1,005 Results Found

Well-behaved densities are typically log-convex with heavy tails and log-concave with light ones. We discuss a benchmark for distinguishing between the two cases, based on the observation that large values of a sum $X_1+X_2$ occur as resu...

In economics, rank-size regressions provide popular estimators of tail exponents of heavy-tailed distributions. We discuss the properties of this approach when the tail of the distribution is regularly varying rather than strictly Pareto. The estimat...

Heavy-tailed Pearson diffusions provide a natural alternative to well-known Ornstein–Uhlenbeck and Cox–Ingersoll–Ross processes in applications that require addressing heavy-tailed behavior. In this paper, all three heavy-tailed Pea...

This paper investigates the randomly stopped sums, minima and maxima of heavy- and light-tailed random variables. The conditions on the primary random variables, which are independent but generally not identically distributed, and counting random var...

Recent mathematical models of reliability computer systems and telecommunication networks are based on distributions with heavy tails. This paper falls into the category of exploring the classical models with heavy tails: Gnedenko–Weibull, Burr...

There exist several estimators of the regression line in the simple linear regression: Least Squares, Least Absolute Deviation, Right Median, Theil–Sen, Weighted Balance, and Least Trimmed Squares. Their performance for heavy tails is compared...

Suppose that ${\xi }^{+}$ is the positive part of a random variable defined on the probability space $(\mathsf{\Omega },\mathcal{F},\mathbb{P})$ with the distribution function $F_{\xi }$. When the moment $\mathbb{E}{\left({\xi }^{+}\right)}^p$ of order $p>0$ is finite, then the truncated moment ${\overline{F}}_{\xi ,p}\left(x\right)=min\left\{1,\mathbb{E}\left({\xi }^{}\right)\right\}$...

Lifetime data arising in engineering reliability, survival analysis, actuarial science, and environmental studies often exhibit substantial right-skewness, extreme observations, and heterogeneous hazard-rate structures. Classical lifetime distributio...

In univariate data, there exist standard procedures for identifying dominating features that produce the largest number of observations. However, in the multivariate setting, the situation is quite different. This paper aims to provide tools and meth...

In actuarial statistics, distributions with heavy tails are of great interest to actuaries, as they represent a better description of risk exposure through a type of indicator with a certain probability. These risk indicators are used to determine co...

Most standard machine learning algorithms are formulated with the implicit assumption that empirical data are “well-behaved”. In this work, we consider heavy-tailed data whose underlying distribution does not necessarily possess finite mo...

This paper addresses the distributed filtering problem for linear systems subject to unknown inputs and heavy-tailed measurement noises. The unknown inputs are modeled using a non-informative prior distribution, while the heavy-tailed noises are mode...

In this paper, we study the problem of misrepresentation under heavy-tailed regression models with the presence of both misrepresented and correctly-measured risk factors. Misrepresentation is a type of fraud when a policy applicant gives a false sta...

Stochastic Configuration Network (SCN) has a powerful capability for regression and classification analysis. Traditionally, it is quite challenging to correctly determine an appropriate architecture for a neural network so that the trained model can...

The massive accumulation of graphite tailings causes serious environmental pollution, mainly from heavy metal pollution. Therefore, this article introduces a method of using graphite tailings as a high-content main material, cement as a small compone...

Forecast combination has been proven to be a very important technique to obtain accurate predictions for various applications in economics, finance, marketing and many other areas. In many applications, forecast errors exhibit heavy-tailed behaviors...

To provide the basic information about the release of heavy metals from the pyrite tailings of Huangjiagou pyrite mine, the pyrite tailings were investigated through a series of batch experiments under different initial pH of extractant, temperature,...

After long-term accumulation, weathering and rainfall of metals and non-metals in tailings ponds, the chemical composition will change, and the surface heavy metals may gradually migrate to the bottom layer, thus showing a cumulative effect. At prese...

Microbial induced carbonate precipitation (MICP) is a natural bio-mediated process that has been investigated for soil stabilization and heavy metal immobilization in soil and groundwater. This study analyzed the effect and mechanism of MICP for the...

Distributed state estimation is one of the critical technologies in the field of target tracking, where the process noise and measurement noise may have a heavy-tailed distribution. Traditionally, heavy-tailed distributions like the student-t distrib...

We provide two examples of the appearance of heavy-tailed distributions in social sciences applications. Among these distributions are the laws of Pareto and Lotka and some new ones. The examples are illustrated through the construction of suitable t...

This work presents a practical approach to improve risk quantification for heavy-tailed insurance claims through model averaging and grid map visualization, addressing the drawbacks of traditional single “best” model selection commonly us...

Mine tailings from an abandoned metal mine in Korea contained high concentrations of arsenic (As) and heavy metals [e.g., As: 67,336, Fe: 137,180, Cu: 764, Pb: 3,572, and Zn: 12,420 (mg/kg)]. US EPA method 6010 was an effective method for analyzing t...

Numerous heavy-tailed distributions are used for modeling financial data and in problems related to the modeling of economics processes. These distributions have higher peaks and heavier tails than normal distributions. Moreover, in some situations,...

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diver...

The purpose of this study was to assess heavy metal contamination and health risks for residents in the vicinity of a tailing pond in Guangdong, southern China. Water, soil, rice, and vegetable samples were collected from the area in the vicinity of...

The Danish fire loss dataset records commercial fire losses under three insurance coverages: building, contents, and profits. Existing research has primarily focused on the heavy-tail behaviour of the losses but ignored the relationship among differe...

This paper considers stationary autoregressive (AR) models with heavy-tailed, general GARCH (G-GARCH) or augmented GARCH noises. Limit theory for the least squares estimator (LSE) of autoregression coefficient $\rho ={\rho }_n$ is derived uniformly over stationar...

In this paper, a ratio test based on bootstrap approximation is proposed to detect the persistence change in heavy-tailed observations. This paper focuses on the symmetry testing problems of $I\left(1\right)$-to-$I\left(0\right)$ and $I\left(0\right)$-to-$I\left(1\right)$. On the basis of residual CUS...

Tailings resulting from mining and smelting activities may cause soil heavy-metal pollution and harm human health. To evaluate the environmental impact of heavy metals from tailings on farmland soils in the surrounding area, heavy metals (As, Cd, Cr,...

In the special case of a heavy-tailed sequence environment, change point monitoring in wireless sensor networks faces many serious challenges, such as high communication overhead, particularly sensitivity to sparse changes, and dependence on strict p...

The rapid growth of aluminum and graphite industries has generated substantial stockpiles of red mud and graphite tailings, which pose environmental risks due to their high heavy metal content and potential for soil and water contamination. This stud...

This paper examined whether portfolio-objective choice or forecasting complexity was more consequential in heavy-tailed commodity ETF allocation. Using daily Bloomberg data for 30 U.S.-listed commodity ETFs from 12 December 2018 to 16 December 2024,...

This paper considers the detection of fluctuating targets in heavy-tailed clutter through the use of dynamic programming based on track-before-detect (DP–TBD) in radar systems. The clutter is modeled in terms of K-distribution, which can be wid...

Aiming towards state estimation and information fusion for nonlinear systems with heavy-tailed measurement noise, a variational Bayesian Student’s t-based cubature information filter (VBST-CIF) is designed. Furthermore, a multi-sensor variation...

Classic machine learning and regime identification methods applied to financial time series lack theoretical guarantees and exhibit systematic failure modes: heavy-tails invalidate moment-based geometry, rendering distances and centroids dominated by...

A multi-hypothesis marginal multi-target Bayes filter for heavy-tailed observation noise is proposed to track multiple targets in the presence of clutter, missed detection, and target appearing and disappearing. The proposed filter propagates the exi...

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and me...

Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie...

The low-altitude airspace of bird flocks is gradually shared by unmanned aerial vehicles (UAVs), posing safety risks that necessitate accurate trajectory forecasting. However, existing vision-based methods often treat trajectory prediction and UAV de...

The increasing demand for mineral resources has generated mine tailings with heavy metals (HM) that negatively impact human and ecosystem health. Therefore, it is necessary to implement strategies that promote the immobilization or elimination of HM,...

This paper deals with the extreme value analysis for the triangular arrays which appear when some parameters of the mixture model vary as the number of observations grows. When the mixing parameter is small, it is natural to associate one of the comp...

In maneuvering target tracking applications, the performance of the traditional interacting multiple model (IMM) filter deteriorates seriously under heavy-tailed measurement noises which are induced by outliers. A robust IMM filter utilizing Student&...

The developed karst caves may become the seepage channels of heavy metal to the soil and underground water in Southwest China. Therefore, it is necessary to apply effective seepage treatments to the base of heavy metal tailing reservoirs. This paper...

Tailings ponds are a main heavy metal pollution source in mining areas. In this study, the geo-accumulation index ($I_{geo}$) and the potential ecological risk index (RI) are used to evaluate the environmental impact of Hongtou Mountain (HTM) tailings pon...

The heavy metal pollution linked to extractive activities has attracted broad public attention. To examine the current state of heavy metal pollution in river sediments around iron tailing zones, this study was carried out to evaluate the distributio...

In airport operations management, accurately estimating the service durations of ground support equipment such as Potable Water Trucks (PWTs) is essential for improving resource allocation efficiency and ensuring timely aircraft turnaround. Tradition...

Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation...

This paper discusses the problem of the mean changes in time series with heavy-tailed AR(p) noise. Firstly, it proposes a modified ratio-type test statistic, and the results show that under the null hypothesis of no mean change, the asymptotic distri...

Estimating skewness and kurtosis from real-world data remains a long-standing challenge in actuarial science and financial risk management, where these higher-order moments are critical for capturing asymmetry and tail risk. Traditional moment-based...