Search Results (568)

We present a new single-parameter bivariate copula, called the Stingray, that is dedicated to representing negative dependence, and it nests the Independence copula. The Stingray copula is generated in a relatively novel way; it has a simple form and is always defined over the full support, unlike many copulas that model negative dependence. We provide visualizations of the copula, derive several dependence properties, and compute basic concordance measures. We compare it with other copulas and joint distributions with respect to the extent of dependence it can capture, and we find that the Stingray copula outperforms most of them while remaining competitive with well-known, widely used copulas such as the Gaussian and Frank copulas. Moreover, we show, through simulation, that the dependence structure it represents cannot be fully captured by these copulas, as it is asymmetric. We also show how the non-parametric Spearman’s rho measure of concordance can be used to formally test the hypothesis of statistical independence. As an illustration, we apply it to a financial data sample from the building construction sector in order to model the negative relationship between the level of capital employed and its gross rate of return. Full article

Copulas are a useful tool to generate bivariate distributions from the univariate marginals. This method is also useful to generate bivariate families of distributions. In this paper, a new copula has been proposed. Some useful properties of the proposed copula have been studied, including the conditional copula. Various dependence measures for the proposed copula have been obtained. A multivariate extension of the proposed copula is also suggested. The proposed copula has been used to obtain a new bivariate family of distributions. Some useful properties of the obtained bivariate family are studied, which include conditional distributions, joint and conditional moments, joint reliability and hazard rate functions, parameter estimation, etc. A specific member of the proposed family has also been discussed. The proposed bivariate distribution has been used to model the energy sector data of the Kingdom of Saudi Arabia. Full article

Coastal lakes are highly vulnerable transitional systems in which sedimentological processes and benthic ecological conditions jointly control contaminant accumulation and preservation, particularly in densely urbanized settings. A robust understanding of the physical and ecological characteristics of bottom sediments is therefore essential for the correct interpretation of contaminant distributions, including those of potentially toxic metals. In this study, an integrated sedimentological–ecological approach was applied to Lake Ganzirri, a Mediterranean shallow coastal lake located in northeastern Sicily (Italy), where recent investigations have identified localized heavy metal anomalies in surface sediments. Sediment texture, petrographic and mineralogical composition, malacofaunal assemblages, and lake-floor morpho-bathymetry were systematically analysed using grain-size statistics, faunistic determinations, GIS-based spatial mapping, and bivariate and multivariate statistical methods. The modern lake bottom is dominated by bioclastic quartzo-lithic sands with low fine-grained fractions and variable but locally high contents of calcareous skeletal remains, mainly derived from molluscs. Sediments are texturally heterogeneous, consisting predominantly of coarse-grained sands with lenses of very coarse sand, along with gravel and subordinate medium-grained sands. Both sedimentological features and malacofaunal death assemblages indicate deposition under open-lagoon conditions characterized by brackish waters and relatively high hydrodynamic energy. Spatial comparison between sedimentological–ecological parameters and previously published heavy metal distributions reveals no significant correlations with metal hotspots. The generally low metal concentrations, mostly below regulatory threshold values, are interpreted as being favoured by the high permeability and mobility of coarse sediments and by energetic hydrodynamic conditions limiting fine-particle accumulation. Overall, the integration of sedimentological and ecological data provides a robust framework for interpreting contaminant patterns and offers valuable insights for the environmental assessment and management of vulnerable coastal lake systems, as well as for the understanding of modern lagoonal sedimentary processes. Full article

This paper investigates the planning problem of AC-integrated wind–photovoltaic–hydro–storage (WPHS) bundled transmission systems. To effectively capture the uncertainty and interdependence in renewable power outputs, a Copula-enhanced distributionally robust optimization (DRO) framework is developed, enabling a unified treatment of stochastic and correlated renewable generation within the system planning process. First, a location and capacity planning model based on DRO for WPHS generation bases is formulated, in which a composite-norm ambiguity set is constructed to describe the uncertainty of renewable resources. Second, the Copula function is employed to characterize the nonlinear dependence structure between wind and photovoltaic (PV) power outputs, providing representative scenarios and initial probability distribution (PD) support for the construction of a bivariate ambiguity set that embeds coupling information. The resulting optimization problem is solved using the column and constraint generation (C&CG) algorithm. In addition, an evaluation metric termed the transmission corridor utilization rate (TCUR) is proposed to quantitatively assess the efficiency of external AC transmission planning schemes, offering a new perspective for the evaluation of regional power transmission strategies. Finally, simulation results validate that the proposed model achieves superior performance in terms of system economic efficiency and TCUR. Full article

Time series analysis is crucial for modeling and forecasting diverse real-world phenomena. Traditional models typically assume continuous-valued data; however, many applications involve integer-valued series, often including negative integers. This paper introduces an approach that combines copula theory with the bivariate Skellam distribution to handle such integer-valued data effectively. Copulas are widely recognized for capturing complex dependencies among variables. By integrating copulas, our proposed method respects integer constraints while modeling positive, negative, and temporal dependencies accurately. Through simulation and an empirical study on a real-life example, we demonstrate that our class of models performs well. This approach has broad applicability in areas such as finance, epidemiology, and environmental science, where modeling series with integer values, both positive and negative, is essential. Full article

Promoting synergistic economic–resource–environmental development in resource-based cities (RBCs) is a fundamental requirement for ensuring national energy security and advancing regional sustainable and coordinated development. This study innovatively proposes the theoretical framework of “green transformation resilience (GTR)” based on evolutionary resilience theory, and then empirically explores the GTR of 114 RBCs in China from the perspective of urban development stages using multiple data models. The findings indicate that the GTR demonstrated an overall upward trend, though it remained at a consistently low level. Regenerative RBCs exhibited the highest GTR levels. GTR exhibits an uneven spatial distribution, primarily caused by super-variation density. The factor detection results indicate that factors such as government intervention, income level, and human capital have strong explanatory power for the spatial variation of GTR. Interaction analysis confirmed the significant nonlinear enhancement or bivariate enhancement of all pairs of factors. This study provides a basis for the differentiated development paths of GTR in China’s RBCs. Moreover, through factor interaction testing, it also offers guidance on policy combinations and prioritization for RBCs in different development stages. Full article

This study investigates the coupled relationship between groundwater chemistry, lithology, and structural features in the dry zone of Netiyagama, Sri Lanka, within a fractured crystalline basement. Groundwater chemistry fundamentally reflects geological conditions determined by rock-water interactions, we hypothesized that the specific spatial patterns of groundwater chemistry in heterogeneous fractured systems are distinctly controlled by integrated effects of lithological variations, structurally driven flow pathways, aquifer stratification, and geochemical processes, including cation exchange and mineral-specific weathering. To test this, we integrated hydrogeochemical signatures with mapped hydrogeological data and applied multi-stage multivariate analyses, including Piper diagrams, Hierarchical Cluster Analysis (HCA), and Principal Component Analysis (PCA), and various bivariate plots. Piper diagrams identified five distinct hydrochemical facies, but these did not correlate directly with specific rock types, highlighting the limitations of traditional methods in heterogeneous settings. Employing a multi-stage multivariate analysis, we identified seven clusters (C1–C7) that exhibited unique spatial distributions across different rock types and provided a more refined classification of groundwater chemistries. These clusters align with a three-unit aquifer framework (shallow weathered zone, intermittent fracture zone at ~80–100 m MSL, and deeper persistent fractures) controlled by a regional syncline and lineaments. Further analysis through bivariate diagrams revealed insights into dominant weathering processes, cation-exchange mechanisms, and groundwater residence times across the identified clusters. Recharge-type clusters (C1, C2, C5) reflect plagioclase-dominated weathering and short flow paths; transitional clusters (C3, C7) show mixed sources and increasing exchange; evolved clusters (C4, C6) exhibit higher mineralization and longer residence. Overall, the integrated workflow (facies plots + PCA/HCA + bivariate/process diagrams) constrains aquifer dynamics, recharge pathways, and flow-path evolution without additional drilling, and provides practical guidance for well siting and treatment. Full article

Blue–green spaces are essential for mitigating urban heat islands. The matching between their supply and demand affects the fairness and effectiveness of urban cooling facilities. This study focuses on the third ring area of Urumqi, Xinjiang, China. Cooling supply indicators and cooling demand indicators for blue–green spaces are established. Using coupling coordination and bivariate spatial autocorrelation models, it evaluates the cooling supply-demand relationship during 2010–2020. Results show that: (1) There is a “suburban cold sources dominated, urban supply turned positive” pattern in the cooling supply of Urumqi’s blue–green spaces. (2) Cooling demand has a significant “dual-core spatial separation”. The physical demands are concentrated in the high-temperature patches around the city, while the social demands are mainly distributed in the core area of the urban district. (3) There is a severe supply–demand spatial mismatch, with extremely low coupling coordination. The core issue is that high-supply cropland cold sources are far from the high-social-demand urban area. This study provides an important scientific basis for formulating effective cooling strategies for oasis cities through the analysis of the supply and demand matching of blue and green space. It uniquely helps safeguard ecological security and residents’ health in arid-zone cities. Full article

This paper introduces a novel bivariate distribution, referred to as the Bivariate Burr XII Inverse Weibull (BBXII-IW) distribution, constructed via the Marshall–Olkin approach from the univariate Burr XII Inverse Weibull (BXII-IW) distribution. The proposed BBXII-IW model provides a flexible framework for modeling dependent bivariate data, including competing risk scenarios. The key statistical properties of the distribution are derived, and parameter estimation is conducted using the maximum likelihood method. The model’s performance is evaluated using two types of real-world datasets: (1) bivariate data and (2) dependent competing risk data related to diabetic retinopathy. The results demonstrate that the BBXII-IW distribution offers an improved fit compared to existing models, highlighting its flexibility and practical relevance in modeling complex dependent structures. Full article

Understanding the ecological processes that shape spatial patterns across different growth stages is crucial for revealing the mechanisms of species coexistence and community dynamics. This study investigates the spatial patterns and associations between the regeneration layer and the overstory layer in Quercus variabilis forests in northern China. Using spatial point pattern analysis, we analyzed the distribution of 2761 seedlings and 449 adult trees across twelve 20 × 20 m plots. Our results revealed a consistent pattern where seedlings exhibited significant spatial aggregation, best fitted by a simple Thomas process with an average cluster radius of 3.89 m calculated across all plots, while adult trees displayed a complete spatial random distribution. A marked reduction in local density from seedlings to adults, indicated by a self-thinning index greater than 1 in most plots, provided evidence for density-dependent mortality during stand development. However, bivariate analysis detected no significant spatial association or mark correlation between adult trees and seedlings in most plots, suggesting limited interaction between these layers after initial seedling establishment. These findings demonstrate a clear transition from clustered regeneration to randomly distributed adults, which is consistent with the potential roles of dispersal limitation, habitat filtering and competition processes, with implications for the management and conservation of temperate Quercus forest ecosystems. Full article

This paper investigates the concomitants of order statistics from the bivariate generalized linear exponential (BGLE) distribution. We obtain the probability density function of a single concomitant and the joint probability density function of two concomitants of order statistics from the BGLE distribution. In addition, expressions for the single and product moments of concomitants of order statistics are derived. Furthermore, we find the best linear unbiased estimator of a scale parameter related to a study variable using various ranked set sampling techniques. Finally, we apply the findings to a real-life dataset. Full article

Local Interpretable Model-agnostic Explanations (LIME) is a widely used technique for interpreting individual predictions of complex “black-box” models by fitting a simple surrogate model to synthetic perturbations of the input. However, its standard perturbation strategy of sampling features independently from a Gaussian distribution often generates unrealistic samples and neglects inter-feature dependencies. This can lead to low local fidelity (poor approximation of the model’s behavior) and unstable explanations across different runs. This paper presents CoLIME, which is a copula-based perturbation generation framework for LIME, designed to capture the underlying data distribution and inter-feature dependencies more accurately. The framework employs bivariate (2D) copula models to jointly sample correlated features while fitting suitable marginal distributions for individual features. Furthermore, perturbation localization strategies were implemented, restricting perturbations to a defined local radius and maintaining specific property values to ensure that the synthesized samples remain representative of the actual local environment. The proposed approach was evaluated on a network intrusion detection dataset, comparing the fidelity and stability of LIME under Gaussian versus copula-based perturbations, using Ridge regression as the surrogate explainer. Empirically, for the most dependent feature pairs, CoLIME increases mean surrogate fidelity by 21.84–50.31% on the merged CIC-IDS2017/2018 dataset and by 29.28–60.24% on the UNSW-NB15 dataset. Stability is similarly improved, with mean Jaccard similarity gains of 3.78–5.45% and 1.95–2.12%, respectively. These improvements demonstrate that dependency-preserving perturbations provide a significantly more reliable foundation for explaining complex network intrusion detection models. Full article

Intangible cultural heritage (ICH) is deeply embedded in everyday social life, yet its officially recognized spatial distribution reflects both the independent influences of cultural traditions, development trajectories, and governance practices, and the complex interactions among them. Focusing on 494 national-level ICH items across ten categories in Jiangsu(J), Zhejiang(Z), and Shanghai(H), this study adopts a social-geographical perspective to examine both the spatio-temporal evolution and the driving mechanisms of ICH recognition in one of China’s most developed regions. After rigorous verification of point-based ICH locations, we combine kernel density estimation and the average nearest neighbor index to trace changes across five batches of national designation, and then employ the univariate and interaction detectors of the Geodetector model to assess the effects of 28 natural, socioeconomic, and cultural-institutional variables. The results show, first, that ICH exhibits significant clustering along river corridors and historical cultural belts, with a persistent high-density core in the Shanghai–southern Jiangsu–northern Zhejiang zone and a clear shift over time from highly concentrated to more dispersed and territorially balanced recognition. Second, human-environment factors—especially factors such as urban and rural income and consumption; residents’ education and cultural expenditures; and public education and cultural facilities—have far greater explanatory power than natural conditions, while different ICH categories embed distinctively in urban and rural socio-economic contexts. Third, bivariate interactions reveal that natural and macroeconomic “background” variables are strongly amplified when combined with demographic and cultural factors, whereas interactions among strong human variables show bivariate enhancement with diminishing marginal returns. In summary, these findings enrich international debates on the geography of ICH by clarifying how recognition processes align with regional development and social equity agendas, and they provide a quantitative basis for category-sensitive, place-based strategies that coordinate income policies, public cultural services, and the joint safeguarding of tangible and intangible heritage in both urban renewal and rural revitalization planning. Full article

This paper introduces the bivariate bounded Gompertz–log-logistic (BBGLL) distribution, a bounded bivariate lifetime model built by coupling two bounded Gompertz–log-logistic marginals through a Clayton copula with an independent dependence parameter. The proposed model effectively describes positively dependent lifetimes within finite support and accommodates increasing, decreasing, and bathtub-shaped hazard rates. Analytical expressions for the survival functions, hazard rate functions, and joint moments are derived, while measures of association such as Kendall’s tau, Spearman’s rho, and tail-dependence coefficients characterize the dependence structure. Parameters are estimated via maximum likelihood, inference functions for margins (IFM), and semi-parametric methods, with performance assessed through Monte Carlo simulations. A real-life data application illustrates the practical relevance of the model, showing that the BBGLL distribution achieves a superior goodness-of-fit relative to existing bivariate alternatives, highlighting its practical usefulness. Full article

Historical irrigation districts (HIDs) are integrated systems of natural and cultural assets, with cultivated land providing critical functions such as food security, environmental conservation, and cultural inheritance. This study presents a research framework for evaluating multifunctional potential, performance, and geographical matching along the “potential-performance” dimensions using analytical tools such as SPSS26.0, ArcGIS pro3.5.2, GeoDa1.22, InVEST3.13, and bivariate spatial autocorrelation. We use Mulanbei HID in China as a case study because of its thousand-year irrigation history and unique location at the intersection of coastal urban and rural communities. The results show the following: (1) In the Mulanbei HID, multifunctional cultivated land exhibits functions in the following order: producing functions, ecological functions, landscape–cultural functions, and social functions. The production function has a homogenous distribution characterized by high values. The ecological function, on the other hand, is distinguished by high-value clusters that decrease significantly as building land approaches its periphery. Social and landscape–cultural roles continue to be undervalued, with high-value places isolated on metropolitan margins. (2) In terms of matching multifunctional potential and performance, in the High-Potential–High-Performance cluster, production and ecological functions account for 19% and 20%, respectively, while in the High-Potential–Low-Performance cluster, social and landscape–cultural functions account for 33% and 27%. The Low-Potential–Low-Performance cluster has 4% production, 4% ecological, 10% social, and 13% landscape–cultural functions, but all four functions are less than 4% in the Low-Potential–High-Performance cluster. These findings provide a scientific foundation for improving cultivated land zoning and governance with a focus on heritage protection. Full article