Search Results (32)

Light from fast radio bursts (FRBs) can be deflected by the gravitational lensing effect of primordial black holes (PBHs), if they are distributed along the path from the FRBs to the observer. Consequently, the PBH mass function can be constrained by the lensing events of FRBs. In this work, four different PBH mass functions are investigated (i.e., the monochromatic, log-normal, skew log-normal, and power-law distributions), and the constraints on the model parameters are obtained, if the PBH abundance $f_{\mathrm{PBH}}$ and the event rate of lensed FRBs $\overline{\mathit{\tau }}$ are given. We find that, if $\overline{\mathit{\tau }}<{10}^{-4}$ in future FRB experiments, $f_{\mathrm{PBH}}$ will be less than ${10}^{-2.5}$ in most of the PBH mass range from 1–$100M_{\odot }$ for the monochromatic mass function. Moreover, for the three extended mass functions, $\overline{\mathit{\tau }}$ increases when the PBH mass distributions spread to larger masses, setting more stringent constraints on $f_{\mathrm{PBH}}$. Full article

This study explores advanced methods for analyzing the two-parameter alpha-power exponential (APE) distribution using data from a novel generalized progressive hybrid censoring scheme. The APE model is inherently asymmetric, exhibiting positive skewness across all valid parameter values due to its right-skewed exponential base, with the alpha-power transformation amplifying or dampening this skewness depending on the power parameter. The proposed censoring design offers new insights into modeling lifetime data that exhibit non-monotonic hazard behaviors. It enhances testing efficiency by simultaneously imposing fixed-time constraints and ensuring a minimum number of failures, thereby improving inference quality over traditional censoring methods. We derive maximum likelihood and Bayesian estimates for the APE distribution parameters and key reliability measures, such as the reliability and hazard rate functions. Bayesian analysis is performed using independent gamma priors under a symmetric squared error loss, implemented via the Metropolis–Hastings algorithm. Interval estimation is addressed using two normality-based asymptotic confidence intervals and two credible intervals obtained through a simulated Markov Chain Monte Carlo procedure. Monte Carlo simulations across various censoring scenarios demonstrate the stable and superior precision of the proposed methods. Optimal censoring patterns are identified based on the observed Fisher information and its inverse. Two real-world case studies—breast cancer remission times and global oil reserve data—illustrate the practical utility of the APE model within the proposed censoring framework. These applications underscore the model’s capability to effectively analyze diverse reliability phenomena, bridging theoretical innovation with empirical relevance in lifetime data analysis. Full article

This paper introduces a flexible distribution called the asymmetric double normal distribution, specifically designed to model univariate data exhibiting asymmetry and either unimodal or bimodal characteristics. This distribution is highly flexible, capable of capturing a wide range of data behaviors, from smooth densities to those with thinner tails. It generalizes the skew-normal distribution as a special case and provides a simpler alternative to mixture models by avoiding issues related to parameter identifiability. This study explores the structural and theoretical properties of the asymmetric double normal distribution, and parameter estimation is carried out using the maximum likelihood method. Simulation experiments assess the performance of the estimators, while applications in regression and real-life data fitting illustrate the practical relevance of this model. This proposed distribution proves to be a powerful tool for modeling asymmetric and bimodal data, offering significant advantages for statistical analysis in diverse applications. Full article

The estimation of drift parameters in the Ornstein–Uhlenbeck (O-U) process with jumps primarily employs methods such as maximum likelihood estimation, least squares estimation, and least absolute deviation estimation. These methods generally assume specific error distributions and finite variances. However, with the increasing uncertainty in financial markets, asset prices exhibit characteristics such as skewness and heavy tails, which lead to biases in traditional estimators. This paper proposes a self-weighted quantile estimator for the drift parameters of the O-U process with jumps and verifies its asymptotic normality under large samples, given certain assumptions. Furthermore, through Monte Carlo simulations, the proposed self-weighted quantile estimator is compared with least squares, quantile, and power variation estimators. The estimation performance is evaluated using metrics such as mean, standard deviation, and mean squared error (MSE). The simulation results show that the self-weighted quantile estimator proposed in this paper performs well across different metrics, such as 8.21% and 8.15% reduction of MSE at the 0.9 quantile for drift parameter $\gamma$ and $\kappa$ compared with the traditional quantile estimator. Finally, the proposed estimator is applied to inter-period statistical arbitrage of the CSI 300 Index Futures. The backtesting results indicate that the self-weighted quantile method proposed in this paper performs well in empirical applications. Full article

We define a new family of random geometric graphs which we call random covering graphs and study its statistical properties. To the best of our knowledge, this family of graphs has not been explored in the past. Our experimental results suggest that there are striking deviations in the expected number of edges, degree distribution, spectrum of adjacency/normalized Laplacian matrix associated with the new family of graphs as compared to both the well-known Erdos–Renyi random graphs and the general random geometric graphs as originally defined by Gilbert. Particularly, degree distribution of the graphs shows some interesting features in low dimensions. To the more applied end, we believe that our random graph family might be effective in modelling some practically useful networks (world wide web, social networks, railway or road networks, etc.). It is observed that the degree distribution of some complex networks arising in practice follow power law distribution or log power distribution; they tend to be right skewed, having a heavy tail unlike the degree distribution of Erdos–Renyi graphs or general geometric random graphs (which follow exponential distribution with a sharp tail). The degree distribution of our random graph family significantly deviates from that of Erdos–Renyi graphs or general geometric random graphs and is closer to a right-skewed power law distribution with a heavy tail. Thus, we believe that this new family of graphs might be more effective in modelling the typical real-world networks mentioned above. The key contribution of the paper is introducing this new random graph family and studying some of its properties experimentally, further investigation into which would be interesting from a purely mathematical perspective. Also, it might be of practical interest in terms of modelling real-world networks. Full article

The problem of model selection in regression analysis through the use of forward selection, backward elimination, and stepwise selection has been well explored in the literature. The main assumption in this, of course, is that the data are normally distributed and the main tool used here is either a t test or an F test. However, the properties of these model selection procedures are not well-known. The purpose of this paper is to study the properties of these procedures within generalized linear regression models, considering the normal linear regression model as a special case. The main tool that is being used is the score test. However, the F test and other large sample tests, such as the likelihood ratio and the Wald test, the AIC, and the BIC, are included for the comparison. A systematic study, through simulations, of the properties of this procedure was conducted, in terms of level and power, for symmetric and asymmetric distributions, such as normal, Poisson, and binomial regression models. Extensions for skewed distributions, over-dispersed Poisson (the negative binomial), and over-dispersed binomial (the beta-binomial) regression models, are also given and evaluated. The methods are applied to analyze two health datasets. Full article

Training-anomaly-based, machine-learning-based, intrusion detection systems (AMiDS) for use in critical Internet of Things (CioT) systems and military Internet of Things (MioT) environments may involve synthetic data or publicly simulated data due to data restrictions, data scarcity, or both. However, synthetic data can be unrealistic and potentially biased, and simulated data are invariably static, unrealistic, and prone to obsolescence. Building an AMiDS logical model to predict the deviation from normal behavior in MioT and CioT devices operating at the sensing or perception layer due to adversarial attacks often requires the model to be trained using current and realistic data. Unfortunately, while real-time data are realistic and relevant, they are largely imbalanced. Imbalanced data have a skewed class distribution and low-similarity index, thus hindering the model’s ability to recognize important features in the dataset and make accurate predictions. Data-driven learning using data sampling, resampling, and generative methods can lessen the adverse impact of a data imbalance on the AMiDS model’s performance and prediction accuracy. Generative methods enable passive adversarial learning. This paper investigates several data sampling, resampling, and generative methods. It examines their impacts on the performance and prediction accuracy of AMiDS models trained using imbalanced data drawn from the UNSW_2018_IoT_Botnet dataset, a publicly available IoT dataset from the IEEEDataPort. Furthermore, it evaluates the performance and predictability of these models when trained using data transformation methods, such as normalization and one-hot encoding, to cover a skewed distribution, data sampling and resampling methods to address data imbalances, and generative methods to train the models to increase the model’s robustness to recognize new but similar attacks. In this initial study, we focus on CioT systems and train PCA-based and oSVM-based AMiDS models constructed using low-complexity PCA and one-class SVM (oSVM) ML algorithms to fit an imbalanced ground truth IoT dataset. Overall, we consider the rare event prediction case where the minority class distribution is disproportionately low compared to the majority class distribution. We plan to use transfer learning in future studies to generalize our initial findings to the MioT environment. We focus on CioT systems and MioT environments instead of traditional or non-critical IoT environments due to the stringent low energy, the minimal response time constraints, and the variety of low-power, situational-aware (or both) things operating at the sensing or perception layer in a highly complex and open environment. Full article

In the clock network design, the trade-off between power consumption and timing closure is an important and difficult issue. The clock tree architecture has a shorter wire length and better power consumption, but it is more difficult to achieve timing closure with it. On the other hand, clock mesh architecture is easier to satisfy the clock skew constraint, but it usually has much more power consumption. Therefore, a hybrid clock network architecture that combines both the clock tree and clock mesh seems to be a promising solution. In a normal hybrid mesh/tree structure, a driving buffer is placed in the intersection of mesh lines. In this paper, we propose a novel cross-mesh architecture, and we distribute the buffers to balance the overall switching capacitance, reducing the number of registers connected to a subtree, and the load capacitance of a buffer. With the average dispersion of the overall driving force, our methodology creates small non-zero skew clock trees. In addition, we integrate clock gating, register clustering, and load balancing techniques to optimize clock skew and load capacitance simultaneously. The proposed methodology has four stages: cross-mesh planning, register clustering, mesh line connecting, and load balancing. Experimental results show that our cross-mesh architecture has high tolerance for process variation, and is robust in all the operation modes. Comparing it to the uniform mesh architecture, our methodology and algorithms reduce 28.9% of load capacitance and 80.4% of clock skew on average. Compared to the non-uniform mesh architecture, we also reduce capacitance by 22.4% and skew by 76.7% on average. This illustrates that we can obtain a feasible solution effectively and improve both power consumption and clock skew simultaneously. Full article

In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model’s parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented. Full article

It is common in many fields of knowledge to assume that the data under study have a normal distribution, which often generates mistakes in the results, since this assumption does not always coincide with the characteristics of the observations under analysis. In some cases, the data may have degrees of skewness and/or kurtosis greater than what the normal model can capture, and in others, they may present two or more modes. In this work, two new families of skewed distributions are presented that fit bimodal data with positive support. The new families were obtained from the extension of the bimodal normal distribution to the alpha-power family class. The proposed distributions were studied for their main properties, such as their probability density function, cumulative distribution function, survival function, and hazard function. The parameter estimation process was performed from a classical perspective using the maximum likelihood method. The non-singularity of Fisher’s information was demonstrated, which made it possible to find the stochastic convergence of the vector of the maximum likelihood estimators and, based on the latter, perform statistical inference via the likelihood ratio. The applicability of the proposed distributions was exemplified using real data sets. Full article

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods. Full article

The lightweight and flexible membrane structure of roofs are susceptible to wind loads with the risk of damage and failure. Compared with uniform and low-level turbulence flow cases (i.e., normal winds) that have been well investigated, the wind-induced vibration problem of membrane structures in high-level turbulence flows such as typhoons has been paid little attention. To address the gap, this paper aimed at investigating the aerodynamic behavior of hyperbolic paraboloid membrane structures in normal and typhoon winds by a series of wind tunnel tests. Some distinct wind characteristics of upcoming normal and typhoon flows in terms of vertical profiles of wind velocity, turbulence intensity, and power spectrum density of fluctuating winds were well simulated in an automatically controlled wind tunnel. The aeroelastic behavior of a scaled model was analyzed and discussed in terms of displacement time-history responses, probability distribution characteristics, and dynamic characteristics including the natural frequency, mode shape, and damping ratio. Results show that the increasing suction in a typhoon leads to significant growth in maximum deformations and more risks to suffer from aeroelastic instability. Non-Gaussian characteristics appear more remarkable with skewness and kurtosis increasing almost two-fold in typhoons. Structural modal parameters are influenced by both turbulence intensity and wind velocity. This study provides basic insights into the deficiency of dynamic response of membrane structures in typhoons, and promotes the applications of membrane structures in green buildings. Full article

Probabilistic models with flexible tail behavior have important applications in engineering and earth science. We introduce a nonlinear normalizing transformation and its inverse based on the deformed lognormal and exponential functions proposed by Kaniadakis. The deformed exponential transform can be used to generate skewed data from normal variates. We apply this transform to a censored autoregressive model for the generation of precipitation time series. We also highlight the connection between the heavy-tailed $\kappa$-Weibull distribution and weakest-link scaling theory, which makes the $\kappa$-Weibull suitable for modeling the mechanical strength distribution of materials. Finally, we introduce the $\kappa$-lognormal probability distribution and calculate the generalized (power) mean of $\kappa$-lognormal variables. The $\kappa$-lognormal distribution is a suitable candidate for the permeability of random porous media. In summary, the $\kappa$-deformations allow for the modification of tails of classical distribution models (e.g., Weibull, lognormal), thus enabling new directions of research in the analysis of spatiotemporal data with skewed distributions. Full article

Several papers on distributions to model rates and proportions have been recently published; their fitting in numerous instances is better than the alternative beta distribution, which has been the distribution to follow when it is necessary to quantify the average of a response variable based on a set of covariates. Despite the great usefulness of this distribution to fit the responses on the $(0,1)$ unit interval, its relevance loses objectivity when the interest is quantifying the influence of these covariates on the quantiles of the variable response in $(0,1)$; being the most critical situation when the distribution presents high asymmetry and/or kurtosis. The main objective of this work is to introduce a distribution for modeling rates and proportions. The introduced distribution is obtained from the alpha-power extension of the skew–normal distribution, which is known in the literature as the power–skew–normal distribution. Full article

In this paper, an extension of the power half-normal (PHN) distribution is introduced. This new model is built on the application of slash methodology for positive random variables. The result is a distribution with greater kurtosis than the PHN; i.e., its right tail is heavier than the PHN distribution. Its probability density, survival and hazard rate function are studied, and moments, skewness and kurtosis coefficientes are obtained, along with relevant properties of interest in reliability. It is also proven that the new model can be expressed as the scale mixture of a PHN and a uniform distribution. Moreover, the new model holds the PHN distribution as a limit case when the new parameter tends to infinity. The parameters in the model are estimated by the method of moments and maximum likelihood. A simulation study is given to illustrate the good behavior of maximum likelihood estimators. Two real applications to survival and fatigue fracture data are included, in which our proposal outperforms other models. Full article