Skew-normal Distribution Research Articles

Three‐dimensional characterization of particle morphology in natural gravel and blasted rock fragments using SfM‐MVS photogrammetry

AbstractThis study aims to develop a high‐precision and cost‐efficient method for the three‐dimensional reconstruction of large particles in natural gravel and blasted rock fragments, utilizing Structure from Motion (SfM) and Multi‐View Stereo (MVS) techniques. The proposed approach was applied to characterize the three‐dimensional morphology of rockfill dam materials at a real construction site. Particle shape was quantitatively analyzed using shape indices of sphericity, convexity, and angularity. The predominant morphology of natural gravel is characterized as slightly elongated and slightly flat, while rock fragments are slightly elongated and not flat. Probability density distributions of shape indices follow a skewed normal distribution: sphericity and convexity show leftward skewness, whereas angularity is right‐skewed. Skewness parameters of sphericity and angularity are consistent between natural gravel and blasted rock fragments, indicating comparable shape asymmetry. Convexity skewness is significantly higher in natural gravel compared to rock fragments, by approximately an order of magnitude. The relationship between size and particle shape shows that form ratios and associated shape descriptors change linearly with the logarithm of size; larger particles approach spherical or cubic forms. The innovative measurements contribute to the particle shape data set of rockfill dam materials, providing valuable insights into the three‐dimensional and statistical morphological characteristics of relatively large particles in natural gravel and blasted rock fragments. This approach enhances understanding of particle morphology's impact on the mechanical behavior of granular materials.

A stochastic process-based degradation modeling framework considering measurement errors: a perspective of dual non-Gaussian assumptions

The stochastic processes are a natural choice for describing the randomness in degradation processes caused by inherent randomness and environmental factors. This article proposes a new modified skew-normal distribution to capture measurement uncertainty, and then establishes a stochastic process-based degradation modeling framework, in which both degradation increments and measurement errors do not follow the Gaussian distributions. Taking the IG process as an example, the basic reliability indicators and the alarm probabilities caused by measurement errors are derived. In addition, a multi-stage parameter estimation algorithm based on moderate particle sizes and comparative tolerances is developed for this stochastic process-based degradation model under dual non-Gaussian assumptions. Finally, the effectiveness and advantages of the proposed model along with the parameter estimation algorithm are demonstrated by a simulation study and a case application, and it is particularly pointed out that the relative size of measurement errors has a significant impact on the precision of degradation reliability assessment.

Resonance of Gravitational Axion-like Particles

The motion of gravitational axion-like particles (ALPs) around a Kerr black hole is analyzed, paying attention to the resonance and distribution of spectral radiation. We first discuss the computation of gR˜μνρρσRμνρσ and its implications with Pontryagin’s theorem, and then a detailed analysis of Teukolsky’s master equation is carried out. After carefully analyzing the Teukolsky master equation, we show that this system exhibits resonance when ω≳μ, where μ is the mass of the ALP, while the homogeneous part of the solution exhibits the superradiance. A skew-normal distribution can approximate the energy distribution of the resonant modes, and we give explicit expressions for its lifetime.

Parameter recovery of skew multidimensional multiple-group item response models (MGM-MIRT): a comparison of MCMC algorithms and assessment of effects of interest

Multidimensional item response theory (MIRT) models are powerful tools to analyse item response data. Most of them rely on the assumption that the latent traits are normally distributed. However, when such assumption does not hold, the item and the latent traits estimates can be inaccurate. This paper deals, in a very detailed way, through simulation studies, with the utility of the class of the MIRT models developed by Padilla et al. [Multidimensional multiple-group IRT models with skew normal latent trait distributions. J Multivariate Anal 2018;167:250–268], where the multivariate skew-normal distribution under the centred parameterization is employed for modelling the latent traits. The impact of important factors of interest on the parameter recovery is investigated. Such factors are the number of subjects, number of items, number of groups and asymmetry level. In a general way, the results show that our approach outperforms some traditional models when the latent traits follow asymmetric distributions. In addition, different Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation are compared, by considering two schemes of data augmentation and a proposal to speed up their convergence, based on approaches found in the literature, for binary regression models. Guidelines are provided for the correct using of Bayesian inferential methods for the MIRT models.

Polygenic Genetic Analysis of Principal Genes for Yield Traits in Land Cotton

Objective: Yield traits are crucial for cotton breeding. Analyzing the yield traits of terrestrial cotton and exploring their genetic mechanisms through a primary gene + multigene hybrid genetic model provide a theoretical basis for selecting high-quality cotton varieties and identifying associated molecular markers. Methods: Completing the construction of the six populations (P1, P2, F1, F2, B1, B2) using Xinluzhong 37 as the female parent and Xinluzhong 51 as the male parent. Six yield traits were assessed: single boll weight, boll number per plant, lint yield per plant, seed cotton per plant, lint percentage, and seed index. Data were tested for normal distribution, and the inheritance patterns of yield traits were analyzed through combined primary gene + polygenic analysis. Results: The coefficients of variation for the six yield traits ranged from 37.368% to 53.905%, 33.335% to 58.524%, 34.132% to 57.686%, 8.721% to 12.808%, 1.842% to 6.283%, and 8.783% to 12.580%, respectively. These traits displayed either normal or skewed normal distributions. The optimal genetic model for single boll weight and seed index was PG-ADI, while MX2-ADI-AD best fit the traits of boll number per plant and lint percentage. For lint yield per plant and seed cotton per plant, the 2MG-ADI model was optimal. The polygenic heritability for single boll weight was 29.58%; for boll number per plant, main gene heritability was 25.19%, with 0% heritability for polygenes; for lint yield per plant, the heritability of the main gene was 23.47%. For seed cotton per plant, the heritability of main genes was 15.38%, with lint percentage showing 63.25% heritability for main genes and 0.08% for polygenes, and seed index with 45.93% heritability due to polygenes. Overall, single boll weight and seed index were predominantly polygenic, while boll number per plant and lint percentage were largely controlled by main gene inheritance. The inheritance of lint yield per plant and seed cotton per plant was also primarily governed by main genes.

Grain boundary segregation spectrum in basal-textured Mg alloys: From solute decoration to structural transition

Mg alloys are promising lightweight structural materials due to their low density and excellent mechanical properties. However, their limited formability and ductility necessitate improvements in these properties, specifically through texture modification via grain boundary segregation. While significant efforts have been made, the segregation behavior in Mg polycrystals, particularly with basal texture, remains largely unexplored. In this study, we performed atomistic simulations to investigate grain boundary segregation in dilute and concentrated solid solution Mg–Al alloys. We computed the segregation energy spectrum of basal-textured Mg polycrystals, highlighting the contribution from specific grain boundary sites, such as junctions, and identified a newly discovered bimodal distribution which is distinct compared to the conventional skew-normal distribution found in randomly-oriented polycrystals. Using a hybrid molecular dynamics/Monte Carlo approach, we simulated segregation behavior at finite temperatures, identifying grain boundary structural transitions, particularly the varied fraction and morphology of topologically close-packed grain boundary phases when changing thermodynamic variables. The outcomes of this study offer crucial insights into basal-textured grain boundary segregation and phase formation, which can be extended to other relevant Mg alloys containing topologically close-packed intermetallics.

Mathematical Formalization and Applications to Data with Excess of Zeros and Ones of the Unit-Proportional Hazard Inflated Models

In this study, we model the rate or proportion of a specific phenomenon using a set of known covariates. To fit the regression model, which explains the phenomenon within the intervals (0,1), [0,1), (0,1], or [0,1], we employ a logit link function. This approach ensures that the model’s predictions remain within the appropriate range of zero to one. In cases of inflation at zero, one, or both, the logit link function is similarly applied to model the dichotomous Bernoulli-type variable with a multinomial response. The findings demonstrate that the model yields a non-singular information matrix, ensuring valid statistical inference. This ensures the invertibility of the information matrix, allowing for hypothesis testing based on likelihood statistics regarding the parameters in the model. This is not possible with other asymmetric models, such as those derived from the skew-normal distribution, which has a singular information matrix at the boundary of the skewness parameter. Finally, empirical results show the model’s effectiveness in analyzing proportion data with inflation at zero and one, proving its robustness and practicality for analyzing bounded data in various fields of research.

Scale mixtures of multivariate centered skew-normal distributions

Scale mixtures of multivariate centered skew-normal distributions

A novel constrained skew-Gaussian filter and its application to maneuverable reentry vehicle tracking

The state of the system generally satisfies specific constraints imposed by material properties or physical laws, so the application of these constraints can improve the accuracy of state estimation. In this paper, a novel recursive filter referred as constrained high-degree cubature skew-Gaussian filter (CHCSGF) is proposed, which achieves soft-constrained state estimation by compressing the probability density of unconstrained states with constraint information. First, the probability density of the state under inequality soft constraints is modeled as a skew-Gaussian (SG) distribution, rather than truncated or single Gaussian distributions. Then, a recursive constrained SG filter is developed to handle inequality soft constraints in linear systems. Addressing nonlinear challenges, a 5th-degree spherical-radial cubature approximation method is presented to numerically calculate SG-weighted integrals for the nonlinear transformation of SG distribution. Finally, the CHCSGF algorithm is proposed using this method to tackle nonlinear filtering problems. The CHCSGF is applied to reentry trajectory tracking to improve estimation accuracy by dealing with heat flow, dynamic pressure and overload constraints during reentry flight. Simulation results demonstrate that the CHCSGF achieves higher estimation accuracy than unconstrained methods under nonlinear inequality soft constraints, and is robust to the constraints with a prior error. Compared to particle filter and moving horizon estimation, the computational complexity of CHCSGF is significantly reduced.

The information matrix of the bivariate extended skew-normal distribution

AbstractFor the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the bivariate case. Specifically, we derive explicit expressions for the score function and the information matrix, in the observed and the expected form; these do not appear to have been examined before in the literature. Ensuing numerical work illustrates some relevant aspects of the expected information matrix.

Bayesian Approach for Estimating the Parameters of the Time-To-Failure Distribution and Its Percentiles Under Power Degradation Model

The degradation models are often applied on the degradation data for studying time-to-failure distribution. In this study, the Bayesian approach is applied on the power degradation model for estimating the parameters of the time-to-failure distribution and its percentiles. Two different distributions are assumed for the degradation parameter of the model. The degradation parameter is firstly assumed to follow the skew-normal distribution with three jointly independently distributed parameters such that the gamma prior is assumed for the shape parameter, while the scale and the location parameters are assumed uniform. The second distribution assumed for the degradation parameter is the log-logistic distribution with two jointly independent random parameters where the shape parameter is assumed gamma, while the scale parameter is assumed uniform. Based on the Gibbs sampling method carried out under the JAGS platform, the models considered are applied on the simulated data and the NASA turbofan Jet engine dataset and the results found are compared. In modeling the time-to-failure distribution, it is shown that based on the simulated data and real data, the Bayesian approach for the power degradation model with the skew-normal degradation parameter outperformed the Bayesian approach for the power degradation model with the log-logistic degradation parameter.

Multivariate skew-normal distribution for modelling skewed spatial data

Multivariate spatial data are commonly modelled using the shared spatial component and multivariate intrinsic conditional autoregressive (MICAR) models where the spatial random variables are assumed to be normally distributed. However, the normality assumption may not be always right as the spatially structured component may show non-normal distributions. We present, multivariate skew-normal spatial distribution in the modelling of multivariate conditional autoregressive models. Simulations and an application to estimate district HIV rates in South Africa are used for illustrating the capabilities of the proposed multivariate skewed spatial model. The estimation is done in a Bayesian framework. A comparison between our suggested approach and the common MICAR model is made using conditional predictive ordinate (CPO). The CPO values indicate that our suggested approach is better than the MICAR model for predicting the outcome variables of both the simulated and HIV data.

A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data

The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced, consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.

Infrared temperature distribution characteristics and state assessment method of sandstone under tension and compression stress

Abnormalities in infrared radiation temperature (IRT) often accompany the loading In this investigation, stress experiments and splitting tests were conducted on sandstone to investigate the IRT characteristics of sandstone under various loading conditions. The results shows that the Maximum Infrared Radiation Temperature (MAXIRT) increases by up to 5 °C, while in splitting tests, the minimum infrared radiation temperature (MINIRT) decreases by approximately 1.5 °C. Compared to the average infrared radiation temperature (AIRT), MAXIRT is more sensitive to compressive stress, whereas (MINIRT) is more responsive to tensile stress. The correlation between IRT indicators and stress were further analyzed. The findings reveal a positive correlation between IRT and compressive stress. At low stress levels, the correlation coefficient fluctuates between −0.4 and 0.6, generally showing low correlation. As stress increases, the correlation coefficient rises, reaching above 0.8, indicating a high correlation. Tensile stress exhibits a negative correlation, with a consistent trend. Additionally, a statistical analysis of the frequency distribution of IRT under different stress conditions was conducted, followed by hypothesis testing. The results demonstrate that the probability distribution of IRT during loading follows a skewed normal distribution. The changes in skewness can be divided into three stages: initial fluctuation, stable variation, and abrupt failure. Under compressive stress, a right-skewed distribution is observed, with skewness exceeding 3.5 before fracture and reaching above 10 near fracture. Under tensile stress, a left-skewed distribution is noted, with skewness reaching −4.5 near fracture. These findings contribute to the assessment of rock stress states and provide early warning information for predicting rock failure.

Joint modeling of mixed skewed longitudinal responses using convolution of normal and log-normal distributions: a Bayesian approach

This paper investigates the joint modeling of mixed ordinal and continuous longitudinal responses using a random effects model and applying a conditional approach. For the ordinal responses, a latent variable model with a logistic distribution is employed. To address skewness in the data, the model incorporates normal and log-normal convolution (NLNC) for both the error term and the random effects in the longitudinal model. Parameter estimation is carried out within a Bayesian framework using Gibbs sampling. The performance of the proposed model is evaluated through simulation studies, comparing it to joint models of mixed ordinal and continuous longitudinal responses assuming skew-normal or normal distributions. The results indicate that joint models using skew-normal or normal distributions can lead to biased parameter estimates, whereas the NLNC joint model performs better overall. Additionally, the proposed method is applied to analyze data from the British Household Panel Survey (BHPS), using life satisfaction and annual income as the correlated ordinal and continuous longitudinal responses, respectively, with annual income showing significant skewness. The results demonstrate that the proposed model provides the best fit for capturing the substantial skewness in the data.

A Bimodal Extension of the Tanh Skew Normal Distribution: Properties and Applications

This article introduces a novel family of skew distributions namely Bimodal Tanh Skew Normal (BTSN)distributions, which incorporates a new skew function with the help of hyperbolic tangent function. Thisnew distribution is designed to accommodate data sets with two modes. Besides, the article presents variousessential mathematical properties, such as moments, moment generating function, characteristic function,mean deviation, characterizations and the method for maximum likelihood estimation of this distribution.A simulation study is also conducted using Metropolis–Hastings algorithm to examine the behavior of theobtained parameters. Furthermore, the practical utility of this new distribution is demonstrated througha real life application involving a specific data set. To assess the suitability of the BTSN distribution, thearticle employs Akaike information criterion (AIC) and Bayesian information criterion (BIC). Finally, alikelihood ratio test is conducted to distinguish between the new model and the existing competing models.

Multivariate doubly truncated moments for generalized skew-elliptical distributions with applications

ABSTRACT In this paper, we focus on multivariate doubly truncated first two moments of generalized skew-elliptical distributions. This class of distributions includes many useful distributions, such as skew-normal, skew Student- t , skew-logistic and skew-Laplace-normal distributions, as special cases. The formulas of multivariate doubly truncated covariance (MDTCov) for generalized skew-elliptical distributions are also given. Further, we compute multivariate doubly truncated expectations (MDTEs) and MDTCovs for 2 -variate skew-normal, skew-Student- t , skew-logistic and skew-Laplace-normal distributions, and use Monte-Carlo method to simulate and compare with the above results. As applications, the results of multivariate tail conditional expectation (MTCE) and multivariate tail covariance (MTCov) for generalized skew-elliptical distributions are derived. In addition, an optimal problem involving MDTE and MDTCov risk measures is proposed. Finally, we use real data to fit skew-normal distribution and to discuss MTCEs and MTCovs of logarithm of adjusted prices for two portfolios consisting of three companies from S&P (Standard & Poor’s) sectors.

Stability analysis of plasma waves driven by runaway electrons in tokamak hot plasmas

The local stability analysis of plasma waves driven by runaway electrons (REs) has been performed considering hot plasma Maxwellian background, with electron and ion temperatures of the order of 1 keV. It is shown that hot plasma waves, namely electron plasma waves (EPWs) and ion Bernstein waves (IBWs) can be driven unstable by RE at their coalescence frequency via Cherenkov resonance by RE with energy distribution peaked at about 8 MeV. A skew-normal distribution is used as a model of the RE energy distribution. The EPW and IBW couples of waves occur between any successive ion-cyclotron harmonics frequencies nf ci, above the lower hybrid resonance. At their confluence, the perpendicular group velocity vanishes and significant RF emissions are expected. The frequency gap between two successive confluences is ∼f ci. Groups of RF line emissions, separated by almost constant frequency gap ∼f ci/2 are detected during various quiescent runaway plasma discharges in the FTU tokamak. The analysis of a specific discharge suggests that the frequencies of the line emissions observed and the frequencies occurring at the EPW-IBW confluences are in reasonable agreement. A possible explanation of the line emissions with ∼f ci/2 gap in terms of nonlinear mode coupling is proposed.

Analyzing method comparison data with skew-normal measurement error models: incorporating generalized scale mixtures and varying degrees of freedom

Comparing two measurement methods is vital in various fields, such as medical research, epidemiology, economics, and environmental studies, to determine whether a new measurement method can be used interchangeably with an existing one. Measurement error models (MEMs) are commonly used for this purpose, where the methods have different measuring scales. However, these models often assume normality, which can be problematic when dealing with skewed and heavy-tailed data. To address this issue, we propose the replicated measurement error model (RMEM) under scale mixtures of skew-normal (SMSN) distributions with different levels of skewness and heavy tails of the true covariate and error distributions. Our primary aim is to assess the extent of similarity and agreement between two measurement methods using this model. The expectation conditional maximization (ECM) approach is applied to fit the model. A simulation study is conducted to evaluate the effectiveness and robustness of the proposed methodology and is illustrated by analyzing systolic blood pressure data. The probability of agreement is used further to assess the agreement between the two measurement methods. The findings indicate that the proposed model effectively analyses replicated method comparison data with measurement errors, even when there are outliers, skewness, and heavy-tailedness.

Intrinsic Mass–Richness Relation of Clusters from THE THREE HUNDRED Hydrodynamic Simulations

The main systematics in cluster cosmology is the uncertainty in the mass–observable relation. In this paper, we focus on the most direct cluster observable in optical surveys, i.e., richness, and constrain the intrinsic mass–richness (MR) relation of clusters in THE THREE HUNDRED hydrodynamic simulations with two runs: GIZMO-SIMBA and GADGET-X. We find that modeling the richness at a fixed halo mass with a skewed Gaussian distribution yields a simpler and smaller scatter compared to the commonly used lognormal distribution. Additionally, we observe that baryon models have a significant impact on the scatter while exhibiting no influence on the mass dependence and a slight effect on the amplitude in the MR relation. We select member galaxies based on both stellar mass M ⋆ and absolute magnitude M . We demonstrate that the MR relations obtained from these two selections can be converted to each other by using the M⋆–M relation. Finally, we provide a seven-parameter fitting result comprehensively capturing the dependence of the MR relation on both stellar mass cutoff and redshift.