Search Results (67)

Environmental condition assessment is essential for the design of floating wind turbines, particularly when determining design sea states that balance safety and economy. The environmental contour method, typically constructed through the Inverse First Order Reliability Method combined with parametric joint distributions, is widely adopted for this purpose. However, conventional models often struggle to adequately characterize complex sea states involving mixed wind and swell systems, which exhibit multimodality and irregular dependence structures. To address this limitation, this study applies the use of Gaussian mixture models (GMM) to construct environmental contours. The GMM-based approach models the joint distribution of environmental variables in a flexible and data-adaptive manner, with the number of mixture components determined by the Bayesian Information Criterion and model parameters estimated via the expectation-maximization algorithm. Compared with the conventional conditional Weibull–Lognormal model, the GMM significantly improves fitting accuracy: the RMSE decreases from approximately 0.06 to below 0.0013, and the R² increases to nearly 1.000 across all three datasets. The KS and χ² tests confirm that the GMM adequately fits the observed data at the 0.05 significance level, whereas the baseline model is rejected in several cases. For the 100-year return period, the GMM yields maximum significant wave heights of 4.19–4.55 m with associated peak periods of 18.8–20.3 s, while the baseline model gives 4.02–4.18 m and 14.3–14.6 s, respectively. These quantitative improvements demonstrate that the mixture-based contours capture the intricate characteristics of wind–swell coexisting sea conditions more accurately, leading to enhanced representativeness of extreme sea states. Consequently, the adopted method enables more refined and reliable design sea state assessments for tested datasets, contributing to the optimization of environmental parameter selection for floating wind turbines. 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

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

Modeling loss data is a crucial aspect of actuarial science. In the insurance industry, small claims occur frequently, while large claims are rare. Traditional heavy-tail distributions, such as Weibull, Log-Normal, and Inverse Gaussian distributions, are not suitable for describing insurance data, which often exhibit skewness and fat tails. The literature has explored classical and Bayesian inference methods for the parameters of composite distributions, such as the Exponential–Pareto, Weibull–Pareto, and Inverse Gamma–Pareto distributions. These models effectively separate small to moderate losses from significant losses using a threshold parameter. This research aims to introduce a new composite distribution, the Gamma–Pareto distribution with two parameters, and employ a numerical computational approach to find the maximum likelihood estimates (MLEs) of its parameters. A novel computational approach for a nonlinear regression model where the loss variable is distributed as the Gamma–Pareto and depends on multiple covariates is proposed. The maximum likelihood (ML) and Approximate Bayesian Computation (ABC) methods are used to estimate the regression parameters. The Fisher information matrix, along with a multivariate normal distribution as the prior distribution, is utilized through the ABC method. Simulation studies indicate that the ABC method outperforms the ML method in terms of accuracy. Full article

This paper presents a comparative evaluation of three distinct methodologies for estimating the parameters of the Inverse Weibull distribution under Type-I right censoring: trimmed linear moments (using Type-AT and Type-BT variants), direct linear moments (using Type-AD and Type-BD variants), and maximum likelihood estimation. The performance of these methods is assessed through Monte Carlo simulations, focusing on estimation accuracy, relative absolute bias, and root mean square error to identify the most appropriate approach. The practical applicability of these techniques is demonstrated through a real-world dataset analysis. Full article

Many scholars are interested in modeling complex data in an effort to create novel probability distributions. This article proposes a novel class of distributions based on the inverse of the exponentiated Weibull hazard rate function. A particular member of this class, the Weibull–Rayleigh distribution (WR), is presented with focus. The WR features diverse probability density functions, including symmetric, right-skewed, left-skewed, and the inverse J-shaped distribution which is flexible in modeling lifetime and systems data. Several significant statistical features of the suggested WR are examined, covering the quantile, moments, characteristic function, probability weighted moment, order statistics, and entropy measures. The model accuracy was verified through Monte Carlo simulations of five different statistical estimation methods. The significance of WR is demonstrated with three real-world data sets, revealing a higher goodness of fit compared to other competing models. Additionally, the change point for the WR model is illustrated using the modified information criterion (MIC) to identify changes in the structures of these data. The MIC and curve analysis captured a potential change point, supporting and proving the effectiveness of WR distribution in describing transitions. Full article

Reliable estimation of extreme waves is essential for offshore wind turbine system design; however, site-specific conditions limit the application of one-size-fits-all statistical methods. We analyzed extreme wave conditions at potential offshore wind farm sites in South Korea using high-resolution hindcast data (1979–2022) based on the Weather Research and Forecasting (WRF) model. While previous studies have typically relied on a limited combination of distribution types and parameter estimation methods, this study systematically applied various Weibull distribution models and parameter estimation techniques to the environmental contour (EC) method. The results show that the optimal statistical approach varied by site according to the tail characteristics of the wave height distribution. The inverse second-order reliability method (I-SORM) provided the highest accuracy in regions with rapidly decaying tails, achieving root mean square error (RMSE) values of 0.21 in Shinan (using the three-parameter Weibull distribution with maximum likelihood estimation, MLE) and 0.34 in Chujado (with the method of moments, MOM). In contrast, the inverse first-order reliability method (I-FORM) yielded superior performance in areas where the tail decays more gradually, such as Yokjido (RMSE = 0.47 with MLE using the exponentiated Weibull distribution) and Ulsan (RMSE = 0.29, with MLE using the exponentiated Weibull distribution). These findings underscore the importance of selecting site-specific combinations of statistical models and estimation techniques based on wave distribution characteristics, thereby improving the accuracy and reliability of extreme design wave predictions. The proposed framework can significantly contribute to the establishment of reliable design criteria for offshore wind turbine systems by reflecting region-specific marine environmental conditions. 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

In recent years, there has been an increasing interest in the application of progressive censoring as a means to reduce both cost and experiment duration. In the absence of explanatory variables, the present study employs a statistical inference approach for the inverse Weibull distribution, using a progressive type II censoring strategy with two independent samples. The article expounds on the maximum likelihood estimation method, utilizing the Fisher information matrix to derive approximate confidence intervals. Moreover, interval estimations are computed by the bootstrap method. We explore the application of Bayesian methods for estimating model parameters under both the squared error and LINEX loss functions. The Bayesian estimates and corresponding credible intervals are calculated via Markov chain Monte Carlo (MCMC). Finally, comprehensive simulation studies and real data analysis are carried out to validate the precision of the proposed estimation methods. Full article

In this paper, two different families are mixed: the exponentiated and new Topp–Leone-G families. This yields a new family, which we named the mixture of the exponentiated and new Topp–Leone-G family. Some statistical properties of the proposed family are obtained. Then, the mixture of two exponentiated new Topp–Leone inverse Weibull distribution is introduced as a sub-model from the mixture of exponentiated and new Topp–Leone-G family. Some related properties are studied, such as the quantile function, moments, moment generating function, and order statistics. Furthermore, the maximum likelihood and Bayes approaches are employed to estimate the unknown parameters, reliability and hazard rate functions of the mixture of exponentiated and new Topp–Leone inverse Weibull distribution. Bayes estimators are derived under both the symmetric squared error loss function and the asymmetric linear exponential loss function. The performance of maximum likelihood and Bayes estimators is evaluated through a Monte Carlo simulation. The applicability and flexibility of the MENTL-IW distribution are demonstrated by well-fitting two real-world engineering datasets. The results demonstrate the superior performance of the MENTL-IW distribution compared to other competing models. Full article

Wind energy is a clean, inexhaustible resource with significant potential to reduce coal dependence, lower carbon emissions, and provide sustainable energy in the off-grid areas of South Africa’s Eastern Cape. However, due to wind variability, site-specific assessments are crucial for accurate resource estimation and investment risk mitigation. This study evaluates the wind energy potential at Fort Hare using six statistical distribution models: Weibull (WEI), Rayleigh (RAY), gamma (GAM), generalized extreme value (GEV), inverse Gaussian (IGA), and Gumbel (GUM). The analysis is based on three years (2021–2023) of hourly wind speed data at 10 m above ground level from the Fort Beaufort weather station. Parameters were estimated using the maximum likelihood method (MLM), and model performance was ranked using the total error (TE) metric. The results indicate an average wind speed of 2.60 m/s with a standard deviation of 1.85 m/s. The GEV distribution was the best fit (TE = 0.020), while the widely used Weibull distribution ranked third (TE = 0.5421), highlighting its limitations in capturing wind variability and extremes. This study underscores the importance of testing multiple models for accurate wind characterization and suggests improving the performance of the Weibull model through advanced parameter optimization, such as artificial intelligence. The wind power density was 31.52 W/m², classifying the site as poor for large-scale electricity generation. The prevailing wind direction was southeast. Recommendations include deploying small-scale turbines and exploring augmentative systems to optimize wind energy utilization in the region. Full article

Animal experiments have long been used as an educational tool in pharmacological education; however, from the perspective of animal welfare, it is necessary to decrease the number of animals used. ingAlthough using of simulators is effective, the development of these simulators is necessary when there is no existing simulator for animal experiments. In this review, we describe free, downloadable, and commercial simulators that are currently used in pharmacological education. Furthermore, we introduce two strategies to create simulators of animal experiments: (1) bioassay, and (2) experiments that measure the reaction time. We also describe five sigmoid curves (logistic curve, cumulative distribution function [CDF] of normal distribution, Gompertz curve, von Bertalanffy curve, and CDF of Weibull curve) to fit the results and their inverse functions. Using this strategy, it is possible to create a simulator that calculates the reaction time following drug administration. Moreover, we introduce a statistical model for local anesthetic agents using hierarchical Bayesian modeling. Considering the correlation among estimated parameters, we suggest it is possible to create simulators that give results more similar to those of animal experiments. The pharmacological education will be possible by these simulators at educational institutions where animal experiments are difficult due to various restrictions. It is expected that the number of simulator-based education programs will increase in the future. Full article

In this paper, we propose statistical inference methodologies for estimating the shape parameter $\alpha$ of inverse generalized Weibull (IGW) distribution. Specifically, we develop two approaches: (1) a bounded-risk point estimation strategy for $\alpha$ and (2) a fixed-accuracy confidence interval estimation method for $\alpha$. For (1), we introduce a purely sequential estimation strategy, which is theoretically shown to possess desirable first-order efficiency properties. For (2), we present a method that allows for the precise determination of sample size without requiring prior knowledge of the other two parameters of the IGW distribution. To validate the proposed methods, we conduct extensive simulation studies that demonstrate their effectiveness and consistency with the theoretical results. Additionally, real-world data applications are provided to further illustrate the practical applicability of the proposed procedures. Full article

This paper investigates statistical methods for estimating unknown lifetime parameters using a progressive first-failure censoring dataset. The failure mode’s lifetime distribution is modeled by the odd-generalized-exponential–inverse-Weibull distribution. Maximum-likelihood estimators for the model parameters, including the survival, hazard, and inverse hazard rate functions, are obtained, though they lack closed-form expressions. The Newton–Raphson method is used to compute these estimations. Confidence intervals for the parameters are approximated via the normal distribution of the maximum-likelihood estimation. The Fisher information matrix is derived using the missing information principle, and the delta method is applied to approximate the confidence intervals for the survival, hazard rate, and inverse hazard rate functions. Bayes estimators were calculated with the squared error, linear exponential, and general entropy loss functions, utilizing independent gamma distributions for informative priors. Markov-chain Monte Carlo sampling provides the highest-posterior-density credible intervals and Bayesian point estimates for the parameters and reliability characteristics. This study evaluates these methods through Monte Carlo simulations, comparing Bayes and maximum-likelihood estimates based on mean squared errors for point estimates, average interval widths, and coverage probabilities for interval estimators. A real dataset is also analyzed to illustrate the proposed methods. Full article

The tensile properties and the Weibull statistical distributions of the tensile strength of poly-(para-phenylene-2,6-benzobisoxazole) (PBO), poly-(para-phenylene terephthalamide) (PPTA), copoly-(para-phenylene-3,4′-oxydiphenylene terephthalamide (PPODTA), polyarylate (PAR), and polyethylene (PE) polymeric fiber epoxy-impregnated bundle composites have been investigated. The results show that the Weibull modulus decreases as the tensile modulus, strength, and inverse of the failure strain increase. The interfacial shear properties were also examined using the microdroplet composite. For the lower interfacial shear strength of polymeric fibers, the Weibull modulus decreases as interfacial shear strength increases. Conversely, for the higher interfacial shear strength of polymeric fibers, the Weibull modulus increases as interfacial shear strength increases. Interestingly, these inflection points were also observed for the 20–30 MPa interfacial shear strength. Full article