This paper conducts a comparative assessment of high-quality hybrid machine learning strategies to predict Years of Life Lost due to air pollution among the countries of South Asia. The models combine wavelet transformation of multi-scale feature decomposition with deep learning and time series Forecasting methods, thus capable of successfully processing complex and non-stationary data in air quality. One of the models uses long-memory features to better accomplish recognition of temporal patterns. Standard error was also used as a measure of the performance of the models, with the Root Mean Square Error, Mean Absolute Error, and Mean Absolute Percentage Error as standard measures. The outcomes indicate that the long-memory-enhanced hybrid model outperformed the other two predictive models (long-memory and hybrid models) by recording lower values of errors in form of differences between predicted and measured values across the three measures used in the data; PM, ozone, and ambient ozone being some of the key pollutants. This concludes that hybrid models are effective in giving precise predictions of air quality and strong health impact estimates. This knowledge will help inform policymakers to come up with effective recommendations to shrink the health threat to the environment and improve the life expectancy of the entire area.
Studentized U-statistics constitute an important class of nonlinear statistics whose asymptotic analysis is considerably more challenging than that of standardized U-statistics because the normalization involves a random variance estimator. Although extensive research has been devoted to Berry–Esseen approximations for U-statistics and self-normalized statistics, comparatively little attention has been given to the combined effects of studentization and random sample sizes. In this paper, we investigate the normal approximation of studentized U-statistics under a finite fourth-moment condition on the kernel. Using a direct probabilistic approach, we establish a Berry–Esseen-type bound of order O(n^-1/4) while requiring only fourth-order integrability, thereby relaxing the classical condition E|h(X_1,X_2)|^9/2<∞ . The analysis is then extended to randomly indexed studentized U-statistics, yielding a normal approximation theorem that explicitly separates the effects of studentization and random-index variability. An expanded Monte Carlo study examines the approximation under normal, Laplace, moderately and highly skewed gamma, standardized Student t_5 , and contaminated normal distributions, together with several random sample-size mechanisms. The results indicate favorable robustness under symmetric heavy tails and moderate contamination, while pronounced skewness produces larger finite-sample deviations. The proposed methodology provides a unified framework for studying studentization and random indexing within U-statistic theory and extends normal approximation techniques to an important class of randomly indexed stochastic systems.
Although advances in artificial intelligence (AI) and machine learning (ML) have transformed financial risk assessment, many early-warning frameworks for systematic risk still rely on isolated macro-financial indicators with limited integration of established statistical models. This study bridges that gap by incorporating classical quantitative financial methodologies such as the Capital Asset Pricing Model (CAPM), Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models, and Monte Carlo simulations within a modern data-driven analytical framework. Integrating these statistical methodologies into an early-warning system should improve its ability to detect both micro-level asset price dynamics and macro-level contagion trends, especially in emerging economies. This paper demonstrates how traditional models can complement AI- and ML-based predictive systems, enhancing the interpretability and robustness of early-warning mechanisms in finance. We apply these models to three notable stocks listed on Bursa Malaysia. Our analysis of market behaviour encompasses various theoretical dimensions, utilising daily data over a 10-year period from 2015 to 2024, resulting in 2,451 observations. CAPM evaluates systematic risk and anticipated returns via beta coefficients, GARCH models time-varying volatility and clustering phenomena, whilst Monte Carlo simulations generate probabilistic price paths under stochastic processes. The consolidated findings reveal varied risk-return characteristics among the equities, providing essential insights into volatility persistence, scenario-based forecasting, and portfolio optimisation. The analysis captures both micro-level asset dynamics and macro-level contagion effects. The results reveal distinct patterns in volatility persistence, systematic risk, and probabilistic return distributions. This paper demonstrates the empirical significance of each model and emphasises their theoretical foundations in contemporary finance literature. The results possess practical significance for investors, policymakers, and educators seeking to improve risk modelling, capital allocation, and financial decision-making in emerging economies.
The group sampling plans represent an enhancement of single sampling plans, wherein evaluators assess multiple items concurrently, thereby optimizing both time and cost. In this paper, an optimal group acceptance sampling plan under time-censoring is proposed when the lifetime of a product follows the generalized half-normal distribution. The design parameters of the plan will be determined by considering the conventional producer and consumer risks at the same time. The test plans are then formulated by limiting a linear combination of the conventional and expected producer and consumer risks and the optimal number of groups and acceptance number are obtained using integer nonlinear programming. An application in reliability testing is presented for illustrative purposes. The effect of the misspecification of the shape parameter has been examined.
One of the most popular methods for assessing the distribution tail thickness parameter (tail index) of a two-parameter PD is the Hill estimator, derived from order statistics. For reliability evaluations and engineering design, an accurate assessment of the distribution’s tails is crucial. Since the original Hill estimator is not shift- and scale-invariant, it must be modified in practice to include at least shift and scale parameters. Note that in a real-world engineering application, distribution tails—such as the Weibull type—are thin rather than thick (heavy). Fortunately, Weibull-type distributions can be estimated using a modified Hill-type estimator. The original two-parameter Weibull-type distribution suffers from the drawback that it resembles the two-parameter PD; without incorporating a shift model parameter, it lacks a shift parameter and is not shift-invariant. By adding shift parameters, the basic two-parameter Weibull distribution is transformed into a three-parameter form. Even so, fitting distributions with only three-parameters does not provide sufficient flexibility for most engineering and design applications; in other words, they often do not fit the underlying raw data. In many facets of statistical inference for rare events, selecting the threshold for the tail distribution is crucial. A novel method for selecting tail distribution thresholds is presented in this study. This study introduces a tailor-made four-parameter Weibull distribution with added q -parameter that bridges it with PD and Extreme Value Theory (EVT) power parameters and thus enables Inverse Hill Statistic (IHS) extension from thick to thin tail distributions. We present a semi-analytical solution that improves accuracy of the design values and failure probability P_F estimates, when the underlying data sample is of limited size. Offshore wind speed dynamics from industrial applications in renewable energy were selected for comparison and validation of the proposed model parameter estimators. Accurate modeling of the ambient wind speed distribution is critical for estimating in situ wind energy potential.
