Heavy-Tailed Distributions Generated by Randomly Sampled Gaussian, Exponential and Power-Law Functions

A simple stochastic mechanism that produces exact and approximate power-law distributions is presented. The model considers radially symmetric Gaussian, exponential and power-law functions inn= 1, 2, 3 dimensions. Randomly sampling these functions with a radially uniform sampling scheme produces heavy-tailed distributions. For two-dimensional Gaussians and one-dimensional exponential functions, exact power-laws with exponent –1 are obtained. In other cases, densities with an approximate power-law behaviour close to the origin arise. These densities are analyzed using Padé approximants in order to show the approximate power-law behaviour. If the sampled function itself follows a power-law with exponent –α, random sampling leads to densities that also follow an exact power-law, with exponent -n/a – 1. The presented mechanism shows that power-laws can arise in generic situations different from previously considered specialized systems such as multi-particle systems close to phase transitions, dynamical systems at bifurcation points or systems displaying self-organized criticality. Thus, the presented mechanism may serve as an alternative hypothesis in system identification problems.

Manpower Systems Operating under Heavy and Light Tailed Inter-Exit Time Distributions

This paper considers a Manpower system where “exits” of employed personnel produce some wastage or loss. This system monitors these wastages over the sequence of exit epochs {t0 = 0 and tk;k = 1, 2,…} that form a recurrent process and admit recruitment when the cumulative loss of man hours crosses a threshold level Y, which is also called the breakdown level. It is assumed that the inter-exit times Tk = tk-1 - tk, k = 1, 2,… are independent and identically distributed random variables with a common cumulative distribution function (CDF) B(t) = P(Tk t) which has a tail 1 – B(t) behaving like t-v with 1 v as t → ∞. The amounts {Xk} of wastages incurred during these inter-exit times {Tk} are independent and identically distributed random variables with CDF P(Xk X) = G(x) and Y is distributed, independently of {Xk} and {tk}, as an exponentiated exponential law with CDF H(y) = P(Y y) = (1 - e-λy)n. The mean waiting time to break down of the system has been obtained assuming B(t) to be heavy tailed and as well as light tailed. For the exponential case of G(x), a comparative study has also been made between heavy tailed mean waiting time to break down and light tailed mean waiting time to break down values. The recruitment policy operating under the heavy tailed case is shown to be more economical in all types of manpower systems.

RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Scrutinizing Distributions Proves That IQ Is Inherited and Explains the Fat Tail

The motivation of this paper is to show how to use the information from given distributions and to fit distributions in order to confirm models. Our examples are especially for disciplines slightly away from mathematics. One minor result is that standard deviation and mean are at most a more or less good approximation to determine the best Gaussian fit. In our first example we scrutinize the distribution of the intelligence quotient (IQ). Because it is an almost perfect Gaussian distribution and correlated to the parents’ IQ, we conclude with mathematical arguments that IQ is inherited only which is assumed by mainstream psychologists. Our second example is income distributions. The number of rich people is much higher than any Gaussian distribution would allow. We present a new distribution consisting of a Gaussian plus a modified exponential distribution. It fits the fat tail perfectly. It is also suitable to explain the old problem of fat tails in stock returns.

HAZARD FUNCTION AND CHARACTERIZATIONS ON DISTRIBUTION TAILS OF NONNEGATIVE RANDOM VARIABLES

Some equivalent conditions on the classes of lighted-tailed and heavily heavy-tailed and lightly heavy-tailed d.f.s are introduced.The limit behavior of xα(x) and e λx(x) are discussed.Some properties of the subclass DKc and subclass DK 1 are obtained.

Importance of Generalized Logistic Distribution in Extreme Value Modeling

We consider a problem from stock market modeling, precisely, choice of adequate distribution of modeling extremal behavior of stock market data. Generalized extreme value (GEV) distribution and generalized Pareto (GP) distribution are the classical distributions for this problem. However, from 2004, [1] and many other researchers have been empirically showing that generalized logistic (GL) distribution is a better model than GEV and GP distributions in modeling extreme movement of stock market data. In this paper, we show that these results are not accidental. We prove the theoretical importance of GL distribution in extreme value modeling. For proving this, we introduce a general multivariate limit theorem and deduce some important multivariate theorems in probability as special cases. By using the theorem, we derive a limit theorem in extreme value theory, where GL distribution plays central role instead of GEV distribution. The proof of this result is parallel to the proof of classical extremal types theorem, in the sense that, it possess important characteristic in classical extreme value theory, for e.g. distributional property, stability, convergence and multivariate extension etc.

Momentum Distribution Functions in Quark-Gluon Plasma

Based on the constituent quasiparticle model of the quark-gluon plasma (QGP), the Wigner function is presented in the form of a color path integral. The Monte Carlo calculations of the quark and gluon densities, pair correlation functions and the momentum distribution functions for strongly coupled QGP plasma in thermal equilibrium at barion chemical potential equal to zero have been carried out. Analysis of the pair correlation functions points out on arising glueballs and related gluon bound states. Comparison results between the momentum distribution functions and Maxwell-Boltzmann distributions show the significant influence of the interparticle interaction on the high energy asymptotics of the momentum distribution functions resulting in the appearance of quantum “tails”.

Higher-order dynamic effects of uncertainty risk under thick-tailed stochastic volatility

Sudden and uncertain events often cause cross-contagion of risk among various sectors of the macroeconomy.This paper introduces the stochastic volatility shock that follows a thick-tailed Student’s t-distribution into a high-order approximate dynamic stochastic general equilibrium(DSGE)model with Epstein–Zin preference to better analyze the dynamic effect of uncertainty risk on macroeconomics.Then,the high-dimensional DSGE model(DSGE-SV-t)is developed to examine the impact of uncertainty risk on the transmission mechanism among macroeconomic sectors.The empirical research found that uncertainty risk generates heterogeneous impacts on macroeconomic dynamics under different inflation levels and economic states.Among them,a technological shock has the strongest impact on employment and consumption channels.The crowding-out effect of a fiscal policy stimulus on consumption and private investments is relatively weakened when considering uncertainty risk but is more pronounced during periods of high inflation.Uncertainty risk can partly explain the decline in investments and the increase in interest rates and employment rates,given the impact of an agent’s risk preferences.Compared with external economic conditions,the inflation factor has a stronger impact on the macro transmission mechanism caused by uncertainty risk.

A Comparison of the Estimators of the Scale Parameter of the Errors Distribution in the L1 Regression

The L1 regression is a robust alternative to the least squares regression whenever there are outliers in the values of the response variable, or the errors follow a long-tailed distribution. To calculate the standard errors of the L1 estimators, construct confidence intervals and test hypotheses about the parameters of the model, or to calculate a robust coefficient of determination, it is necessary to have an estimate of a scale parameterτ. This parameter is such that τ2/n is the variance of the median of a sample of size n from the errors distribution. [1] proposed the use of , a consistent, and so, an asymptotically unbiased estimator of τ. However, this estimator is not stable in small samples, in the sense that it can increase with the introduction of new independent variables in the model. When the errors follow the Laplace distribution, the maximum likelihood estimator of τ, say , is the mean absolute error, that is, the mean of the absolute residuals. This estimator always decreases when new independent variables are added to the model. Our objective is to develop asymptotic properties of under several errors distributions analytically. We also performed a simulation study to compare the distributions of both estimators in small samples with the objective to establish conditions in which is a good alternative to for such situations.

A Modification of the Quasi Lindley Distribution

In this paper, we introduce a modification of the Quasi Lindley distribution which has various advantageous properties for the lifetime data. Several fundamental structural properties of the distribution are explored. Its density function can be left-skewed, symmetrical, and right-skewed shapes with various rages of tail-weights and dispersions. The failure rate function of the new distribution has the flexibility to be increasing, decreasing, constant, and bathtub shapes. A simulation study is done to examine the performance of maximum likelihood and moment estimation methods in its unknown parameter estimations based on the asymptotic theory. The potentiality of the new distribution is illustrated by means of applications to the simulated and three real-world data sets.

Characterizations on Heavy-tailed Distributions by Means of Hazard Rate

Abstract Let F(x) be a distribution function supported on [0,X), with an equilibrium distribution function Fe(x). In this paper we shall study the function $r_e(x)( - {\rm ln}{\overline F}_e ( x ))\prime = {\overline F}( x )/\int_x^\infty {\overline F}( u )du $, which is called the equilibrium hazard rate of F. By the limiting behavior of re(x) we give a criterion to identify F to be heavy-tailed or light-tailed. Two broad classes of heavy-tailed distributions are also introduced and studied.

Influence of coarse tailings on flocculation settlement

The composition of tailings particles in mines plays a key role in the flocculation settlement of slurries.To study the influence of coarse particle tailings(CPTs)on the flocculation settlement of tailings slurries(TSs),static flocculent settling tests,scanning electron microscopy observations,and laser particle size analyses were conducted using the tailings obtained from a copper mine.The results demonstrate that(i)in the accelerated and free settling process,CPTs did not directly settle at the bottom of graduated cylinders;instead,they were netted by the flocculent structures(FSs)and settled together more quickly.The CPTs accelerate the rapid settlement of TSs;the acceleration effect is more obvious when the CPTs content is greater than 50 wt%.(ii)The most appropriate flocculant unit consumption(FUC)is 20 g·t-1,and no substantial increase is observed in the flocculant settling velocity with an increase in the flocculant because the effective FSs did not substantially change and thus did not lead to a notable increase in the settling velocity of the solid–liquid interface(SLI).(iii)In the effective settling space of the thickening facility,free water quickly flowed from the pores of FSs,which is reflected in the period from 0 to 1 min.

Distributed Estimator of Market Beta under Extreme Conditions

Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.

Asymptotic behavior for sums of non-identically distributed random variables

For any given positive integer m, let X_i, 1 ≤ i ≤ m be m independent random variables with distributions F_i, 1 ≤ i ≤ m. When all the summands are nonnegative and at least one of them is heavy-tailed, we prove that the lower limit of the ratio ■equals 1 as x →∞. When the summands are real-valued, we also obtain some asymptotic results for the tail probability of the sums. Besides, a local version as well as a density version of the above results is also presented.

改进YOLOv8的轻量化无人机目标检测算法

针对无人机目标检测算法计算复杂难以部署,且长尾分布的无人机数据导致检测精度较低的问题,提出了基于改进YOLOv8的轻量化无人机目标检测算法(PC-YOLOv8-n),可均衡网络检测精度与计算量,并对长尾分布数据有一定泛化能力。使用部分卷积层(PConv)替换YOLOv8中的3×3卷积层,对网络进行轻量化处理,解决网络冗余和计算量复杂的问题;融合双通道特征金字塔,增加自上而下的路径,将深层信息与浅层信息进行融合,同层引入轻量化注意力机制,提升网络的特征提取能力;采用均衡焦点损失(EFL)作为类别损失函数,通过均衡尾部类别在网络训练时的梯度权重,增加网络的类别检测能力。实验结果表明,PC-YOLOv8-n在VisDrone2019数据集中具有良好的表现,在mAP50精度上比原始YOLOv8-n算法提高了1.6个百分点,同时模型的参数和计算量分别降低为2.6×10^(6)和7.6 GFLOPs,检测速度达到77.2 FPS。

扩展目标跟踪Student’s t逆Wishart平滑算法

脉冲干扰和离群量测信息等因素通常会导致异常的厚尾噪声,这使得以高斯假设为前提的扩展目标跟踪(ETT)估计器的性能急剧降低,针对该问题该文提出一种基于扩展目标随机矩阵模型(RMM)的Student’s t逆Wishart平滑(StIWS)算法。首先,将目标的运动状态以及过程噪声和量测噪声建模为Student’s t分布以表征异常噪声对扩展目标概率分布的影响,将目标扩展状态建模为服从逆Wishart分布的随机矩阵。然后,在Student’s t贝叶斯平滑框架下,详细推导了能在扩展目标的多重特征动态演变的过程中有效估计目标状态的StIWS算法。最后,通过扩展目标跟踪的仿真实验结果和真实场景实验结果验证了所提算法的有效性。

南芬选矿厂综合尾矿工艺矿物学研究

南芬选矿厂为实现综合尾矿的回收利用及为合理选择选矿工艺及参数提供参考,以综合尾矿为研究对象,采用MLA矿物自动分析系统进行了尾矿矿物学特性研究。研究结果表明:综合尾矿全铁品位为9.64%,铁主要以赤、褐铁矿的形式存在,分布率为63.49%;其次以磁铁矿的形式存在,分布率为12.20%;主要脉石矿物为石英、镁铁闪石、绿泥石和透闪石,其他矿物含量少。磁、赤铁矿的嵌布粒度-75μm含量占85.71%,单体解离度为63.88%;其中,单体的磁、赤铁矿包裹少量石英,被包裹的磁、赤铁矿则主要被石英等矿物包裹,富连生体中含有较多的石英和少量的菱铁矿。

长尾分布下的微藻显微图像轻量级目标检测

微藻显微图像目标检测技术是生物学研究和环境监测等领域重要研究方向之一。电子显微镜采集到的微藻图像数据集存在长尾数据问题。传统的微藻检测方法需要大量人工操作,耗时长且结果容易受到操作人员技术经验的影响。结合解决长尾分布的方法,本文提出了一种基于延迟重采样和知识蒸馏相结合的目标检测算法(DDM-YOLO)。先对微藻显微图像进行数据增强,然后针对长尾分布数据,采用延迟重采样,并在二阶段采用反向采样,关注难以分类的少数类别样本,改善目标检测性能。设计了一种轻量级目标检测网络架构,通过知识蒸馏来减少模型复杂度和计算量。实验结果表明,DDM-YOLO算法的mAP@0.5/%为77.1%,与YOLOv5s相比提高了6.1%,模型参数量为3.88 MiB,减少了45.4%。所提出的方法在微藻显微图像数据上取得了显著的性能提升,同时在资源受限条件下实现了高效的目标检测,大大降低了检测人员的工作量。

中美ICT产品贸易演变研究——基于空间模式可视化的分析方法

在全球进入数字技术驱动和引领的创新时代,信息通信技术(ICT)已经成为衡量一个国家数字贸易实力的重要标志。以2003—2022年中美ICT产品双边贸易数据为样本,基于空间模式可视化的分析方法,从微观和宏观角度分析了中美ICT产品贸易的特征和地位。首先,通过绘制贸易空间结构分析了中国向美国出口的ICT产品种类。其次,通过应用头尾断裂法和绘制希尔伯特曲线,对ICT产品分类的重要性进行了空间模式可视化呈现。结果表明:中美ICT产品双边贸易结构稳定,产品贸易变化程度均匀,存在贸易增长的空间和发展潜力。从产品看,“重量≤10kg的便携自动数据处理设备”在中美ICT产品贸易中表现出极其重要和稳定的特征。通过位序-规模法发现,中美ICT产品贸易呈现典型的重尾分布特征,78%的尾部产品对于保持和巩固ICT产品贸易结构的稳定性至关重要,22%的头部产品在中美贸易中扮演着重要的角色;从空间网格分布看,中美ICT产品贸易呈现出显著的正向空间溢出效应。

喀斯特地区尾矿库周边植物重金属富集特征及空间分布

目的:了解典型喀斯特地区尾矿库周边植物的重金属富集特性和空间分布特征,筛选优势植物品种。方法:计算富集系数来判断不同植物对不同重金属的富集能力;采用地理信息分析软件(GIS)通过普通克里金插值和半变异函数分析,建立植物重金属空间分布模型;计算皮尔逊相关系数,以分析植物体内各重金属之间及与土壤pH值的相关性。结果:该尾矿库周边28种植物中,茄科植物红丝线、菊科的野茼蒿和荨麻科的八角麻对Cd有较强富集能力,植物中Cd污染严重;乌毛蕨科的苏铁蕨、海金沙科的小叶海金沙和大戟科的禾串树对Pb有较强富集能力;各植物对Cu和Zn均无富集作用。重金属空间分布模型显示,Cd主要分布在尾矿库南面、西南面、东南面和西北面;Pb主要分布在东南部、坝下小溪及正南面;Cu主要分布在正南、西南和坝下小溪方向;Zn主要分布在西面、西南、西北和正北面。在半变异函数模型参数中,Cd和Zn以随机性因素误差为主,各点的空间相关性弱,Pb、Cu以结构性因素误差为主,空间相关性较强;植物体内重金属含量空间变异性和空间相关性排序为Zn<Cd<Cu<Pb。Cd与Cu存在中等程度正相关关系,Cd与Pb、Zn呈正弱相关关系;植物体内各重金属含量与土壤pH值相关性不强。结论:筛选出的部分优势植物可作为矿区土壤重金属富集转移和生物修复的备选品种,初步了解了该区域重金属在土壤和植物之间的迁移规律,为开展矿区重金属污染治理提供了依据。