrap resampling technique was performed for each task to evaluate the number of modes in each distribution. Wilcoxon signed-ranks tests were also performed for each distribution to confirm significant compensation in response to the perturbation. Modality analyses were not significant (p > .05) for any group or task, indicating unimodal distributions. Our analyses also confirmed compensatory reflexive responses to pitch and formant perturbations across all groups, as well as adaptive responses to sustained formant perturbations. However, analyses of sustained pitch perturbations only revealed evidence of adaptation in studies with younger adults. The demonstration of a clear unimodal distribution across all tasks suggests that following responses do not represent a distinct response pattern, but rather the tail of a unimodal distribution. https://doi.org/10.23641/asha.24282676.

Asymptotic behavior of a system of two coupled queues when the content of one queue is very high

We consider a system of two parallel discrete-time single-server queues, queue 1 and queue 2. The service time of any customer in either queue is equal to 1 time slot. Arrivals during consecutive slots occur independently from slot to slot. However, the arrival streams into both queues are possibly mutually interdependent, i.e., during any slot, the numbers of arrivals in queue 1 and queue 2 need not be statistically independent. Their joint probability generating function (pgf) A(x, y) fully characterizes the queueing model. As a consequence of the possible intra-slot correlation in the arrival process, the numbers of customers present (“system contents”) in queues 1 and 2, at any given slot boundary, are not necessarily independent either. In a previous paper, we have already discussed the mathematical difficulty of computing their steady-state joint pgf U(z_1,z_2); explicit closed-form results can only be obtained for specific choices of A(x, y). In this paper, we therefore look at the problem from an other angle. Specifically, we study the (asymptotic) conditional steady-state behavior of the system under the condition that the content of queue 1 is (temporarily) very high (goes to infinity). For ease of terminology, we refer to the system as the “asymptotic system” in these circumstances. We prove that the asymptotic system is nearly identical to the original (unconditional) system, but with a modified joint arrival pgf A^*(x,y) that can be computed explicitly from A(x, y). This fundamental result allows us to determine the stability condition of queue 2 in the asymptotic system, and explicitly compute the classical queueing performance metrics of queue 2, such as the pgf, the moments and the approximate tail distribution of its system content, when this condition is fulfilled. It also leads to accurate approximative closed-form expressions for the joint tail distribution of the system contents in both queues, in the original (unconditional) system. We extensively illustrate our methodology by means of various specific (popular) choices of A(x, y). In some examples, where an explicit solution for U(z_1,z_2) or for the (approximative) joint tail distribution is known, we retrieve the known results easily. In other cases, new results are found for arrival pgfs A(x, y) for which no explicit results were known until now.

Characterizing Imbalance in the Tails of the Propensity Score Distribution.

Understanding characteristics of patients with propensity scores in the tails of the propensity score (PS) distribution has relevance for inverse-probability-of-treatment-weighted and PS-based estimation in observational studies. Here we outline a method for identifying variables most responsible for extreme propensity scores. The approach is illustrated in 3 scenarios: 1) a plasmode simulation of adult patients in the National Ambulatory Medical Care Survey (2011-2015) and 2) timing of dexamethasone initiation and 3) timing of remdesivir initiation in patients hospitalized for coronavirus disease 2019 from February 2020 through January 2021. PS models were fitted using relevant baseline covariates, and tails of the PS distribution were defined using asymmetric first and 99th percentiles. After fitting of the PS model in each original data set, values of each key covariate were permuted and model-agnostic variable importance measures were examined. Visualization and variable importance techniques were helpful in identifying variables most responsible for extreme propensity scores and may help identify individual characteristics that might make patients inappropriate for inclusion in a study (e.g., off-label use). Subsetting or restricting the study sample based on variables identified using this approach may help investigators avoid the need for trimming or overlap weights in studies.

Prediction of dragon king extreme events using machine learning approaches and its characterizations

In this study, we employ a machine learning approach to infer the complex dynamics of dragon king extreme events. Specifically, we utilize two distinct machine learning techniques: Echo State Network and Gated Recurrent Unit. To do so, we consider three distinct systems for predicting dragon kings behavior: a pair of electronic circuits, coupled logistic maps, and Hindmarsh-Rose neurons. We discover that a few actual time series data points, accompanied by their corresponding system parameters, are adequate to capture dragon kings nature. Initially, we demonstrate that systems under consideration possess characteristics of extreme events, with signal amplitudes greater than the critical amplitude threshold. The presence of dragon kings within these observed extreme events is discerned by the emergence of hump-like behavior in the tail distribution of the probability density function and the statistical measures. Finally, we calculate the root mean square error to determine the accuracy of the predicted dynamics.

A comprehensive decision support system for the characterization of probability distribution tails for daily precipitation

A conventional Decision Support System (DSS) can be used to characterize tails of probability distributions into distribution families using various graphical methods. Existing DSSs lack efficient segregation of the Lognormal distribution from the Regularly varying and Subexponential distribution families. Also, they lack the ability to identify the distributions from the hyper-exponential distributions. Recently developed graphical diagnostic tools, such as concentration profile, concentration adjusted expected shortfall, discriminant moment ratio plot, maximum-to-sum plot, and Zenga plot can classify the tails of distributions into various classes if used in an appropriate order in combination with tools of conventional DSS. The present study proposes a comprehensive DSS that alleviates the shortcomings associated with the conventional DSS and characterizes the tails of distributions into classes B\\A (Pareto type), C\\B (regularly varying), D\\C (subexponential), E (Exponential type), hyper-exponential class (outside class E) and LN (Lognormal) distribution (the limiting case between class C and D). The robustness of the proposed DSS over the conventional DSS is established through a simulation experiment. Further, this study also evaluates the influence of the sample size on the effective implementation of the proposed DSS. Finally, the proposed DSS is applied to characterize the tails of daily gridded precipitation data over India. Results indicate that precipitation data from about 98% of grids over India exhibit distributions from heavy-tailed families. The study recommends the use of heavy-tailed distributions to model daily precipitation data over India. The study also suggests that one should rely on more than one graphical method for deducing rational conclusions regarding tail characterization.

The asymptotic tails of limit distributions of continuous-time Markov chains

AbstractThis paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we establish identities for stationary measures and QSDs, which we use to derive tail asymptotics. In particular, for continuous-time Markov chains with asymptotic power law transition rates, tail asymptotics for stationary distributions and QSDs are classified into three types using three easily computable parameters: (i) super-exponential distributions, (ii) exponential-tailed distributions, and (iii) sub-exponential distributions. Our approach to establish tail asymptotics of stationary distributions is different from the classical semimartingale approach, and we do not impose ergodicity or moment bound conditions. In particular, the results also hold for explosive Markov chains, for which multiple stationary distributions may exist. Furthermore, our results on tail asymptotics of QSDs seem new. We apply our results to biochemical reaction networks, a general single-cell stochastic gene expression model, an extended class of branching processes, and stochastic population processes with bursty reproduction, none of which are birth–death processes. Our approach, together with the identities, easily extends to discrete-time Markov chains.

Analysis of the Irregularity of Regional Development Based on the Asymmetry of the Empirical Distribution of GRP Per Capita of the Russian Federation Regions

Purpose of the study. The implementation of the spatial development strategy of the Russian Federation has led to an increase in scientific and practical interest in the research of interregional differences and the assessment of uneven regional development at all levels of the national economic system. The purpose of this study is to verify the conformity (inconformity) of the empirical distribution of per capita Gross Regional Product (GRP) values of the Russian Federation regions with the normal distribution law to substantiate the specifics of the interregional development of the national economy based on the identification of statistical characteristics of the empirical distribution of GRP per capita.Materials and methods. To achieve this goal, the article developed a methodology for measuring the uneven development of Russian regions by assessing the deviation of the empirical distribution of a sample of per capita GRP data from the normal distribution and determining the degree of asymmetry. The methodological basis was the analytical toolkit of the hypothesis of the normal distribution of the sample set of per capita GRP values for the Russian Federation regions. The article tested the methodology on a statistical sample of data on per capita GRP of the regions of the Russian Federation for 2010-2020; the level of uneven regional development of the economy of the Russian Federation was assessed and the statistical specificity of the revealed uneven development of the regions of the Russian Federation was identified. Identification of statistical outliers in the sample was carried out using the interquartile range method.Results. During the analysis of the sample, statistical outliers were identified. It has been proven that the distribution of per capita GRP of the regions of the Russian Federation is mostly right skewed handed or positively skewed. The observed right-handed orientation of the empirical distribution demonstrated the asymmetry of the distribution of the Russian Federation regions by per capita GRP. The increase in the irregularity of interregional development in the more advanced subjects of the Russian Federation with the per capita GRP index exceeding the average value for the analyzed sample was justified by statistical calculations and the construction of histograms of the empirical distribution of the per capita GRP of the Russian Federation regions.Conclusion. During the analyzed period, the stability of the uneven regional development of the Russian economy is observed. The stability of the positive asymmetry of the empirical distribution means that the basis for the divergence of regional development is the stability of the “club of the majority” of the Russian Federation regions, which form the left tail, and the “club of the minority”, which forms the long right tail of the empirical distribution. The approximation of the Pareto wealth distribution is a good approximation of the profile of the uneven distribution of per capita GRP of the regions of the Russian Federation.

The Sky and the Stratosphere: Wealth Concentration in India During the Last (Lost) Decade

AbstractThis paper provides new and improved estimates of wealth concentration in India during 2012–2018. Official surveys show a decline in wealth inequality and mean wealth per adult for the first time in three decades. We argue that although these wealth surveys are meant to be nationally representative, they underestimate the upper tail of the Indian wealth distribution—top wealth levels appear orders of magnitudes below externally measured estimates and unrepresentative of increasing stock‐market participation over this period. By combining official surveys and rich lists, we provide new estimates of top wealth shares and total personal wealth in India. We find that personal wealth is underestimated by nearly 54 percent in official data, and this gap increased sharply during the 2010s. Our revised estimates show wealth concentration to have sharply increased during 2012–2018. The share of India's top 1 percent is higher than similar estimates for Asia, and second only to Russia.

Quantile dependencies across BRICS currency markets in time of crisis: Analysis of the Russia–Ukraine war

ABSTRACT This paper examines the spillovers across BRICS currency markets during the Russia–Ukraine war. We observe that the connectedness across the BRICS currency markets is stronger during than before the war and the average-based connectedness framework shows a moderate level of connectedness across the BRICS currencies. However, using a quantile approach, the level of connectedness across the currencies is much higher at both tails of the conditional distribution. Overall, the result shows that war in Ukraine affect the connectedness among the BRICS currency markets and are stronger during extreme positive and negative events such as the war, indicating that the application of the average-based framework of connectedness to BRICS currencies is inadequate and restrictive.

Generation of random sea clutter amplitude sequence with quantitative control on distribution tail

AbstractThis letter proposes a data‐driven method to simulate random sea clutter amplitude sequence with distribution and correlation characteristics directly inherited from the measured clutter. First, a generation model is developed to simulate clutter amplitude sequence with desired distribution. By multiplying the measured amplitudes with random disturbance coefficients, the model introduces sample diversity between the simulated and measured sequences. Meanwhile, to quantitatively control the difference of the distribution tails between the simulated and measured sequences (i.e. to ensure their distributions are similar), the threshold error metric is introduced to set the disturbance variance. Second, a scheme combining the generation model with the correlation transfer technique is presented, which allows to simulate clutter amplitude sequence with both desired distribution and correlation for engineering purpose. Experiments based on different measured clutter sets indicate the proposed method works very well.

The impact of the Large Magellanic Cloud on dark matter direct detection signals

We study the effect of the Large Magellanic Cloud (LMC) on the dark matter (DM) distribution in the Solar neighborhood, utilizing the Auriga magneto-hydrodynamical simulations of Milky Way (MW) analogues that have an LMC-like system. We extract the local DM velocity distribution at different times during the orbit of the LMC around the MW in the simulations. As found in previous idealized simulations of the MW-LMC system, we find that the DM particles in the Solar neighborhood originating from the LMC analogue dominate the high speed tail of the local DM speed distribution. Furthermore, the native DM particles of the MW in the Solar region are boosted to higher speeds as a result of a response to the LMC's motion.We simulate the signals expected in near future xenon, germanium, and silicon direct detection experiments, considering DM interactions with target nuclei or electrons. We find that the presence of the LMC causes a considerable shift in the expected direct detection exclusion limits towards smaller cross sections and DM masses, with the effect being more prominent for low mass DM. Hence, our study shows, for the first time, that the LMC's influence on the local DM distribution is significant even in fully cosmological MW analogues.

Toward Robust Detections of Nanohertz Gravitational Waves

The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings–Downs curve—the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modeling of pulsar noise. Without proper care, misspecified noise models can lead to false-positive detections. Background estimation using “quasi-resampling” methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with “quasi-independent” scrambles—characterized by a statistical “match” below the fiducial value: ∣M∣ < 0.1. We show that sky scrambling is affected by “saturation” after quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show that phase scrambling saturates after quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the ≳5σ tail of the null distribution of the detection statistic. We sketch out various methods by which one may increase the number of independent scrambles. We also consider an alternative approach, wherein one reframes the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting p-value is in principle well defined, but may be susceptible to failure if assumptions about the data are incorrect.

Modelization and Calibration of the Power-Law Distribution in Stock Market by Maximization of Varma Entropy

Proper description of the return distribution is crucial for investment practitioners. The underestimation of the tail risk may lead to severe consequences, even for assets with moderate fluctuations. However, many empirical studies found that the distribution tails of many financial assets drop off more slowly than the Gaussian distributions. Therefore, we intend to model and calibrate the heavy tails observed in financial fluctuations in this study. By maximizing the Varma entropy with value-at-risk and expected shortfall constraints, we obtain the probability distribution of stock return and observe that the tail of stock return distribution is a power law. Since the variance of the real stock portfolio may be a random variable, using the mean-VaR-ES constraints to maximize the Varma entropy effectively avoids the problem of assuming that the variance is a constant value under the traditional mean-variance constraint. Therefore, the deduced theoretical model would be more consistent with the real market. Using high-frequency data from China’s stock markets, we calibrate our theoretical model and give the concrete form of probability density distribution p(x) for different time intervals. The calibration results show that the tail of the stock return distribution is a power law with most of the power-law orders between −2 and −7. We prove the robustness of our results by calibrating the Varma entropy for S&amp;P 500 of the USA stock market and different stock market indices in China’s A-share market. Our research’s findings not only offer a theoretical perspective for researchers but also give investing professionals a theoretical foundation on which to base their decisions.

Application of measures of heavy-tailedness in problems for analysis of financial time series

An important feature when working with financial data is the fact that the residuals of GARCH-models often have fatter tails than the tails of a normal distribution due to the large number of “outliers” in the data. This requires more detailed study. Kurtosis and quantile-based measure of heavy-tailedness were analyzed and compared in the article in relation to the problem of choosing the GARCH(1,1)-model specification. The data of indices of the Moscow Exchange were considered for the period from April 01, 2019 to February 22, 2022. Kurtosis values ​​ranged from 3 to 52. Empirical data showed that kurtosis was very sensitive to “outliers” in the data, which made it difficult to make assumptions about the distribution of model residuals. The approach considered in this paper based on the heavy-tailedness measure made it possible to justify the choice of degrees of freedom of the t-distribution for the model residuals to explain the fat tails in financial data. It was found that GARCH(1,1)-models with t(5)-distribution in the residuals are common.

A Monte Carlo Method for Calculating Lynden-Bell Equilibrium in Self-Gravitating Systems.

We present a Monte Carlo approach that allows us to easily implement Lynden-Bell (LB) entropy maximization for an arbitrary initial particle distribution. The direct maximization of LB entropy for an arbitrary initial distribution requires an infinite number of Lagrange multipliers to account for the Casimir invariants. This has restricted studies of Lynden-Bell's violent relaxation theory to only a very small class of initial conditions of a very simple waterbag form, for which the entropy maximization can be performed numerically. In the present approach, an arbitrary initial distribution is discretized into density levels which are then evolved using an efficient Monte Carlo algorithm towards the final equilibrium state. A comparison is also made between the LB equilibrium and explicit Molecular Dynamics simulations. We find that for most initial distributions, relaxation is incomplete and the system is not able to reach the state of maximum LB entropy. In particular, we see that the tail of the stationary particle distribution is very different from the one predicted by the theory of violent relaxation, with a hard cutoff instead of an algebraic decay predicted by LB's theory.

The role of dimers in the efficient growth of nanoparticles

The early stage of nanoparticle formation in gas aggregation systems is studied with the ambition to reveal the role of atomic dimers acting as cluster nuclei. The initial formation of a dimer nucleus, serving as a seed for subsequent atom attachment growth, is believed to be the bottleneck of the nanoparticle gas-aggregated synthesis. We thus examined the nature of the underlying process by employing energy-resolved mass-spectrometry and imaging of deposited nanoparticles. The production of dimers with origin in the discharge gas phase (ArCu+, Ar2+) and dimers preferentially sputtered directly from the target (Cu2+) was studied. The study demonstrates that sputtered Cu2+ dimers, carrying the high energy tail of Thompson energy distribution, play a major role as agents responsible for the formation of initial cluster nuclei, followed by a significant contribution of ArCu+; the population of these dimers is proportional to nanoparticle transported mass to the substrate. The proposed mechanism and the role of the dimer might be material independent since the qualitative agreement was also obtained for Ag NPs.

Temperature-mediated diffusion of nanoparticles in semidilute polymer solutions.

The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.

Probing light DM via the Migdal effect with spherical proportional counter* *Supported by the National Natural Science Foundation of China (12275134, 12275232, 12335005, 12147228), and the Natural Science Foundation of Shandong Province, China (ZR2018QA007)

Owing to its low electronic noise and flexible target materials, the Spherical Proportional Counter (SPC) with a single electron detection threshold can be utilized to search for sub-GeV dark matter (DM). In this study, we investigate the prospects for light DM direct detection via the DM-nucleus Migdal effect in the DARKSPHERE detector. We consider different DM velocity distributions and momentum-transfer effects. For Xenon and Neon targets, we find that the DM mass can be probed down to as low as (10) MeV, and the derived bounds on the DM-nucleus scattering cross section are sensitive to the high-velocity tails of the DM velocity distribution, which can be altered by orders of magnitude for the different DM velocity distributions in the region MeV.

Ability composition in the class and the school performance of immigrant students

Using longitudinal data from the Italian National Institute for the Evaluation of the Education System (INVALSI), this paper investigates whether the ability of peers affects the educational attainment of immigrant students. We not only focus on the average quality of peers in the class, but also further investigate which part of the ability distribution of peers drives the effect, by assessing the role played by the extreme tails of the ability distribution. Our empirical strategy addresses students’ endogenous sorting into classes by exploiting the within-student across-subjects variation in achievements and the simultaneity problem by using predetermined measures of peers’ ability. We show that peers’ ability matters. While native students are mostly influenced by the average quality of their peers, immigrant children are detrimentally affected by the share of very low achievers in the classroom. Our findings provide valuable guidance to policymakers concerning the allocation of students to classes in order to foster immigrant students’ integration and learning.