Search Results (146)

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 estimators are known to be highly sensitive to outliers and often fail when the assumption of normality is violated. Despite numerous extensions—from robust moment-based methods to quantile-based measures—being proposed over the decades, no universally satisfactory solution has been reported, and many existing methods exhibit limited effectiveness, particularly under challenging distributional shapes. In this paper we propose a novel method that jointly estimates skewness and kurtosis based on a regression adaptation of the Cornish–Fisher expansion. By modeling the empirical quantiles as a cubic polynomial of the standard normal variable, the proposed approach produces a reliable and efficient estimator that better captures distributional shape without strong parametric assumptions. Our comprehensive simulation studies show that the proposed method performs much better than existing estimators across a wide range of distributions, especially when the data are skewed or heavy-tailed, as is typical in actuarial and financial applications. Full article

Hydrological time series frequently exhibit periodic trends with variables such as rainfall, runoff, and evaporation rates often following annual cycles. Seasonal variations further contribute to the complexity of these data sets. A critical aspect of analyzing such phenomena is estimating realistic return intervals, making the precise determination of these values essential. Given this importance, selecting an appropriate probability distribution is paramount. To address this need, we introduce a flexible probability model specifically designed to capture periodicity in hydrological data. We thoroughly examine its fundamental mathematical and statistical properties, including the asymptotic behavior of the probability density function (PDF) and hazard rate function (HRF), to enhance predictive accuracy. Our analysis reveals that the PDF exhibits polynomial decay as $x\to \infty$, ensuring heavy-tailed behavior suitable for extreme events. The HRF demonstrates decreasing or non-monotonic trends, reflecting variable failure risks over time. Additionally, we conduct a simulation study to evaluate the performance of the estimation method. Based on these results, we refine return period estimates, providing more reliable and robust hydrological assessments. This approach ensures that the model not only fits observed data but also captures the underlying dynamics of hydrological extremes. Full article

Highly alkaline and highly toxic red mud and other bulk industrial solid wastes become severely accumulated, posing huge risks such as soil degradation and environmental pollution. It is urgent to develop a long-term and stable resource disposal method. In the present research, artificial lightweight aggregates were fabricated utilizing industrial solid residues including red mud, phosphate tailing powder, and fly ash as raw materials. The physical characteristics, microstructure, heavy metal leaching attributes, and freeze–thaw resistance under different mixed water and curing conditions were studied. The results showed that, under the optimal curing condition (steam curing temperature of 80 °C and curing time of 10 h), lightweight aggregates exhibited the best comprehensive performance, with favorable trends in bulk density, apparent density, softening coefficient, and 1 h water absorption. In addition, the impact of extending the curing time on the further enhancement of the cylinder crush strength is limited. The microscopic morphology study showed that the hydration products in lightweight aggregates are primarily N-A-S-H and C-(A)-S-H, forming a strong colloidal structure and evenly dispersed on the particle surface, thereby improving its strength. Moreover, the heavy metal leachates (Cr, Pb, As, Cu, and Ni) from the lightweight aggregates met the environmental discharge criteria for non-hazardous substances. Full article

This study investigates the behavior of South African stock prices during divestment periods using mixture distributions. Divestment often triggers significant market reactions, necessitating a deeper understanding of stock return distributions in such events. Given the complexities of emerging markets like South Africa, this research models stock price behavior to assess associated risks. A mixture distribution approach is employed to capture the return dynamics of stocks listed on the Johannesburg Stock Exchange (JSE) between 2015 and 2024. Gaussian Mixture Models (GMMs), Lognormal Mixture, and Student’s t mixture models are applied to financial, technology, and energy stocks affected by divestment. Statistical tests including AIC and BIC assess the model performance. Mixture distributions outperform single-distribution models, effectively capturing heavy tails, volatility clustering, and asymmetry in stock returns. The GMM and Student’s t mixture models provide the best fit, revealing increased volatility and extreme negative returns following divestment events. Mixture distributions offer a robust framework for modeling South African stock prices during divestment periods. These models enhance the understanding of market dynamics, supporting better financial modeling and risk management in emerging markets. Full article

This paper develops a novel entropy-based framework to quantify tail risk and detect speculative bubbles in financial markets. By integrating extreme value theory with information theory, I introduce the Tail-Weighted Entropy (TWE) measure, which captures how information scales with extremeness in asset price distributions. I derive explicit bounds for TWE under heavy-tailed models and establish its connection to tail index parameters, revealing a phase transition in entropy decay rates during bubble formation. Empirically, I demonstrate that TWE-based signals detect crises in equities, commodities, and cryptocurrencies days earlier than traditional variance-ratio tests, with Bitcoin’s 2021 collapse identified weeks prior to the peak. The results show that entropy decay—not volatility explosions—serves as the primary precursor to systemic risk, offering policymakers a robust tool for preemptive crisis management. Full article

As investment portfolios become increasingly diversified and financial asset risks grow more complex, accurately forecasting the risk of multiple asset classes through mathematical modeling and identifying their heterogeneity has emerged as a critical topic in financial research. This study examines the volatility and tail risk of gold, crude oil, Bitcoin, and selected stock markets. Methodologically, we propose two improved Value at Risk (VaR) forecasting models that combine the autoregressive (AR) model, Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) model, Extreme Value Theory (EVT), skewed heavy-tailed distributions, and a rolling window estimation approach. The model’s performance is evaluated using the Kupiec test and the Christoffersen test, both of which indicate that traditional VaR models have become inadequate under current complex risk conditions. The proposed models demonstrate superior accuracy in predicting VaR and are applicable to a wide range of financial assets. Empirical results reveal that Bitcoin and the Chinese stock market exhibit no leverage effect, indicating distinct risk profiles. Among the assets analyzed, Bitcoin and crude oil are associated with the highest levels of risk, gold with the lowest, and stock markets occupy an intermediate position. The findings offer practical implications for asset allocation and policy design. Full article

Assessing the risks associated with waste disposal is essential for environmental protection and sustainable development, especially given concerns about the impact of industrial activities on the environment. This study analyses soil contamination in the Defor Petrila tailings-dump area caused by the deposition of waste material resulting from coal exploitation. To characterise the heavy-metal contamination in detail, we applied a comprehensive methodology that includes the calculation of the geo-accumulation index (I_geo), contamination factor (Cf), and potential ecological risk index (PERI), along with an analysis of the heavy-metal concentration isolines and a statistical analysis using the Pearson correlation coefficient. The results reveal varying levels of heavy-metal concentrations, as indicated by the calculated indices. The findings underscore the need for remediation and ongoing monitoring to mitigate the environmental impacts. This study provides a scientific basis for decision making in environmental management and highlights the importance of assessing mining-waste disposal near human settlements using various contamination-assessment methods. Full article

The utilization of iron tailings in road construction poses significant environmental risks due to the complex release mechanisms of pollutants and varying regional conditions. This study integrates an exponential decay model with an instantaneous pollutant transport model, employing Monte Carlo simulations to assess risks and regional characteristics. Results show high Potential Hazard Indices (PHIs) for arsenic, manganese, barium, nickel, and lead, with PHI values between 4.2 and 22.7. Simulations indicate that manganese and nickel concentrations may exceed groundwater standards, particularly in humid areas. The study recommends controlling the iron tailings mixing ratio based on climate, suggesting limits of 35% in humid, 60% in semi-humid, and more lenient ratios in arid and semi-arid regions. It also underscores the need for improved risk assessment methodologies and region-specific management strategies at the national level. Full article

Carbonaceous–siliceous–argillaceous rock-type uranium deposits, a major uranium resource in China, pose significant environmental risks due to heavy metal contamination. Geochemical investigations in the former Zoige uranium mine revealed elevated As, Cd, Cr, Cu, Ni, U, and Zn concentrations in soils and sediments, particularly at river confluences and downstream regions, attributed to leachate migration from ore bodies and tailings ponds. Surface samples exhibited high Cd bioavailability. The integrated BCR and mineral analysis reveals that Acid-soluble and reducible fractions of Ni, Cu, Zn, As, and Pb are governed by carbonate dissolution and Fe-Mn oxide dynamics via silicate weathering, while residual and oxidizable fractions show weak mineral-phase dependencies. Positive Matrix Factorization identified natural lithogenic, anthropogenic–natural composite, mining-related sources. Pollution assessments using geo-accumulation index and contamination factor demonstrated severe contamination disparities: soils showed extreme Cd pollution, moderate U, As, Zn contamination, and no Cr, Pb pollution (overall moderate risk); sediments exhibited extreme Cd pollution, moderate Ni, Zn, U levels, and negligible Cr, Pb impacts (overall extreme risk). USEPA health risk models indicated notable non-carcinogenic (higher in adults) and carcinogenic risks (higher in children) for both age groups. Ecological risk assessments categorized As, Cr, Cu, Ni, Pb, and Zn as low risk, contrasting with Cd (extremely high risk) and sediment-bound U (high risk). These findings underscore mining legacy as a critical environmental stressor and highlight the necessity for multi-source pollution mitigation strategies. Full article

Competing risk models are essential in survival analysis for studying systems with multiple mutually exclusive failure events. This study investigates the application of competing risk models in the presence of progressively Type-II censored data for the Dagum distribution, a flexible distribution suited for modeling data with heavy tails and varying skewness and kurtosis. The methodology includes maximum likelihood estimation of the unknown parameters, with a focus on the special case of a common shape parameter, which allows for a closed-form expression of the relative risks. A hypothesis test is developed to assess the validity of this assumption, and both asymptotic and bootstrap confidence intervals are constructed. The performance of the proposed methods is evaluated through Monte Carlo simulations, and their applicability is demonstrated with a real-world example. Full article

Flotation tailings (FT), as a product of the exploitation and processing of copper ore, represent a significant environmental and health risk due to the high content of heavy metals and sulfide compounds. Contemporary concepts of sustainable development and circular economy increasingly emphasize the need for rational use of resources and minimization of all types of waste, including mining waste. In this context, the reuse of flotation tailings in the construction industry represents a significant step towards closing the material flow in the mining and construction sectors. In order to reduce the negative impact of FT on the environment, the possibility of its application as a substitute for a portion of cement in the production of concrete was investigated. The main challenge is to reduce the negative impact of sulfides, originating from sulfide compounds, in order to achieve the desired concrete quality. Limestone aggregates of different size fractions (0/4, 4/8, 8/16 mm) were used for sulfide neutralization. Pyrite concentrate was used as a sulfide source, which together with FT provides the mixtures FT-7, FT-14, FT-25, and FT-40, with sulfur contents of 7.56, 13.84, 25.02, and 39.82%, respectively. FT mixtures were used as a substitute for Portland cement (PC) in the preparation of concrete. Test methods included XRD (X-ray diffraction), XRF (X-ray fluorescence), SEM (scanning electron microscopy), LP (leaching procedure), TCLP (toxicity characterization leaching procedure), assessment of acid eluate generation potential (AP—acid potential, NP—neutralization potential, and NNP—net neutralization potential), NEN (determination of heavy metals in cured concrete eluate), and UCS (uniaxial compressive strength of cured concrete). The results showed that the chemical characteristics of FT, as well as the chemical and mechanical properties of hardened concrete, allow the efficient use of these tailings in concrete mixes, which significantly utilizes FT, reduces the generation of mining waste, and contributes to the reduction of the negative impact on the environment and achieving sustainable development in mining. Full article

We propose the financial generative adversarial network–bidirectional long short-term memory (FINGAN-BiLSTM) model to accurately reproduce the complex statistical properties and stylized facts, namely, heavy-tailed behavior, volatility clustering, and leverage effects observed in the log returns of the foreign exchange (FX) market. The proposed model integrates a bidirectional LSTM (BiLSTM) into the conventional FINGAN framework so that the generator, discriminator, and predictor networks simultaneously incorporate both past and future information, thereby overcoming the information loss inherent in unidirectional LSTM architectures. Experimental results, assessed using metrics such as the Kolmogorov–Smirnov statistic, demonstrate that FINGAN-BiLSTM effectively mimics the distributional and dynamic patterns of actual FX data. In particular, the model significantly reduces the maximum cumulative distribution discrepancy in assets with high standard deviations and extreme values, such as the Canadian dollar (CAD) and the Mexican Peso (MXN), while precisely replicating dynamic features like volatility clustering and leverage effects, thereby outperforming conventional models. The findings suggest that the proposed deep learning–based forecasting model holds significant promise for practical applications in financial risk assessment, derivative pricing, and portfolio optimization, and they highlight the need for further research to enhance its generalization capabilities through the integration of exogenous economic variables. Full article

This study presented a comprehensive physical–statistical analysis of atmospheric particulate matter (PM₁₀ and PM_2.5) and trace gases (SO₂ and O₃) over Faial Island in the Azores archipelago during 2024. We collected real-time data at the Espalhafatos rural background station, covering 35,137 observations per pollutant, with 15 min intervals. Descriptive statistics, probability distribution fitting (Normal, Lognormal, Weibull, Gamma), and correlation analyses were employed to characterize pollutant dynamics and identify extreme pollution episodes. The results revealed that PM_2.5 (fine particles) concentrations are best modeled by a Lognormal distribution, while PM₁₀ concentrations fit a Gamma distribution, highlighting the presence of heavy-tailed, positively skewed behavior in both cases. Seasonal and episodic variability was significant, with multiple Saharan dust transport events contributing to PM exceedances, particularly during winter and spring months. These events, confirmed by CAMS and SKIRON dust dispersion models, affected not only southern Europe but also the Northeast Atlantic, including the Azores region. Weak to moderate correlations were observed between PM concentrations and meteorological variables, indicating complex interactions influenced by atmospheric stability and long-range transport processes. Linear regression analyses between SO₂ and O₃, and between SO₂ and PM_2.5, showed statistically significant but low-explanatory relationships, suggesting that other meteorological and chemical factors play a dominant role. This result highlights the importance of developing air quality policies that address both local emissions and long-range transport phenomena. They support the implementation of early warning systems and health risk assessments based on probabilistic modeling of particulate matter concentrations, even in remote Atlantic locations such as the Azores. Full article

This article describes a robust Gaussian Prior process state space modeling (GPSSM) approach to assess the impact of an intervention in a time series. Numerous applications can benefit from this approach. Examples include: (1) time series could be the stock price of a company and the intervention could be the acquisition of another company; (2) the time series under concern could be the noise coming out of an engine, and the intervention could be a corrective step taken to reduce the noise; (3) the time series could be the number of visits to a web service, and the intervention is changes done to the user interface; and so on. The approach we describe in this article applies to any times series and intervention combination. It is well known that Gaussian process (GP) prior models provide flexibility by placing a non-parametric prior on the functional form of the model. While GPSSMs enable us to model a time series in a state space framework by placing a Gaussian Process (GP) prior over the state transition function, probabilistic recurrent state space models (PRSSM) employ variational approximations for handling complicated posterior distributions in GPSSMs. The robust PRSSMs (R-PRSSMs) discussed in this article assume a scale mixture of normal distributions instead of the usually proposed normal distribution. This assumption will accommodate heavy-tailed behavior or anomalous observations in the time series. On any exogenous intervention, we use R-PRSSM for Bayesian fitting and forecasting of the IoT time series. By comparing forecasts with the future internal temperature observations, we can assess with a high level of confidence the impact of an intervention. The techniques presented in this paper are very generic and apply to any time series and intervention combination. To illustrate our techniques clearly, we employ a concrete example. The time series of interest will be an Internet of Things (IoT) stream of internal temperatures measured by an insurance firm to address the risk of pipe-freeze hazard in a building. We treat the pipe-freeze hazard alert as an exogenous intervention. A comparison of forecasts and the future observed temperatures will be utilized to assess whether an alerted customer took preventive action to prevent pipe-freeze loss. Full article