ABSTRACT This study applies Multivariate Adaptive Regression Splines (MARS) and Generalized Additive Models (GAM) within a Peaks Over Threshold (POT) framework for regional flood frequency analysis (RFFA) in southeastern Australia using data from 145 catchments. Seven physiographic and meteorological variables were used as predictors, and flood quantiles were estimated via the Generalized Pareto distribution. Model performance was assessed using Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE) via Leave-One-Out Cross-Validation (LOOCV). Our results indicate that GAM consistently outperforms MARS, exhibiting lower error variability, narrower residual distributions, and superior generalizability, particularly in data-sparse inland catchments. GAM’s smooth function framework effectively captures non-linear hydrological relationships, while MARS shows greater prediction biases and higher variability. Across all return periods, the GAM model achieved median relative errors generally within ±10–15% and prediction ratios concentrated around unity, indicating unbiased and stable estimates.

A generally interesting question in metabolomics relates to circumstances in which the concentration of a particular metabolite is higher in those who do not have a disease compared to those who are more likely to. The question then arises as to what level of that metabolite has a particular statistical probability of being associated with avoiding the disease. A similar question relates to predicting the statistical longevity of individuals given the existing, typically S-shaped, survival distributions. The most appropriate method for predicting the tails of these distributions is an important part of Extreme Value Theory and is known as the Generalised Pareto distribution (GPD). The GPD has two free parameters once a 'threshold' has been set. We here apply it to a published study of the relationship between the concentration of ergothioneine in plasma and the likelihood of developing pre-eclampsia (PE). We first rehearse that the statistical distributions of ergothioneine concentrations in the women with pre-eclampsia and those without pre-eclampsia are indeed different. From the empirical dataset of individuals who experienced pre-eclampsia (whether early- or late-onset) we note that the 90th percentile falls at∼380ng.mL-1. This was also the value found to give the lowest value of the mean excess in a GPD analysis. We can then use the GPD to fit the high ergothioneine observations in PE cases. Using this approach, we found that the probability of observing ergothioneine concentrations above 650ng.mL-1 in PE cases is lower than one in 1,000. This compares very favourably with the normal incidence of PE, that is 2-7%.

Study region: Pakistan exhibits pronounced spatial and seasonal variability in rainfall patterns, with extreme precipitation posing major challenges for flood risk management, agriculture, and infrastructure planning. Accurate estimation of return levels remains difficult due to sampling variability, threshold selection, and the presence of zero-inflation associated with dry days. The present study analyzes daily precipitation data from 135 districts across Pakistan for the period 2001–2023, encompassing diverse climatic changes. Study focus: A zero-inflated Extended Generalized Pareto Distribution (ziEGPD) model is introduced to characterize the full precipitation spectrum, including dry days, within a regional modeling framework. Within the regional model setting, homogeneous regions based on upper-tail behavior were constructed using the Δ ˆ ratio method. To capture spatial variation in the region, the parameters of ziEGPD were modeled as functions of covariates using Generalized Additive Models (GAMs). The developed model was estimated through maximum-likelihood and Bayesian frameworks and evaluated via cross-validation using accuracy and robustness measures. New hydrological insights: Results indicate that the Bayesian GAM–ziEGPD model with covariates provides the highest accuracy and consistently outperforms the MLE-based approach across all seasons and clusters. This model is therefore adopted as the optimal framework for estimating regional quantiles across a range of return periods. Regional analysis further shows that the monsoon period exhibits the highest 100-year return levels, with intense rainfall concentrated in southern and southeastern Pakistan. • Comprehensive modeling of rainfall including zero values and extremes. • Integration of regional frequency analysis and spatial GAM framework. • MLE along with Bayesian inference for robust and accurate estimation. • Return levels for climate resilience and flood risk management.

Interdepartmental consultations are essential for managing complex inpatient care but are often inefficient. Hospital-wide, data-driven analyses are needed to guide process improvements, yet most existing studies have focused on single departments or specific diseases, leaving a gap in understanding hospital-level collaboration networks. Understanding these patterns is crucial for optimizing clinical workflows, reducing delays, and improving patient outcomes in large tertiary hospitals. To analyze the distribution and network characteristics of interdepartmental consultations across a large tertiary hospital, focusing on high-frequency collaboration pairs and their disease associations. This retrospective cohort study included all interdepartmental consultations for inpatients and emergency patients at Peking Union Medical College Hospital (Beijing, China) from January 1 to December 31, 2024. Secondary data were extracted from the Hospital Information System. In total, 102,858 valid consultations involving 42 clinical departments were analyzed. Outcome measures included consultation requests/receptions per department, per capita request intensity, and pairwise collaboration volume. High-frequency collaboration pairs were defined as those with an annual consultation volume ≥300. Descriptive statistics (medians, interquartile ranges) and proportions with 95% confidence intervals were used. Consultation activity exhibited marked concentration. The Emergency Department issued the most consultation requests (n=19,698, 19.15%), far exceeding the median departmental request volume of 1,899.5 (interquartile range (IQR): 1,359.5-3,759.25). Meanwhile, the Internal Medicine Consultation Service received the highest number of consultations (n=10,428, 10.14%), substantially above the median reception volume of 1,886.0 (IQR: 521.25-4,056.75) across departments. The per capita request intensity varied widely, with Critical Care Medicine highest (21.64) versus a hospital-wide average of 0.32. Collaboration demonstrated a strong Pareto distribution: the top 5.37% of department pairs (65 pairs) accounted for 42.02% (n=43,221) of the total 102,858 consultations. These high-volume pairs were predominantly disease-specific. Examples include: Endocrinology-Ophthalmology primarily for diabetic and thyroid eye disease (n=1,287, 1.25%); General Surgery-Otolaryngology mainly for preoperative thyroid airway assessment (n=1,225, 1.19%); General Surgery-Clinical Nutrition for perioperative support (n=1,032, 1.00%); Endocrinology-Clinical Nutrition for metabolic disease management (n=703, 0.68%); Orthopedics-Rehabilitation Medicine for postoperative rehabilitation (n=686, 0.67%); and Oncology Medical Center-Clinical Nutrition for cancer patient nutrition support (n=681, 0.66%) ; and Rheumatology Immunology-Ophthalmology primarily for immune-related eye disease (n=678, 0.66%). Recurring clinical scenarios generated these stable, predictable consultation pathways. This study provides a novel, hospital‑wide, network‑based mapping of interdepartmental consultations using real‑world data. Unlike prior work limited to single departments or diseases, it reveals that collaboration is concentrated, Pareto‑like, and disease‑driven. The identification of stable, disease-specific consultation pairs offers a data-driven framework for understanding multidisciplinary collaboration. These findings offer a data‑driven framework for understanding multidisciplinary collaboration as a networked system. In practice, administrators and clinicians can use this evidence to prioritize resources, design standardized multidisciplinary team pathways, and implement spatial or digital interventions to reduce delays and improve patient flow and outcomes.

Traditional tsunami prediction relies on binary classification using machine learning, which lacks physical interpretability and extrapolation capability. This study introduces a novel probabilistic framework for tsunami genesis characterization using Multivariate Extreme Value Theory (MEVT) and Archimedean copula dependence modeling. We analyse an expanded dataset of 1,002 significant earthquakes [Formula: see text] drawn from the USGS/NEIC catalog spanning 1976-2022 and supplemented with moment-magnitude conversions following Scordilis (2006), yielding 391 confirmed tsunami events (39.0%). Generalized Extreme Value and Generalized Pareto distributions are fitted to the marginal parameters; negative shape parameters [Formula: see text] confirm light-tailed magnitude behavior consistent with tectonic fault-dimension constraints. Among three competing Archimedean families, the Clayton copula provides the best fit for magnitude-significance dependence ([Formula: see text] = 2.367, AIC = -725.17, AIC weight = 98.4%) with strong lower tail dependence ([Formula: see text] = 0.746, Kendall’s [Formula: see text] = 0.542), while magnitude-depth and depth-significance pairs display near-independence best described by the Frank copula. These bivariate structures are embedded in a trivariate nested Gumbel-Hougaard copula for complete joint modelling. A closed-form limit state equation is derived via the First Order Reliability Method (FORM): [Formula: see text], where inverse depth contributes 26.4% of total variance. Cross-validation yields AUC = 0.607 ± 0.038, Brier score = 0.233, and ECE = 0.031. This framework provides engineers with a physics-based, directly calculable tool for probabilistic tsunami hazard assessment (PTHA), bridging structural reliability theory with seismological practice.

In this paper, the authors propose a novel method for analyzing random sequences that exhibit or lack a clearly expressed trend. The idea is based on calculating the roots defined by the intersection of the horizontal line with the given sequence. The final Roots Distribution (RD) curve formally resembles conventional statistical distributions or histograms; however, it has one key difference: the number of roots is obtained using a distinct algorithm compared to the conventional method for calculating histograms. The Generalized Pareto Distribution (GPD), incorporating three power-law exponents, can be used to fit the obtained branches of the RD. It is possible for complex-conjugated exponents to appear during this fitting procedure. When this method is applied to sequences with a trend, the RD transforms into a specific spectrum that features many peaks. This proposed methodology is applied to the detection and quantitative description of extremely weak gravitational wave (GW) signals, such as those emitted by Extreme Mass Ratio Inspirals (EMRIs). This RD enables the quantitative description of the GW signal and the noise that completely obscures it. Furthermore, one can subtract the expected GW (obtained a priori or analytically from the detected noise) and transform it to the RD of the second type as a specific fingerprint for its certain detection.

Electricity networks are vulnerable to weather damage, with severe events often leading to faults and power outages. Timely forecasts of fault occurrences, ranging from nowcasts to several days ahead, can enhance preparedness, support faster response, and reduce outage durations. To be operationally useful, such forecasts must quantify uncertainty, enabling risk-informed resource allocation. We present a novel probabilistic framework for forecasting fault counts that captures typical and extreme events. Non-extreme faults are modeled linearly interpolating estimates from multiple additive quantile regressions, while extreme events are described through a discrete generalized Pareto distribution. To incorporate the impact of weather fluctuations, we use ensemble numerical weather predictions, which help to quantify uncertainty in the forecasts. This approach is designed to provide reliable fault predictions up to four days ahead. We evaluate the model through numerical experiments and apply it to historical fault data from two electricity distribution networks in Great Britain. The resulting forecasts demonstrate substantial improvements over business-as-usual and alternative modeling approaches. A practitioner trial conducted with Scottish Power Energy Networks from October 2024 to March 2025 further demonstrates the operational value of the forecasts. Engineers found them sufficiently reliable to inform decision-making, offering benefits to both network operators and electricity consumers.

Two monitoring schemes for the Pareto distribution with known and unknown parameters

When is an Exponentiated Pareto distribution infinitely divisible?

In this paper, we investigate the problem of estimating the mean of the length-biased (LB) Pareto distribution. We highlight the limitations of the existing fixed-sample statistical methodologies to tackle the LB data, which leads us to introduce a robust sequential interval estimation methodology for the proposed problem. The sequential rule ensures that the estimated mean is captured within a pre-specified accuracy with high confidence. We prove some interesting properties that exhibit the achieved optimality. To demonstrate the robustness and versatility of our approach, we delve into two captivating case studies, namely (i) the net worth of the Indian Billionaires, and (ii) the fastest winning times of male marathon runners in the Olympics. These cases highlight the practical significance of the proposed methodology in real-world scenarios. For the aforementioned datasets, we establish that the LB Pareto distribution is a much better model in comparison to some other existing models.

On conditional m-spacings and their stochastic properties under surviving series systems

Eyelid tumors represent a diverse group of ocular adnexal pathologies, ranging from innocuous benign lesions to highly aggressive malignant forms. Recognizing the demographic and clinical determinants associated with these tumors is crucial for improving diagnostic accuracy and selecting appropriate surgical strategies. The present study evaluates the demographic profile, histopathological spectrum, anatomical distribution, and surgical approaches for eyelid tumors managed at a tertiary ophthalmology center. A retrospective analysis was performed on 194 patients who underwent excision or biopsy of eyelid lesions between January 2020 and October 2025. Collected variables included patient age, sex, occupation, tumor laterality and anatomical site, histopathological diagnosis, surgical technique, anesthesia type, and biological behavior. Both descriptive and analytical statistical methods were applied, supplemented by visual tools such as kernel density plots, Pareto distribution charts, and malignancy risk mapping. Among the 194 cases reviewed, 97 were male and 97 females, with a mean age of 47.8 years (2–91 years). Benign tumors accounted for 128 patients (66%), whereas malignant lesions were identified in 66 individuals (34%). Chalazion, intradermal nevus, and verruca vulgaris were the most common benign diagnoses. Basal cell carcinoma was the most common malignant tumor, followed by squamous cell carcinoma and sebaceous carcinoma. Malignant tumors occurred in significantly older patients (p<0.01). A greater incidence of malignancy was observed in tumors located on the lower eyelid. The majority of excisions (88.1%) were performed under local anesthesia. Eyelid tumors in our cohort demonstrated a predominance of benign lesions, though malignant tumors represented a substantial minority. Age and anatomical location were strong predictors of malignancy. Our findings underscore the importance of regional epidemiologic data in guiding clinical suspicion and surgical decision-making.

Quantile estimation in frequency analysis of hydrologic variables for the generalized Pareto distribution: An approach based on specially formulated pivotal quantities

Gaseous emissions from coal combustion during electricity generation continue to be a challenge in South Africa. To meet the regulatory limits, it is crucial to understand the statistical distribution of such emissions from the power generating plants. The current paper characterises the nitrogen dioxide (NO2) emissions from Eskom’s Majuba coal-fired power station by making use of the quantile–quantile (QQ) plots and derivative plots of three statistical parent distributions, namely, the Weibull, Lognormal, and Pareto distributions. These distributions are fitted and compared according to their tail heaviness as they cater for data that may have tails lighter or heavier than that of the Exponential distribution. Of the three distributions evaluated here, the Lognormal gave the best fit for the full body of the data according to the QQ and derivative plots, and the goodness-of-fit tools (bootstrap Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Akaike Information Criterion (AIC), Schwarz’s Bayesian Information Criterion (BIC), and the BIC-corrected Vuong test for non-nested distributions). The Lognormal distribution also gave the best fit for the overall upper tail, while at the very top six largest NO2 emission observations in the upper tail, a Pareto-type tail was observed. The practical implication of a heavy tail like the Pareto is that it models more frequent larger sized NO2 emissions compared to lighter tails like the Weibull and Lognormal tails. The methods used in this study give a framework on how emissions of NO2 from a coal-fired power station can be modelled using statistical parent distributions whilst also taking into account the distribution of the data in the tails which is mostly ignored when fitting statistical parent distributions. Understanding the distribution of the upper tail is very important since higher and rare emissions are of the most concern and are dangerous to human health and the environment.

To determine the effective temperatures for railway concrete bridges in the Plateau region of China, this study collects meteorological data from 23 national reference stations in Xizang between 1979 and 2018. A 40-year numerical simulation of the temperature field based on these records is conducted to generate statistical samples of effective temperatures. Using the generalized Pareto distribution (GPD) model, representative values of effective temperatures corresponding to a 100-year return period are calculated, and spatial interpolation is applied to produce isotherm maps of the effective temperatures. The results indicate that the effective temperatures in most parts of Xizang exceed the values specified in current Chinese design standards, suggesting a potential underestimation of thermal effects. Moreover, the effective temperatures of concrete bridges show high sensitivity to local climatic and environmental conditions, with regional variations reaching up to 16°C for maximum and 18°C for minimum values. These findings show the necessity of incorporating local climate conditions into the detailed design of plateau bridges. The isotherm maps developed in this study provide an intuitive visualization of extreme temperature distribution with enhanced geographical resolution, offering a valuable reference for refining temperature-related provisions in Chinese bridge design codes.

Extreme sea levels along the Mexican coasts pose an increasing risk to coastal infrastructure and communities, particularly under the combined influence of tropical cyclones and ongoing sea-level rise. This study analyzes tide-gauge records from the Mexican Pacific and Gulf of Mexico–Caribbean coasts to characterize the statistical behavior and seasonal modulation of extreme sea-level residuals. Astronomical tides were removed through harmonic analysis to isolate the meteorological residual associated with storm-driven processes. Extreme events were evaluated using complementary extreme-value frameworks, including Generalized Extreme Value (GEV) distributions applied to monthly maxima and a Peaks-Over-Threshold (POT) approach applied to the continuous residual series with temporal declustering and Generalized Pareto Distribution (GPD) fitting. While both approaches consistently capture regional patterns, the POT–GPD framework is adopted as the primary basis for return-level estimation due to its explicit representation of event-scale extremes. The results reveal marked regional variability. Pacific stations exhibit bounded or near-Gumbel behavior (ξ ≈ −0.30 to −0.02) and a strong seasonal concentration of extremes during the tropical cyclone season. In contrast, Gulf of Mexico–Caribbean stations display higher absolute extremes and a broader seasonal footprint, with Veracruz showing a tendency toward heavier-tailed behavior (ξ ≈ 0.13). Return levels for a 25-year return period range from approximately 0.85–0.95 m in the Pacific to about 1.7 m in Veracruz. Longer return periods (e.g., 100 years) exceed 2.2 m in Veracruz but are associated with substantial uncertainty due to record-length limitations. The analysis of ENSO variability indicates that ENSO acts primarily as a secondary modulator of background sea-level variability rather than a deterministic driver of extreme events, with the largest anomalies typically associated with tropical cyclone activity. Overall, the results demonstrate that extreme sea levels along the Mexican coasts are governed by region-specific forcing and tail behavior requiring localized extreme-value modeling strategies. The proposed framework provides a robust and reproducible baseline for coastal hazard assessment and supports the integration of sea-level rise into future risk and design analyses.

ABSTRACT Effective CAD data management is crucial for engineering design productivity, yet challenges in file organization, interoperability, and workflow efficiency persist. While prior studies addressed technical aspects of PDM systems and file formats, the interaction between technical solutions and human factors remains underexplored. This study bridges this gap by examining the combined impact of structured training and file format standardization on CAD workflow performance, evaluating 120 professionals in control and experimental groups and assessing improvements in archiving, project categorization, security practices, and employing a QFD analysis to assess 35 CAD formats through expert testing, establishing performance hierarchies for manufacturing, AEC, and media applications. Key findings revealed a significant improvement after training, with large effect sizes across variables, reflecting meaningful enhancements in consistency, file retrieval, storage management, and security practices. Furthermore, based on expert ratings and normalized weighting, this study revealed a Pareto distribution where dwg, dxf, IGES, STEP, STL, and SVG collectively accounted for the majority of the weighted TIR, guiding format selection for specific industry applications. Manufacturing workflows benefited most from IGES and STEP formats, whereas AEC collaboration prioritized DWG and DXF. Media and entertainment pipelines relied on SVG, OBJ, and mb/.ma formats for texture and animation efficiency. These results show that human competency and technical interoperability in CAD data management must be developed together. By highlighting practical improvements in human–technical interactions and providing data-driven format hierarchies, the study offers actionable insights for workflow optimization, cross-platform collaboration, and adoption of interoperable CAD formats in professional settings, enhancing efficiency and standardized data management.

Tail risk assessment is crucial in financial markets, especially for commodities such as Brent crude oil, where extreme price fluctuations pose a risk for investors and policymakers. Risk models such as generalised autoregressive conditional heteroscedasticity (GARCH) often struggle to capture these extreme movements accurately, leading to potential underestimation of risk exposure. To solve this problem, we combine an alpha-recurrent neural network with a generalised Pareto distribution to better predict extreme price changes and improve tail risk estimation. Our findings demonstrate that this approach effectively captures downside risk, with backtesting results yielding high p-values, confirming its statistical reliability. The results from the shape parameter reveal that losses in crude oil markets are significantly riskier than gains, highlighting the asymmetric nature of price movements. Risk estimates indicate that the model provides robust assessments for both long- and short-term trading positions, making it a valuable tool for risk management. Nevertheless, these results have broader implications for financial risk modelling, particularly in commodity markets, where macroeconomic and geopolitical factors influence price volatility. Future work should focus on expanding the data set, enhancing computational efficiency and adding external risk factors such as liquidity constraints and regulatory shifts. Better calibration methods and the ability to adjust in real-time can make predictions more accurate, helping risk assessment models stay useful in changing market conditions.

Extreme heat events pose increasing risks to public health, energy systems, and urban sustainability, particularly in rapidly urbanizing regions of sub Saharan Africa.This study applies Extreme Value Theory (EVT) to model daily maximum temperature extremes for Lagos, Abuja, and Kano, Nigeria, using satellite derived data spanning 1981 to 2023.A Peaks Over Threshold (POT) framework is adopted to extract extreme temperature exceedances.The classical Generalized Pareto Distribution (GPD), which arises as the asymptotic limit model under EVT, is compared with the recently proposed Lindley Exponentiated Gumbel (LEG) distribution, introduced as a flexible parametric alternative for empirical tail modeling.Model parameters are estimated via maximum likelihood, and uncertainty is quantified using nonparametric bootstrap resampling.Model performance is evaluated using Akaike and Bayesian Information Criteria alongside graphical diagnostics.Results reveal pronounced spatial heterogeneity in heat extremes, with Kano exhibiting the most intense extremes and Lagos the least.While GPD shape parameters are negative across all cities, indicating physically bounded temperature tails, the LEG distribution consistently provides superior statistical fit, particularly in the upper tail.Although return level estimates from both models are numerically similar, the LEG model demonstrates improved tail alignment and greater robustness for risk assessment over long return periods.These findings highlight the value of flexible tail models for climate risk analysis in regions where classical EVT assumptions may be restrictive.

This article uses upper record values to estimate the stress-strength reliability parameter, defined as $$\dddot \delta = P(Z < T).$$ We assume that both strength (T) and stress (Z) are independent random variables that follow the inverted exponentiated Pareto distribution with a common second shape parameter. The maximum likelihood and Bayesian estimators of $$\dddot \delta$$are obtained. Using informative and non-informative priors, the Bayesian estimators are obtained under symmetric and asymmetric loss functions. Two bootstrap-type confidence intervals and highest posterior credible intervals are constructed. Gibbs and Metropolis-Hasting samplers are used to generate Bayesian estimates of reliability $$\dddot \delta$$ based on the suggested loss functions. To investigate the behavior of suggested approaches, extensive simulation studies are carried out using some accuracy measures. Simulation experiment findings validated the consistency of the Bayesian and non-Bayesian estimates of $$\dddot \delta .$$ According to specific metrics, Bayesian estimates under symmetric loss function showed more precision than those under asymmetric loss functions. The lengths of credible intervals for Bayesian estimates are less than the bootstrap confidence intervals for different record numbers. The bootstrap-p confidence intervals give more accurate outcomes than bootstrap-t in most cases. The analysis employs two representative datasets. The first includes the timing of goals scored in the final rounds of the European Champions League over two consecutive seasons. The second dataset contains monthly observations of sulfur dioxide concentration in Long Beach, California, spanning the years 1956 to 1974.