Search Results (935)

In many scientific and engineering fields (e.g., measurement science), a probability density function often models a system comprising a signal embedded in noise. Conventional measures, such as the mean, variance, entropy, and informity, characterize signal strength and uncertainty (or noise level) separately. However, the true performance of a system depends on the interaction between signal and noise. In this paper, we propose a novel measure, called “inforpower”, for quantifying the system’s informational power that explicitly captures the interaction between signal and noise. We also propose a new measure of central tendency, called “information-energy center”. Closed-form expressions for inforpower and information-energy center are provided for ten well known continuous distributions. Moreover, we propose a maximum inforpower criterion, which can complement the Akaike information criterion (AIC), the minimum entropy criterion, and the maximum informity criterion for selecting the best distribution from a set of candidate distributions. Two examples (synthetic Weibull distribution data and Tana River annual maximum streamflow) are presented to demonstrate the effectiveness of the proposed maximum inforpower criterion and compare it with existing goodness-of-fit criteria. Full article

In this paper, a statistical model with three parameters is proposed which is called New Modified Generalized Inverted Exponential Distribution (MGIE). In addition, several statistical characteristics of the MGIE distribution are obtained, including quantile function, median, moments, mode, mean deviation, harmonic mean, reliability, hazard and odds functions and Rényi entropy. Moreover, the estimators of parameters are found using the maximum likelihood estimation method. A simulation study using the Monte Carlo method is performed to assess the behavior of the parameters. Finally, three real data sets are applied to demonstrate the importance of the proposed distribution. Full article

The choice of probability distribution is strongly data-dependent, as observed in several studies. Given the central role of statistical distribution in predictive analytics, researchers have continued to develop new models that accurately capture underlying data behaviours. This study proposes the Hybrid Weibull–Exponentiated Rayleigh distribution developed by compounding the Weibull and Exponentiated Rayleigh distributions via the T-X transformation framework. The new three-parameter distribution is formulated to provide a flexible modelling framework capable of handling data exhibiting non-monotone failure rates. The properties of the proposed distribution, such as the cumulative distribution function, probability density function, survival function, hazard function, linear representation, moments, and entropy, are studied. We estimate the parameters of the distribution using the Maximum Likelihood Estimation technique. Furthermore, the impact of the proposed distribution parameters on the distribution’s shape is studied, particularly its symmetry properties. The shape of the distribution varies with its parameter values, thereby enabling it to model diverse data patterns. This flexibility makes it especially useful for describing the presence or absence of symmetry in real-world failure processes. Simulation studies are conducted to assess the behaviour of the estimators under different parameter settings. The proposed distribution is applied to real-world data to demonstrate its performance. Comparative analysis is performed against other well-established models. The results indicate that the proposed distribution outperforms other models in terms of goodness-of-fit, demonstrating its potential as a superior alternative for modelling lifetime data and reliability analysis based on Akaike Information Criterion and Bayesian Information Criterion. Full article

Against the backdrop of China’s “Dual Carbon” strategy (peak carbon emissions and carbon neutrality), timber forests serve the dual function of wood supply and carbon sink enhancement. In this study, we employed the Kuenm package in R to optimize Maximum Entropy model (MaxEnt) parameters. Based on the distribution data of six timber tree species in Sichuan Province and 43 environmental factors, we utilized the MaxEnt outputs and ArcGIS 10.8 software to map the geographic distribution of the suitable habitats for these species from the present day into the future (2061–2080) under different climate scenarios (SSP126 and SSP585). Furthermore, we analyzed the migration trend of their future distribution centers. The model optimization significantly improved both fit and predictive performance, with AUC values ranging from 0.8552 to 0.9637 and TSS values ranging from 0.6289 to 0.84, indicating high predictive capability and stability of the model. Analysis of environmental factors, including altitude, precipitation, and temperature, revealed that altitude plays a dominant role in species distribution. Future climate scenario simulations indicated that climate change will significantly alter the distribution of suitable habitats for these timber tree species. The suitable areas for some species contracted, with changes being particularly pronounced under the SSP585 scenario, in which the high-suitability area for Phoebe zhennan is projected to increase from 12,788 km² to 20,004 km², whereas the high-suitability area for Eucalyptus robusta is expected to contract from 8706 km² to 7715 km². The migration distances of suitable habitats for timber tree species in Sichuan range from 5 km to 101 km southwestward under different climate scenarios, and these shifts are statistically significant (p < 0.01), with shifts in elevation and precipitation patterns, reflecting species-specific responses to climate change. This study aims to predict future suitable habitats of timber tree species in Sichuan, providing scientific support for forestry planning, forest quality improvement, and climate risk mitigation. Full article

Ecosystem vulnerability assessment is paramount for local environmental stability and lasting economic progress. This study selects Hubei Province as the research area, applying multi-source spatiotemporal datasets spanning the period 2000–2023. A pressure–state–response (PSR) framework, incorporating 14 distinct indicators, was developed. The selection criteria for these indicators adhered to principles of scientific rigor, all-encompassing scope, statistical representativeness, and practical applicability. The chosen indicators effectively encompass natural, anthropogenic, and socio-economic drivers, aligning with the specific ecological attributes and key vulnerability factors pertinent to Hubei Province. The analytic network process (ANP) method and entropy weighting (EW) method were integrated to ascertain comprehensive weights, thereby computing the ecological vulnerability index (EVI). In the meantime, we analyzed temporal and spatial EVI shifts. Spatial autocorrelation analysis, the geodetic detector, the Theil–Sen median, the Mann–Kendall trend test, and the Grey–Markov model were employed to elucidate spatial distribution, driving factors, and future trends. Results indicate that Hubei Province exhibited mild ecological vulnerability from 2000 to 2023, but with a notable deteriorating trend: extreme vulnerability areas expanded from 0.34% to 0.94%, while moderate and severe vulnerability zones also increased. Eastern regions demonstrate elevated vulnerability, but they were lower in the west, correlating with human activity intensity. The global Moran’s I index ranged from 0.8579 to 0.8725, signifying a significant positive spatial correlation of ecological vulnerability, with the highly vulnerable areas concentrated in regions with intense human activities, while the less vulnerable areas are located in ecologically intact areas. Habitat quality index and carbon sinks emerged as key drivers, possibly stemming from the forest–wetland composite ecosystem’s high dependence on water conservation, biodiversity maintenance, and carbon storage functions. Future projections based on Grey–Markov models indicate that ecological fragility in Hubei Province will exhibit an upward trend, with ecological conservation pressures continuing to intensify. This research offers a preliminary reference basis of grounds for ecological zoning, as well as sustainable regional development in Hubei Province, while also providing a theoretical and practical framework for constructing an ecological security pattern within the Yangtze River Economic Belt (YREB) and facilitating ecological governance in analogous river basins globally, thereby contributing to regional sustainable development goals. Full article

The Aquila Optimizer (AO), inspired by the hunting behavior of Aquila birds, is a recent nature-inspired metaheuristic algorithm recognized for its simplicity and low computational cost. However, the conventional AO often suffers from premature convergence and an imbalance between exploration and exploitation when applied to complex engineering optimization problems. To overcome these limitations, this study proposes a modified Aquila Optimizer (m-AO) incorporating three enhancement strategies: an adaptive chaotic reverse learning mechanism to improve population diversity, an elite alternative pooling strategy to balance global exploration and local exploitation, and a shifted distribution estimation strategy to accelerate convergence toward promising regions of the search space. The performance of the proposed m-AO is evaluated using 23 classical benchmark functions, IEEE CEC 2022 benchmark problems, and a practical plate–fin heat exchanger (PFHE) design optimization problem. Numerical simulations demonstrate that m-AO achieves faster convergence, higher solution accuracy, and improved robustness compared with the original AO and several state-of-the-art metaheuristic algorithms. In the PFHE application, the proposed method yields a significant improvement in thermal performance, accompanied by a reduction in entropy generation and pressure drop under prescribed design constraints. Statistical analyses further confirm the superiority and stability of the proposed approach. These results indicate that the modified Aquila Optimizer is an effective and reliable tool for solving complex thermal system design optimization problems. Full article

Rainfall, as the main driving force of natural disasters such as floods and droughts, has strong non-linear and abrupt characteristics, which makes it difficult to predict. As extreme weather events occur frequently in the Yellow River Basin, it is especially critical to reveal the physical mechanism of rainfall in the basin and integrate monthly scale meteorological data to achieve monthly rainfall prediction. In this paper, we propose a rainfall prediction model coupled with a physical mechanism and a temporal convolutional network (TCN) to achieve the prediction of monthly rainfall in the basin, aiming to reveal the physical mechanism between rainfall factors in the basin based on the transfer entropy and the multidimensional Copula function and based on the physical mechanism which is embedded into the TCN to construct a dual-driven prediction model with both physical knowledge and data, while the SHAP is used to analyze the interpretability of the prediction model. The results are as follows: (1) Temperature, relative humidity, and evaporation are key characteristic factors driving rainfall. (2) The physical mechanism features between temperature, relative humidity, and evaporation can be described by the three-dimensional Gumbel–Hougaard Copula function, with a more concentrated data distribution of their joint distribution probability. (3) The PHY-TCN model can accurately fit the extremes of the rainfall series, improving the model accuracy in the training set by 3.82%, 1.39%, and 9.82% compared to TCN, CNN, and LSTM, respectively, and in the test set by 6.04%, 2.55%, and 8.91%, respectively. (4) Embedding physical mechanisms enhances the contribution of individual feature variables in the PHY-TCN model and increases the persuasiveness of the model. This study provides a new research framework for rainfall prediction in the YRB and analyzes the physical relationship between the input data and output results of the deep learning model. It has important practical significance and strategic value for guiding the optimal scheduling of water resources, improving the risk management level of the basin, and promoting the ecological protection and high-quality development of the YRB. Full article

Accurate Short-Term Load Forecasting (STLF) is paramount for the stable and economical operation of power systems, particularly in the context of high renewable energy penetration, which exacerbates load volatility and non-stationarity. The prevailing advanced “decomposition–ensemble” paradigm, however, faces two significant challenges when processing non-stationary signals: (1) The performance of Variational Mode Decomposition (VMD) is highly dependent on its hyperparameters (K, α), and traditional meta-heuristic algorithms (e.g., GA, GWO, PSO) are prone to converging to local optima during the optimization process; (2) Deep learning predictors struggle to dynamically weigh the importance of multi-dimensional, heterogeneous features (such as the decomposed Intrinsic Mode Functions (IMFs) and external climatic factors). To address these issues, this paper proposes a novel, adaptive hybrid forecasting framework, namely IRIME-VMD-CDA-LSTNet. Firstly, an Improved Rime Optimization Algorithm (IRIME) integrated with a Gaussian Mutation strategy is proposed. This algorithm adaptively optimizes the VMD hyperparameters by targeting the minimization of average sample entropy, enabling it to effectively escape local optima. Secondly, the optimally decomposed IMFs are combined with climatic features to construct a multi-dimensional information matrix. Finally, this matrix is fed into an innovative Cross-Dimensional Attention (CDA) LSTNet model, which dynamically allocates weights to each feature dimension. Ablation experiments conducted on a real-world dataset from a distribution substation demonstrate that, compared to GA-VMD, GWO-VMD, and PSO-VMD, the proposed IRIME-VMD method achieves a reduction in Root Mean Square Error (RMSE) of up to 18.9%. More importantly, the proposed model effectively mitigates the “prediction lag” phenomenon commonly observed in baseline models, especially during peak load periods. This framework provides a robust and high-accuracy solution for non-stationary load forecasting, holding significant practical value for the operation of modern power systems. Full article

In this paper, we propose FedENLC, an end-to-end noisy label correction model that performs model training and label correction simultaneously to fundamentally mitigate the label noise problem of federated learning (FL). FedENLC consists of two stages. In the first stage, the proposed model employs Symmetric Cross Entropy (SCE), a robust loss function for noisy labels, and label smoothing to prevent the model from being biased by incorrect information in noisy environments. Subsequently, a Bayesian Gaussian Mixture Model (BGMM) is utilized to detect noisy clients. BGMM mitigates extreme parameter bias through its prior distribution, enabling stable and reliable detection in FL environments where data heterogeneity and noisy labels coexist. In the second stage, only the top noisy clients with high noise ratios are selectively included in the label correction process. The selection of top noisy clients is determined dynamically by considering the number of classes, posterior probabilities, and the degree of data heterogeneity. Through this approach, the proposed model prevents performance degradation caused by incorrect detection, while improving both computational efficiency and training stability. Experimental results show that FedENLC achieves significantly improved performance over existing models on the CIFAR-10 and CIFAR-100 datasets under data heterogeneity settings along with four noise settings. Full article

The energy transition in Ibero-American countries demands significant diversification, yet the vast potential of offshore renewable energies (ORE) remains largely untapped. Slow adoption is often attributed to the hostile marine environment, high investment costs, and a lack of institutional, regulatory, and industrial readiness. A critical barrier for policymakers is the absence of methodologically robust tools to assess national preparedness. Existing indices typically rely on simplistic weighting schemes or are susceptible to known flaws, such as the rank reversal phenomenon, which undermines their credibility for strategic decision-making. This study addresses this gap by developing a multi-criteria decision-making (MCDM) framework based on a problem-specific synthesis of established optimization principles to construct a comprehensive Offshore Readiness Index (ORI) for 13 Ibero-American countries. The framework moves beyond traditional methods by employing an advanced weight-elicitation model rooted in the Robust Ordinal Regression (ROR) paradigm to analyze 42 sub-criteria across five domains: Regulation, Planning, Resource, Industry, and Grid. Its methodological core is a non-linear objective function that synergistically combines a Shannon entropy term to promote a maximally unbiased weight distribution and to prevent criterion exclusion, with an epistemic regularization penalty that anchors the solution to expert-derived priorities within each domain. The model is guided by high-level hierarchical constraints that reflect overarching policy assumptions, such as the primacy of Regulation and Planning, thereby ensuring strategic alignment. The resulting ORI ranks Spain first, followed by Mexico and Costa Rica. Spain’s leadership is underpinned by its exceptional performance in key domains, supported by specific enablers, such as a dedicated renewable energy roadmap. The optimized block weights validate the model’s structure, with Regulation (0.272) and Electric Grid (0.272) receiving the highest importance. In contrast, lower-ranked countries exhibit systemic deficiencies across multiple domains. This research offers a dual contribution: methodological innovation in readiness assessment and an actionable tool for policy instruments. The primary policy conclusion is clear: robust regulatory frameworks and strategic planning are the pivotal enabling conditions for ORE development, while industrial capacity and infrastructure are consequent steps that must follow, not precede, a solid policy foundation. Full article

This article introduces a new flexible distribution, called the alpha power Topp–Leone Dagum (APTLDa) distribution, which extends the classical Dagum model by combining the Topp–Leone generator with the alpha power transformation (APT). The proposed distribution is capable of modeling data with symmetrical and asymmetrical shapes for the probability density and hazard rate functions. This makes it suitable for lifetime and reliability data analysis. Several important statistical properties of the new distribution are derived, including the quantile function, moments, entropy measures, order statistics, and reliability-related functions. Parameter estimation is carried out using the maximum likelihood method, and the performance of the estimators is examined through an extensive simulation study under different sample sizes and parameter settings. The simulation results demonstrate the consistency and good finite-sample behavior of the estimators. The practical usefulness of the proposed distribution is illustrated through applications to two real datasets, where its performance is compared with several competing models. The results show that the APTLDa distribution provides a flexible and effective alternative for modeling lifetime data. Full article

The paper presents a statistical model based on the two-weighted exponential distribution (TWED) to examine censored Human Immunodeficiency Virus (HIV) survival information. Identifying HIV as a disability, the study endorses an inclusive and sustainable health policy framework through some predictive findings. The TWED provides an accurate representation of the inherent hazard patterns and also improves the modelling of survival data. The parameter estimation is achieved in both a classical maximum likelihood estimation (MLE) and a Bayesian approach. Bayesian inference can be carried out under general entropy loss conditions and the symmetric squared error loss function through the Markov Chain Monte Carlo (MCMC) method. Based on the symmetric properties of the inverse of the Fisher information matrix, the asymptotic confidence intervals (ACLs) for the MLEs are constructed. Moreover, two-sided symmetric credible intervals (CRIs) of Bayesian estimates are also constructed based on the MCMC results that are based on symmetric normal proposals. The simulation studies are very important for indicating the correctness and probability of a statistical estimator. Implementing the model on actual HIV data illustrates its usefulness. Altogether, the paper supports the idea that statistics play an essential role in promoting disability-friendly and sustainable research in the field of public health in general. Full article

The Yangtze River Economic Belt is a crucial driver of China’s economy, and its shoreline is a strategic, finite resource vital for ecological security, flood control, navigation, and socioeconomic development. However, intensive development has resulted in functional conflicts and ecological degradation, underscoring the need for accurate identification and suitability assessment of shoreline functions. Conventional methods, which predominantly rely on land use data and remote sensing imagery, are often limited in their ability to capture dynamic changes in large river systems. This study introduces an integrated framework combining macro-level “Three-Zone Space” (urban, agricultural, ecological) theory with micro-level Point of Interest (POI) data to rapidly identify shoreline functions along the Yichang section of the Yangtze River. We further developed a multi-criteria evaluation system incorporating ecological, production, developmental, and risk constraints, utilizing a combined AHP-Entropy weight method to assess suitability. The results reveal a clear upstream-downstream gradient: ecological functions dominate upstream, while agricultural and urban functions increase downstream. POI data enabled refined classification into five functional types, revealing that ecological conservation shorelines are extensively distributed upstream, port and urban development shorelines concentrate in downstream nodal zones, and agricultural production shorelines are widespread yet exhibit a spatial mismatch with suitability scores. The comprehensive evaluation identified high-suitability units, primarily in downstream urban cores with superior development conditions and lower risks, whereas low-suitability units are constrained by high geological hazards and poor infrastructure. These findings provide a scientific basis for differentiated shoreline management strategies. The proposed framework offers a transferable approach for the sustainable planning of major river corridors, offering insights applicable to similar contexts. Full article

With the expansion of urban scale, forests and water areas have suffered a reduction. This reduction has resulted in insufficient carbon sequestration capacity. Strengthening environmental protection, especially enhancing the function of carbon sinks, is of great significance to the ecologically friendly development of the region. This study aims to clarify the distribution of regional ecological vulnerability and carbon storage capacity, and proposes a scientifically optimized ecological functional zoning plan. Specifically, we conducted a comprehensive assessment of land use and zoning in Huinan County by integrating ecological sensitivity with the InVEST model. First, based on the DPSIRM model, we evaluated the weights of ecological sensitivity influencing factors by combining the Analytic Hierarchy Process (AHP) and Entropy Weight Method (EWM). Using ArcGIS, we overlaid these factors with their respective weights to obtain the distribution of overall ecological sensitivity. Referencing relevant literature, we classified Huinan County’s ecological sensitivity into five categories. These categories include insensitive areas, low-sensitivity areas, medium-sensitivity areas, high-sensitivity areas, and extremely sensitive areas. Second, the carbon sequestration capacity of this region was visualized using the InVEST model to analyze Huinan County’s carbon storage potential. Finally, using the ArcGIS spatial overlay, we combined sensitivity levels with carbon storage zones. Based on varying degrees of ecological sensitivity and carbon storage distribution, we established five ecological conservation zones. These five ecological protection zones were: ecological buffer zone, restoration zone, stabilization zone, potential zone, and fragility zone. We implemented differentiated measures tailored to distinct regions, thereby advancing ecological restoration and sustainable development. This study provides a policy basis for ecological restoration in Huinan County and offers a replicable framework for ecological conservation in urbanized areas. Consequently, it holds practical significance for enhancing landscape multifunctionality and resilience. Full article

We investigate the fundamental trade-off between entropy and the Gini index within income distributions, employing a stochastic framework to expose deficiencies in conventional inequality metrics. Anchored in the principle of maximum entropy (ME), we position entropy as a key marker of societal robustness, while the Gini index, identical to the (second-order) K-spread coefficient, captures spread but neglects dynamics in distribution tails. We recommend supplanting Lorenz profiles with simpler graphs such as the odds and probability density functions, and a core set of numerical indicators (K-spread $K_2/\mu$, standardized entropy ${\Phi }_{\mu }$, and upper and lower tail indices, $\xi , \zeta$) for deeper diagnostics. This approach fuses ME into disparity evaluation, highlighting a path to harmonize fairness with structural endurance. Drawing from percentile records in the World Income Inequality Database from 1947 to 2023, we fit flexible models (Pareto–Burr–Feller, Dagum) and extract K-moments and tail indices. The results unveil a concave frontier: moderate Gini reductions have little effect on entropy, but aggressive equalization incurs steep stability costs. Country-level analyses (Argentina, Brazil, South Africa, Bulgaria) link entropy declines to political ruptures, positioning low entropy as a precursor to instability. On the other hand, analyses based on the core set of indicators for present-day geopolitical powers show that they are positioned in a high stability area. Full article