Search Results (683)

This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and incomplete moments, entropy, and the moment generating function, are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for the duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., power Zeghdoudi, power Ishita, power Prakaamy, and logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and the Kolmogorov–Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling. Full article

Accurate extraction of representative operating conditions is crucial for optimizing systems in renewable energy applications. This study proposes a novel framework that combines the Parzen window estimation method, ideal for nonparametric modeling of wind, solar, and load datasets, with a game theory-based time scale selection mechanism. The novelty of this work lies in integrating probabilistic density modeling with multi-indicator evaluation to derive realistic operational profiles. We first validate the superiority of the Parzen window approach over traditional Weibull and Beta distributions in estimating wind and solar probability density functions. In addition, we analyze the influence of key meteorological parameters such as wind direction, temperature, and solar irradiance on energy production. Using three evaluation metrics, the main result shows that a 3-day representative time scale offers optimal accuracy when determined through game theory methods. Validation with real-world data from Inner Mongolia confirms the robustness of the proposed method, yielding low errors in wind, solar, and load profiles. This study contributes a novel 3-day typical profile extraction method validated on real meteorological data, providing a data-driven foundation for optimizing energy storage systems under renewable uncertainty. This framework supports energy sustainability by ensuring realistic modeling under renewable intermittency. Full article

This study evaluates six parameter estimation methods for the generalized extreme value (GEV) distribution: maximum likelihood estimation (MLE), two probability-weighted moments (PWM-UE and PWM-PP), and three robust two-stage order statistics estimators (TSOS-ME, TSOS-LMS, and TSOS-LTS). Their performance was assessed using simulation experiments under varying tail behaviors, represented by three types of GEV distributions: Weibull (short-tailed), Gumbel (light-tailed), and Fréchet (heavy-tailed) distributions, based on the mean squared error (MSE) and mean absolute percentage error (MAPE). The results showed that TSOS-LTS consistently achieved the lowest MSE and MAPE, indicating high robustness and forecasting accuracy, particularly for short-tailed distributions. Notably, PWM-PP performed well for the light-tailed distribution, providing accurate and efficient estimates in this specific setting. For heavy-tailed distributions, TSOS-LTS exhibited superior estimation accuracy, while PWM-PP showed a better predictive performance in terms of MAPE. The methods were further applied to real-world monthly maximum PM2.5 data from three air quality stations in Bangkok. TSOS-LTS again demonstrated superior performance, especially at Thon Buri station. This research highlights the importance of tailoring estimation techniques to the distribution’s tail behavior and supports the use of robust approaches for modeling environmental extremes. Full article

Underground hydrogen storage (UHS) in geological formations offers a promising solution for large-scale energy buffering, but its long-term safety and mechanical stability remain concerns, particularly in fractured rock environments. This study develops a fully coupled thermo-mechanical model to investigate the cyclic response of a dual-cavern hydrogen storage system with polymer-based sealing layers. The model incorporates non-isothermal gas behavior, rock heterogeneity via a Weibull distribution, and fracture networks represented through stochastic geometry. Two operational scenarios, single-cavern and dual-cavern cycling, are simulated to evaluate stress evolution, displacement, and inter-cavity interaction under repeated pressurization. Results reveal that simultaneous operation of adjacent caverns amplifies tensile and compressive stress concentrations, especially in inter-cavity rock bridges (i.e., the intact rock zones separating adjacent caverns) and fracture-dense zones. Polymer sealing layers remain under compressive stress but exhibit increased residual deformation under cyclic loading. Contour analyses further show that fracture orientation and spatial distribution significantly influence stress redistribution and deformation localization. The findings highlight the importance of considering thermo-mechanical coupling and rock fracture mechanics in the design and operation of multicavity UHS systems. This modeling framework provides a robust tool for evaluating storage performance and informing safe deployment in complex geological environments. Full article

In this study, a new fibre combination for an interlayer hybrid fibre-reinforced polymer laminate was investigated to achieve pseudo-ductile behaviour in tensile tests. The chosen high-strain fibre for this purpose was S-Glass, and the low-strain fibre was flax. These materials were chosen because of their relatively low environmental impact compared to carbon/carbon and carbon/glass hybrids. An analytical model was used to find an ideal combination of the two materials. With that model, the expected stress–strain relation could also be predicted analytically. The modelling was based on preliminary tensile tests of the two basic components investigated in this research: unidirectional laminates reinforced with either flax fibres or S-Glass fibres. Hybrid specimens were then designed, produced in a heat-assisted pressing process, and subjected to tensile tests. The strain measurement was performed using distributed fibre optic sensing. Ultimately, it was possible to obtain repeatable pseudo-ductile stress–strain behaviour with the chosen hybrid when the specimens were subjected to quasi-static uniaxial tension in the direction of the fibres. The intended damage-mode, consisting of a controlled delamination at the flax-fibre/glass-fibre interface after the flax fibres failed, followed by a load transfer to the glass fibre layers, was successfully achieved. The pseudo-ductile strain averaged 0.52% with a standard deviation of 0.09%, and the average load reserve after delamination was 145.5 MPa with a standard deviation of 48.5 MPa. The integrated fibre optic sensors allowed us to monitor and verify the damage process with increasing strain and load. Finally, the analytical model was compared to the measurements and was partially modified by neglecting the Weibull strength distribution of the high-strain material. Full article

Italy strives to meet its renewable energy targets for 2030 and 2050, with photovoltaic (PV) technology playing a central role. However, the push for increased solar adoption, spurred by past incentive schemes such as “Conto Energia” and “Superbonus 110%”, raises long-term challenges related to PV waste management. In this study, we present a multi-scale approach to forecast End-of-Life (EoL) PV waste across Italy’s 20 regions, aiming to support national circular economy strategies. Historical installation data (2008–2024) were collected and combined with socio-economic and energy-related indicators to train a Backpropagation Neural Network (BPNN) for regional PV capacity forecasting up to 2050. Each model was optimised and validated using R² and RMSE metrics. The projections indicate that current trends fall short of meeting Italy’s decarbonisation targets. Subsequently, by applying a Weibull reliability function under two distinct scenarios (Early-loss and Regular-loss), we estimated the annual and regional distribution of PV panels reaching their EoL. This analysis provides spatially explicit insights into future PV waste flows, essential for planning regional recycling infrastructures and ensuring sustainable energy transitions. Full article

This study provides a comprehensive analysis of the fatigue cracking behavior of super martensitic stainless steel in air and water environments, highlighting the critical influence of environmental factors on its mechanical properties. By examining the distribution of fatigue test data, the Weibull three-parameter model was identified as the most accurate descriptor of fatigue life data in both environments. Key findings reveal that, in air, cracks predominantly propagate along the densest crystallographic planes, whereas, in water, corrosive media significantly accelerate crack initiation and propagation, reducing fatigue resistance, creating more tortuous crack paths, and inducing microvoids and secondary cracks at the crack tip. These corrosive effects adversely alter the material’s microstructure, profoundly impacting fatigue life and crack propagation rates. The insights gained from this research are crucial for understanding the performance of super martensitic stainless steel in aqueous environments, offering a reliable basis for its engineering applications and contributing to the development of more effective design and maintenance strategies. Full article

To develop cement-based composite materials with exceptional impact resistance, this study investigates the impact resistance performance of steel fiber- and glass fiber-reinforced specimens, as well as steel fiber and glass fiber textile-reinforced specimens, through drop weight impact tests. The results showed that the impact resistance of specimens increases with the number of glass fiber textile layers, glass fiber volume fractions, and glass fiber lengths, with 36GF1.5SF1.0 exhibitinh ultra-high impact resistance with a failure impact energy of 114 kJ. Compared to the specimens reinforced with glass textiles, the specimens with glass fiber showed better impact resistance at the same volume fraction. The failure mode of unreinforced specimens is divided into several pieces, while fiber-reinforced specimens have local punching shear failure at the impact site, maintaining better integrity. An impact damage evolution equation and life prediction model based on a two-parameter Weibull distribution are developed. The research results will provide a reference for the selection of fibers for engineering applications. Full article

This study focuses on estimating the unknown parameters and the reliability function of the inverted-Weibull distribution, using an improved adaptive progressive Type-II censoring scheme under a competing risks model. Both classical and Bayesian estimation approaches are explored to offer a thorough analysis. Under the classical approach, maximum likelihood estimators are obtained for the unknown parameters and the reliability function. Approximate confidence intervals are also constructed to assess the uncertainty in the estimates. From a Bayesian standpoint, symmetric Bayes estimates and highest posterior density credible intervals are computed using Markov Chain Monte Carlo sampling, assuming a symmetric squared error loss function. An extensive simulation study is carried out to assess how well the proposed methods perform under different experimental conditions, showing promising accuracy. To demonstrate the practical use of these methods, a real dataset is analyzed, consisting of the survival times of male mice aged 35 to 42 days after being exposed to 300 roentgens of X-ray radiation. The analysis demonstrated that the inverted Weibull distribution is well-suited for modeling the given dataset. Furthermore, the Bayesian estimation method, considering both point estimates and interval estimates, was found to be more effective than the classical approach in estimating the model parameters as well as the reliability function. Full article

Green roofs are increasingly recognized as effective Nature-Based Solutions (NBS) for urban stormwater management, contributing to sustainable and climate-resilient cities. The Soil Conservation Service Curve Number (SCS-CN) model is commonly used to simulate their hydrological performance due to its simplicity and low data requirements. However, the standard assumption of a fixed initial abstraction ratio (Ia/S = 0.2), long debated in hydrology, has been largely overlooked in green roof applications. This study investigates the variability of Ia/S and its impact on runoff simulation accuracy for a green roof under a humid subtropical climate. Event-based analysis across multiple storms revealed Ia/S values ranging from 0.01 to 0.62, with a calibrated optimal value of 0.17. This variability is primarily driven by the physical and biological characteristics of the green roof rather than short-term rainfall conditions. Using the fixed ratio introduced consistent biases in runoff estimation, while intermediate ratios (0.17–0.22) provided higher accuracy, with the optimal ratio yielding a median Curve Number (CN) of 89 and high model performance (NSE = 0.95). Additionally, CN values followed a positively skewed Weibull distribution, highlighting the value of probabilistic modeling. Though limited to one green roof design, the findings underscore the importance of site-specific parameter calibration to improve predictive reliability. By enhancing model accuracy, this research supports better design, evaluation, and management of green roofs, reinforcing their contribution to integrated urban water systems and global sustainability goals. Full article

The Rayleigh distribution is a continuous probability distribution that is inherently asymmetric and commonly used to model right-skewed data. It holds significant importance across a wide range of scientific and engineering disciplines and exhibits structural relationships with several other asymmetric probability distributions, for example, Weibull and exponential distribution. This research proposes techniques for establishing credible intervals and confidence intervals for the single mean of the zero-inflated two-parameter Rayleigh distribution. The study introduces methods such as the percentile bootstrap, generalized confidence interval, standard confidence interval, approximate normal using the delta method, Bayesian credible interval, and Bayesian highest posterior density. The effectiveness of the proposed methods is assessed by evaluating coverage probability and expected length through Monte Carlo simulations. The results indicate that the Bayesian highest posterior density method outperforms the other approaches. Finally, the study applies the proposed methods to construct confidence intervals for the single mean using real-world data on COVID-19 total deaths in Singapore during October 2022. Full article

For the last decade, social networking services (SNS), such as X, Facebook, and Instagram, have become mainstream media for advertising and marketing. In SNS marketing, word-of-mouth among users can spread posted advertising information, which is known as viral marketing. In this study, we first analyzed the time series of user reactions to Instagram posts to clarify the characteristics of user behavior. Second, we modeled these variations using statistical distributions to predict the information diffusion of future posts and to provide some insights into the factors that affect users’ reactions on Instagram using the estimated parameters of the modeling. Our results demonstrate that user reactions have a peak value immediately after posting and decrease drastically and exponentially as time elapses. In addition, modeling with the Weibull distribution is the most suitable for user reactions, and the estimated parameters help identify key factors that influence user reactions. Full article

This work proposes a novel extension for a new extended Weibull distribution. Some statistical properties of the proposed distribution are studied including quantile, moments, skewness, and kurtosis. The hazard rate function of the new distribution has certain elastic qualities, allowing it to take increasing, upside-down bathtub, and modified upside-down bathtub shapes commonly observed in medical contexts. Different methods of estimation are studied using complete data. Two real data sets from the medical field are analyzed to demonstrate that the proposed model has adaptability in practice. In comparison to some well-known distributions, the suggested distribution fits the tested data better based on both parametric and non-parametric statistical criteria. A simulation study is presented to compare the obtained estimates based on mean square error and average absolute bias. Full article

Bayesian methods have attracted increasing interest in the design and analysis of clinical trials. Many of these clinical trials investigate time-to-event endpoints. The Weibull distribution is often used in survival and reliability analysis to model time-to-event data. We propose a process to elicit information about the parameters of the Weibull distribution for pharmaceutical applications. Our method is based on an expert’s answers to questions about the median and upper quartile of the distribution. Using the elicited information, a joint prior is constructed for the median and upper quartile of the Weibull distribution, which induces a joint prior distribution on the shape and rate parameters of the Weibull. To illustrate, we apply our elicitation methodology to a pediatric clinical trial, where information is elicited from a subject-matter expert for the control arm. Full article

The remaining lifetime of the cable insulation is an important but hard topic for the industry and research groups as there are more and more cables nearing their designed life in China. However, it is hard to accurately and efficiently obtain the ageing characteristic parameters of cross-linked polyethylene (XLPE) cable insulation. This study systematically analyzes the evolution of the remaining insulation lifetime of XLPE cables under different ageing states using the step-stress method combined with the inverse power model (IPM) and a physical-driven model (Crine model). By comparing un-aged and accelerated-aged specimens, the step-stress breakdown tests were conducted to obtain the Weibull distribution characteristics of breakdown voltage and breakdown time. Experimental results demonstrate that the characteristic breakdown field strength and remaining lifetime of the specimens decrease significantly with prolonged ageing. The ageing parameter of the IPM was calculated. It is found that the ageing parameter of IPM increases with the ageing time. However, it can hardly link to the other properties or physic parameters of the material. The activation energy and electron acceleration distance of the Crine model were also calculated. It is found that ageing activation energy stays almost the same in samples with different ageing time, showing that it is a material intrinsic parameter that will not change with the ageing; the electron acceleration distance increases with the ageing time, it makes sense that the ageing process may break the molecule chain of XLPE and increase the size of the free volume. It shows that the Crine model can better fit the physic process of ageing in theory and mathematic, and the acceleration distance of the Crine model is a physical driven parameter that can greatly reflect the ageing degree of the cable insulation and be used as an indicator of the ageing states. Full article