Search Results (62)

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

The analysis of road traffic accidents often reveals asymmetric patterns, providing insights that support the development of preventive measures, reduce fatalities, and improve road safety interventions. The Rayleigh distribution, a continuous distribution with inherent asymmetry, is well suited for modeling right-skewed data and is widely used in scientific and engineering fields. It also shares structural characteristics with other skewed distributions, such as the Weibull and exponential distributions, and is particularly effective for analyzing right-skewed accident data. This study considers several approaches for constructing confidence intervals, including the percentile bootstrap, bootstrap with standard error, generalized confidence interval, method of variance estimates recovery, normal approximation, Bayesian Markov Chain Monte Carlo, and Bayesian highest posterior density methods. Their performance was evaluated through Monte Carlo simulation based on coverage probabilities and expected lengths. The results show that the HPD method achieved coverage probabilities at or above the nominal confidence level while providing the shortest expected lengths. Finally, all proposed confidence intervals were applied to fatalities recorded during the seven hazardous days of Thailand’s Songkran festival in 2024 and 2025. Full article

The Rician distribution, which arises in radar, communications, and magnetic resonance imaging, is characterized by a noncentrality parameter and a scale parameter. The Rayleigh distribution is a special case of the Rician distribution with a noncentrality parameter of zero. This paper considers generalized hypothesis testing for Rayleigh and Rician distributions using Rissanen’s stochastic complexity, particularly his approximation employing Fisher information matrices. The Rayleigh distribution is a member of the exponential family, so its normalized maximum likelihood density is readily computed, and shown to asymptotically match the Fisher information approximation. Since the Rician distribution is not a member of the exponential family, its normalizing term is difficult to compute directly, so the Fisher information approximation is employed. Because the square root of the determinant of the Fisher information matrix is not integrable, we restrict the integral to a subset of its range, and separately encode the choice of subset. Full article

This paper presents a comprehensive study on the estimation of multicomponent stress–strength reliability under progressively censored data, assuming the inverse Rayleigh distribution. Both maximum likelihood estimation and Bayesian estimation methods are considered. The loss function and prior distribution play crucial roles in Bayesian inference. Therefore, Bayes estimators of the unknown model parameters are obtained under symmetric (squared error loss function) and asymmetric (linear exponential and general entropy) loss functions using gamma priors. Lindley and MCMC approximation methods are used for Bayesian calculations. Additionally, asymptotic confidence intervals based on maximum likelihood estimators and Bayesian credible intervals constructed via Markov Chain Monte Carlo methods are presented. An extensive Monte Carlo simulation study compares the efficiencies of classical and Bayesian estimators, revealing that Bayesian estimators outperform classical ones. Finally, a real-life data example is provided to illustrate the practical applicability of the proposed methods. Full article

Increasing the amount of data with complex dynamics requires the constant updating of statistical distributions. This study aimed to introduce a new three-parameter distribution, named the new exponentiated Weibull (NEW) distribution, by applying the logarithmic transformation to the exponentiated Weibull distribution. The exponentiated Weibull distribution is a powerful generalization of the Weibull distribution that includes several classical distributions as special cases—Weibull, exponential, Rayleigh, and exponentiated exponential—which make it capable of capturing diverse forms of hazard functions. By combining the advantages of the logarithmic transformation and exponentiated Weibull, the new distribution offers great flexibility in modeling different forms of hazard functions, including increasing, J-shaped, reverse-J-shaped, and bathtub-shaped functions. Some mathematical properties of the NEW distribution were studied. Moreover, four different methods of estimation—the maximum likelihood (ML), least squares (LS), Cramer–Von Mises (CVM), and percentile (PE) methods—were employed to estimate the distribution parameters. To assess the performance of the estimates, three simulation studies were conducted, showing the benefit of the ML method, followed by the PE method, in estimating the model parameters. Additionally, five datasets were used to evaluate the effectiveness of the new distribution in fitting real data. Compared with some Weibull-type extensions, the results demonstrate the superiority of the new distribution in modeling various forms of real data and provide evidence for the applicability of the new distribution. Full article

With accelerating urbanization and the exponential growth in vehicle populations, high-precision traffic monitoring has become indispensable for intelligent transportation systems (ITSs). Conventional sensing technologies—including inductive loops, cameras, and radar—suffer from inherent limitations: restrictive spatial coverage, prohibitive installation costs, and vulnerability to adverse weather. Distributed Acoustic Sensing (DAS), leveraging Rayleigh backscattering to convert standard optical fibers into kilometer-scale, real-time vibration sensor networks, presents a transformative alternative. This paper provides a comprehensive review of the principles and system architecture of DAS for roadway traffic monitoring, with a focus on signal processing techniques, feature extraction methods, and recent advances in vehicle detection, classification, and speed/flow estimation. Special attention is given to the integration of deep learning approaches, which enhance noise suppression and feature recognition under complex, multi-lane traffic conditions. Real-world deployment cases on highways, urban roads, and bridges are analyzed to demonstrate DAS’s practical value. Finally, this paper delineates emerging research trends and technical hurdles, providing actionable insights for the scalable implementation of DAS-enhanced ITS infrastructures. 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

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

This paper investigates an understudied generalization of the classical exponential, Rayleigh, and Weibull distributions, known as the power generalized Weibull distribution, particularly in the context of censored data. Characterized by one scale parameter and two shape parameters, the proposed model offers enhanced flexibility for modeling diverse lifetime data patterns and hazard rate behaviors. Notably, its hazard rate function can exhibit five distinct shapes, including upside-down bathtub and bathtub shapes. The study focuses on classical and Bayesian estimation frameworks for the model parameters and associated reliability metrics under a unified hybrid censoring scheme. Methodologies include both point estimation (maximum likelihood and posterior mean estimators) and interval estimation (approximate confidence intervals and Bayesian credible intervals). To evaluate the performance of these estimators, a comprehensive simulation study is conducted under varied experimental conditions. Furthermore, two empirical applications on real-world cancer datasets underscore the efficacy of the proposed estimation methods and the practical viability and flexibility of the explored model compared to eleven other existing lifespan models. Full article

This study innovatively explores vibrational control with reference to elliptical thickness variation. Traditionally, plate vibrations have been analysed by incorporating circular, linear, parabolic, and exponential thickness variations. However, these variations often fall short in optimizing vibrational characteristics. So, we develop a new formula specifically for orthotropic as well as isotropic plates with elliptical thickness profiles and employ the Rayleigh–Ritz method to calculate the vibrational frequencies of the plate. This research demonstrates that elliptical variation significantly reduces vibrational frequencies compared to conventional thickness profiles. The findings indicate that this unique configuration enhances vibrational control, offering potential applications in engineering fields where vibration reduction is essential. The results provide a foundation for further exploration of non-standard thickness variations in the design of advanced structural components. The study reveals that the elliptical variation in tapering parameter is a much better choice than other variation parameters studied in the literature for the purpose of optimizing the vibrational frequency of plates. Full article

We study the large-time behavior of solutions to Darcy–Boussinesq equations with a non-vanishing scalar acceleration coefficient, which model buoyancy-driven flows in porous media with spatially varying gravity. First, we show that the system admits steady-state solutions of the form $(\mathbf{u},\rho ,p)=(\mathbf{0},{\rho }_s,p_s)$, where ${\rho }_s$ is characterised by the hydrostatic balance $\nabla p_s=-{\rho }_s\nabla \mathrm{\Psi }$. Second, we prove that the steady-state solution satisfying $\nabla {\rho }_s=\delta (x,y)\nabla \mathrm{\Psi }$ is linearly stable provided that $\delta (x,y)<{\delta }_0<0$, while the system exhibits Rayleigh–Taylor instability if $\mathrm{\Psi }=gy$, ${\rho }_s={\delta }_{0}g$ and ${\delta }_0>0$. Finally, despite the inherent Rayleigh–Taylor instability that may trigger exponential growth in time, we prove that for any sufficiently regular initial data, the solutions of the system asymptotically converge towards the vicinity of a steady-state solution, where the velocity field is zero, and the new state is determined by hydrostatic balance. This work advances porous media modeling for geophysical and engineering applications, emphasizing the critical interplay of gravity, inertia, and boundary conditions. Full article

In this paper, a new generalization of continuous distributions using the Marshall–Olkin distribution as a generator is proposed and studied. Many important mathematical properties are derived from the proposed distribution, including moments, the moment generating function, order statistics, entropy, and the quantile function. Two different estimation methods are used, namely, maximum likelihood estimation and Bayesian methods. A Monte Carlo simulation is conducted to estimate the parameters and study the behavior of the proposed distribution. Bayesian estimation is obtained using the Gibbs sampler and Metropolis–Hastings algorithm. Finally, two real-world datasets are used to compare the performance of non-Bayesian and Bayesian methods. Full article

Two enigmatic gamma-ray features in the galactic central region, known as Fermi Bubbles (FBs), were found from Fermi-LAT data. An energy release, (e.g., by tidal disruption events in the Galactic Center, GC), generates a cavity with a shock that expands into the local ambient medium of the galactic halo. A decade or so ago, a phenomenological model of the FBs was suggested as a result of routine star disruptions by the supermassive black hole in the GC which might provide enough energy for large-scale structures, like the FBs. In 2020, analytical and numerical models of the FBs as a process of routine tidal disruption of stars near the GC were developed; these disruption events can provide enough cumulative energy to form and maintain large-scale structures like the FBs. The disruption events are expected to be ${10}^{-4}\sim {10}^{-5}{\mathrm{yr}}^{-1}$, providing an average power of energy release from the GC into the halo of $\dot{\mathcal{E}}\sim 3\times {10}^{41}$ erg ${\mathrm{s}}^{-1}$, which is needed to support the FBs. Analysis of the evolution of superbubbles in exponentially stratified disks concluded that the FB envelope would be destroyed by the Rayleigh–Taylor (RT) instabilities at late stages. The shell is composed of swept-up gas of the bubble, whose thickness is much thinner in comparison to the size of the envelope. We assume that hydrodynamic turbulence is excited in the FB envelope by the RT instability. In this case, the universal energy spectrum of turbulence may be developed in the inertial range of wavenumbers of fluctuations (the Kolmogorov–Obukhov spectrum). From our model we suppose the power of the FBs is transformed partly into the energy of hydrodynamic turbulence in the envelope. If so, hydrodynamic turbulence may generate MHD fluctuations, which accelerate cosmic rays there and generate gamma-ray and radio emission from the FBs. We hope that this model may interpret the observed nonthermal emission from the bubbles. Full article

The acoustoelectric (AE) effect induced by the absorption of ultraviolet (UV) light at 365 nm in piezoelectric ZnO films was theoretically and experimentally studied. c-ZnO films 4.0 µm thick were grown by the RF reactive magnetron sputtering technique onto fused silica substrates at 200 °C. A surface acoustic wave (SAW) delay line was fabricated with two split-finger Al interdigital transducers (IDTs) photolithographically implemented onto the ZnO-free surface to excite and reveal the propagation of the fundamental Rayleigh wave and its third harmonic at about 39 and 104 MHz. A small area of a few square millimeters on the surface of the ZnO layer, in between the two IDTs, was illuminated by UV light at different light power values (from about 10 mW up to 1.2 W) through the back surface of the SiO₂ substrate, which is optically transparent. The UV absorption caused a change of the ZnO electrical conductivity, which in turn affected the velocity and insertion loss (IL) of the two waves. It was experimentally observed that the phase velocity of the fundamental and third harmonic waves decreased with an increase in the UV power, while the IL vs. UV power behavior differed at large UV power values: the Rayleigh wave underwent a single peak in attenuation, while its third harmonic underwent a further peak. A two-dimensional finite element study was performed to simulate the waves IL and phase velocity vs. the ZnO electrical conductivity, under the assumption that the ZnO layer conductivity undergoes an in-depth inhomogeneous change according to an exponential decay law, with a penetration depth of 325 nm. The theoretical results predicted single- and double-peak IL behavior for the fundamental and harmonic wave due to volume conductivity changes, as opposed to the AE effect induced by surface conductivity changes for which a single-peak IL behavior is expected. The phenomena predicted by the theoretical models were confirmed by the experimental results. Full article

We explore properties of matter and characteristics of Rayleigh–Taylor mixing by analyzing data gathered in the state-of-the-art fine-resolution experiments in high-energy density plasmas. The eminent quality data represent fluctuations spectra of the X-ray imagery intensity versus spatial frequency. We find, by using the rigorous statistical method, that the fluctuations spectra are accurately captured by a compound function, being a product of a power law and an exponential and describing, respectively, self-similar and scale-dependent spectral parts. From the self-similar part, we find that Rayleigh–Taylor mixing has steep spectra and strong correlations. From the scale-dependent part, we derive the first data-based value of the kinematic viscosity in high-energy density plasmas. Our results explain the experiments, agree with the group theory and other experiments, and _carve the path for better understanding Rayleigh–Taylor mixing in nature and technology. Full article