Parameters Of Normal Distribution Research Articles

Estimating freeway travel time and its reliability using radar sensor data

ABSTRACTTravel time and its reliability are intuitive system performance measures for freeway traffic operations. This paper proposes a method to estimate travel times based on data collected from roadside radar sensors, considering spatially correlated traffic conditions. Link-level and corridor-level travel time distributions are estimated using these travel time estimates and compared with the ones estimated based on probe vehicle data. The maximum likelihood estimation is used to estimate the parameters of Weibull, gamma, normal, and lognormal distributions. According to the log-likelihood values, lognormal distribution is the best fit among all the tested distributions. Corridor-level travel time reliability measures are extracted from the travel time distributions. The proposed travel time estimation model can well capture the temporal pattern of travel time and its distribution.

Multi-Feature Based Multiple Particle Filters for Object Tracking

Multiple Object tracking is a fundamental step for many computer vision applications. However, detecting and tracking objects in complex background is still a challenging task. This paper proposes an approach, which combines an improved Gaussian mixture modeling with multiple particle filters for automatic multiple targets detecting and tracking. For Gaussian mixture modeling, we make improvement on Gaussian mixture modeling in the phase of model updating by using the expectation maximization algorithm and M recent frames with weight parameters of Gaussian distributions. In the tracking stage, we integrate multiple features of targets, including color, edge and depth, into multiple particle filters to improve the performance of object tracking. By comparing with various particle filter approaches, the experimental results show that our approach can track multiple targets in complex backgrounds automatically and accurately.

An improved high-order statistical moment method for structural reliability analysis with insufficient data

The fourth-order moment method for reliability analysis of structural systems can be practically applied to effectively address the problem of reliability calculation and analysis with insufficient probability data. For complicated reliability analysis problems, however, this method can lead to inaccurate and unstable reliability calculation results. In this paper, an improved high-order statistical moment method for structural reliability analysis with insufficient data is presented. The presented method is inferred using the properties of statistical moment of standard normal distribution parameter and therefore is possible to obtain more stable and accurate calculation of the reliability indexes of a structural system with insufficient probability data. Two numerical examples are provided to show the performance of the presented method. The example results have shown that the method proposed in this paper not only improves the calculation accuracy and stability, but also brings the calculation results closer to the project conditions. The developed high-moment method for reliability calculation of structural systems provides a practical and effective theoretical base and technical support for the reliability design of structural systems.

Modified molecular matrix model for predicting molecular composition of naphtha

To improve the naphtha composition prediction model based on molecular type homologous series matrix (MTHS), this paper puts forward a novel molecular matrix to characterize the naphtha composition and the normal distribution hypothesis to better describe the molecular composition distribution within each homologous series of the molecular matrix. Through prediction calculation of eight groups of naphtha samples and eight groups of gasoline samples, it is verified that the normal distribution hypothesis is more applicable than gamma distribution hypothesis for the prediction model. According to the prediction results of the samples, the restrain range of normal distribution parameters during model computing process is summarized. With the bulk properties of naphtha samples and the value range of distribution parameters as input conditions, this study utilizes the improved novel molecular matrix to predict the composition of naphtha samples. As the results show, the novel molecular matrix can predict more detailed composition information of naphtha and improve prediction accuracy with less unknown parameters.

Multiple Object Detection and Tracking in Complex Background

Multiple object tracking is a fundamental step for many computer vision applications. However, detecting and tracking objects in complex background is still a challenging task. This paper proposes an approach, which combines an improved Gaussian mixture modeling (GMM) with multiple particle filters (MPFs) for automatic multiple targets detecting and tracking. For GMM, we make improvement on GMM in the phase of model updating by using the expectation maximization algorithm and [Formula: see text] recent frames with weight parameters of Gaussian distributions. In the tracking stage, we integrate multiple features of targets, including color, edge and depth, into MPFs to improve the performance of object tracking. By comparing with various particle filter approaches, the experimental results show that our approach can track multiple targets in complex backgrounds automatically and accurately.

Understanding Corona discharge activity in titania nanoparticles dispersed in transformer oil under AC and DC voltages

Titania (TiO2) nanoparticles dispersed transformer oil has high Corona Inception Voltage (CIV) and breakdown strength, and gets further enhanced on insertion of the barrier in the electrode gap. The volume of nanoparticles and the amount of surfactant have a strong influence on the dispersion of nanoparticles in transformer oil and were characterized through viscosity measurement, particle size analysis and by zeta potential measurements. It was also observed that with needle plane configuration, negative DC voltages have high breakdown voltage as compared to positive DC and AC voltages. Improvement in breakdown voltage with barrier can be obtained by placing the barrier at 20–80% of electrode gap from the tip of the high-voltage electrode. The breakdown voltage of needle plane electrode configuration was calculated based on normal distribution parameters. It was observed that the corona activity generates Ultra High Frequency (UHF) signal in the frequency range of 0.7–2 GHZ with its dominant frequency at 0.9 GHz and was characterized using a ternary plot. The discharge activity was studied by using a spectrum analyzer by operating it in zero span mode with 0.9 GHz as center frequency. It was observed that for a given voltage under AC and DC voltages, the magnitude of discharges is less with nanoparticles dispersed transformer oil. A pyrolysis study indicated no variation in the composition of the oil with the addition of titania. It was observed that the esters present in the oils were alkyl substituted oxalic acid and alkyl substituted sulfurous acid esters.

Model Selection for Gaussian Mixture Models

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models. The proposed method is shown to be statistically consistent in determining of the number of components. A modified EM algorithm is developed to simultaneously select the number of components and to estimate the mixing weights, i.e. the mixing probabilities, and unknown parameters of Gaussian distributions. Simulations and a real data analysis are presented to illustrate the performance of the proposed method.

Remote sensing-based estimation for Gaussian distribution parameters of vertical structure of algal biomass in Lake Chaohu

藻类垂向分布异质性导致了遥感反演的湖泊表层叶绿素a浓度结果与单元水柱内藻类生物量间不存在一一对应的关系，因此有效确定藻类垂向分布结构是遥感反演湖泊藻类生物量的基础.受自身因素和外环境条件的影响，藻类垂向分布结构呈现出多种类型，其中高斯类型应用最广.本文基于3200组HydroLight模拟的高斯垂向数据构建BP神经网络，实现用MODIS数据相对应的3个波段的遥感反射比R_rs（469）、R_rs（555）、R_rs（645）和表层叶绿素a浓度共同估算高斯垂向分布结构参数h和σ.经巢湖地面实测数据验证显示，h和σ的估算值与实测值的相关系数分别为0.97和0.95，对应的相对误差分别为13.20%和12.36%，两者相对误差同时小于30%的占总数据量的87.5%，表明该BP神经网络估算巢湖藻类高斯垂向分布结构的有效性和准确性，为基于卫星遥感数据获取湖泊藻类生物量提供了重要的理论基础.;The relationship between water surface reflectance and total depth integrated algae biomass can be very complex as different kinds of algal vertical distributions can occur. For this reason, effectively identifying the algae vertical profiles is fundamental to estimate algal biomass. Gaussian profiles are the most typical algae vertical profiles which occur in most environmental conditions (including external and internal system). In this research, a back propagation (BP) neural network was established to estimate Gaussian distribution parameters of the vertical structure h and σ by wave bands R_rs(469), R_rs(555), R_rs(645) and chlorophyll-a concentration band C_Chl.a(0). The BP neural network was trained by using 3000 simulated datasets (radiative transfer simulation based on in-situ measured data by HydroLight), and verified by another 200 groups of simulated data and measured data. The correlation coefficient between estimated and measured h and σ were 0.97 and 0.95, while the relative errors were 13.20% and 12.36%, respectively. The relative error of h and σ was mostly less than 30%. This indicated that it is a good effectiveness of BP neural networks to estimate the vertical distribution parameters and able to explore the three dimensional algal distribution in Lake Chaohu, thereby providing a significant theoretical basis for remote sensing estimation of algal biomass.

CEP Calculation Based on Weighted Bayesian Mixture Model

CEP is an important accuracy index in the test evaluation for guidance weapon systems. As for the samples origin from diverse populations, which is a general case in the practice, traditional method with one population is inaccurate to give estimate directly. A weighted method considering the credibility of the prior information is proposed for Bayesian estimation algorithm and the weighted estimation of normal distribution parameters is provided. And the statistical diversity between the weighted and classical methods is quantified, and upper bound of the calculation errors caused by prior distortion is deduced for mixture of finite normal distributions. Taking the estimation of the dispersion of the guided weapon impact points as an example, the conclusion is drawn that our method is credible.

Uncertainty quantification in ion–solid interaction simulations

Within the framework of Bayesian uncertainty quantification we propose a non-intrusive reduced-order spectral approach (polynomial chaos expansion) to the simulation of ion–solid interactions. The method not only reduces the number of function evaluations but provides simultaneously a quantitative measure for which combinations of inputs have the most important impact on the result. It is applied to SDTRIM-simulations (Möller et al., 1988) with several uncertain and Gaussian distributed input parameters (i.e. angle, projectile energy, surface binding energy, target composition) and the results are compared to full-grid based approaches and sampling based methods with respect to reliability, efficiency and scalability.

Simulation of solidification microstructure of Fe-6.5%Si alloy using cellular automaton-finite element method

3D microstructures of Fe–6.5%Si (mass fraction) alloys prepared under different cooling conditions were simulated via finite element-cellular automaton (CAFE) method. The simulated results were compared to experimental results and found to be in accordance. Variations in the temperature field and solid-liquid region, which plays important roles in determining solidification structures, were also examined under various cooling conditions. The proposed model was utilized to determine the effects of Gaussian distribution parameters to find that the lower the mean undercooling, the higher the equiaxed crystal zone ratio; also, the larger the maximum nucleation density, the smaller the grain size. The influence of superheat on solidification structure and columnar to equiaxed transition (CET) in the cast ingot was also investigated to find that decrease in superheat from 52 K to 20 K causes the equiaxed crystal zone ratio to increase from 58.13% to 65.6%, the mean gain radius to decrease from 2.102 mm to 1.871 mm, and the CET to occur ahead of schedule. To this effect, low superheat casting is beneficial to obtain finer equiaxed gains and higher equiaxed dendrite zone ratio in Fe–6.5%Si alloy cast ingots.

COMPARISON OF WEIBULL AND NORMAL PROBABILITY DISTRIBUTION OF FLEXURAL STRENGTH OF DENSE AND POROUS FIRED CLAY

In this research, dense and porous fired clay were produced at a firing temperature of 1300°C. The flexural strength data of the dense and the porous fired clay were determined using three point bending test. Two-parameter Weibull and normal probability distributions were used to estimate the reliability of the flexural strength data of the dense and the porous fired clay. From the result, the Weibull probability distribution scale parameter for the dense (36.31MPa) and Porous (18.85MPa) fired clay are higher than the mean strength value for the dense (33.84MPa) and the porous (17.87MPa) of the normal distribution. Distributions of flaws in the dense and the porous fired clay have a significant effect on the Weibull and normal distribution parameters. The fractured surface of the dense fired clay shows a random distribution of cracks while that of the porous fired clay shows a distribution of pores in the morphology. The normal distribution considers failure at 50% of the flexural strength data while Weibull probability distribution is failure at 62.3% of the strength data. Therefore, two-parameter Weibull is the suitable tool to model failure strength data of the dense and porous fired clay.

Scattering of relativistic and ultra-relativistic electrons by obliquely propagating Electromagnetic Ion Cyclotron waves

Electromagnetic Ion Cyclotron (EMIC) waves are transverse plasma waves that are generated in the Earth magnetosphere by ring current protons with temperature anisotropy in three different bands: below the H+, He+ and O+ ion gyrofrequencies. EMIC events are enhanced during the main phase of a geomagnetic storm when intensifications in the electric field result in enhanced injections of ions and are usually confined to high-density regions just inside the plasmapause or within drainage plumes. EMIC waves are capable of scattering radiation belt electrons and thus provide an important link between the intensification of the electric field, ion populations, and radiation belt electrons. Bounce-averaged diffusion coefficients computed with the assumption of parallel wave propagation are compared to the results of the code that uses the full cold plasma dispersion relation taking into account oblique propagation of waves and higher-order resonances. We study the sensitivity of the scattering rates to a number of included higher-order resonances, wave spectral distribution parameters, wave normal angle distribution parameters, ambient plasma density, and ion composition. Inaccuracies associated with the neglect of higher-order resonances and oblique propagation of waves are compared to potential errors introduced by uncertainties in the model input parameters.

Life estimation of the beam with normal distribution parameters and subjected to cyclic load

This research aims at estimating the life of the beam with normal distribution parameters and subjected to cyclic load. It is tested by Monte-Carlo simulation that the generalized displacement and velocity are normally distributed when the coefficient of variation (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>V</mml:mi></mml:math>) of the random parameter is small (generally <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>V</mml:mi><mml:mo>≤</mml:mo></mml:math> 0.01). The random perturbation method is employed to estimate the mean and variance of the generalized displacement and velocity. The random dynamic stress and its derivative with respect to the time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math> of the beam is formulated according to the shape function of beam element and the stress equation in a Euler-Bernoulli beam. Their mean, variance and correlation coefficient are given using the first-order approximation in a Taylor series. Based on Palmgren-Miner rule, the expected cumulative damage equation is given and is used to estimate the life where the random dynamic stress is non-stationary and follows the normal distribution with the nonzero mean at any time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>t</mml:mi></mml:math>. The presented method could also estimate the life of other structure or component which has several normal random parameters, is subjected to cyclic load and obeys the linear dynamics and elastic theory when the random parameter’s <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mi>V</mml:mi></mml:math> is small.

Some Integrated Squared Error Procedures for Multivariate Normal Data

Abstract : Two methods of estimation for the parameters of the multivariate normal distribution based on the sample characteristic function are given. These methods are shown to have an equivalent basis in terms of Parzen kernel-like density estimation. The estimators for the mean vector and covariance matrix are dependent on a user-specified parameter. Variation of the user-specified parameter produces a response surface in the parameter estimates and therefore allows for an informal sensitivity analysis of the data with respect to a tentative working model. The informal sensitivity analysis is intricately related to formal tests of fit of the model. The estimators of mean vector and covariance matrix have desirable robustness properties, are easy to compute and use, are relatively efficient at the multivariate normal, and are useful in identifying potential outliers and inconsistencies in some statistical assumptions. These methods are directly applicable to structured data such as multivariate experimental designs. Several illustrations are provided.

Bayesian testing for the homogeneity of the shape parameters of several inverse Gaussian distributions

We develop the testing procedures about the homogeneity of the shape parameters of several inverse Gaussian distributions in our paper. We propose default Bayesian testing procedures for the shape parameters under the reference priors. The Bayes factor based on the proper priors gives the successful results for Bayesian hypothesis testing. For the case of the lack of information, the noninformative priors such as Jereys' prior or the reference prior can be used. Jereys' prior or the reference prior involves the undefined constants in the computation of the Bayes factors. Therefore under the reference priors, we develop the Bayesian testing procedures with the intrinsic Bayes factors and the fractional Bayes factor. Simulation study for the performance of the developed testing procedures is given, and an example for illustration is given.

Maximum Likelihood Estimation of Parameters in a Mixture Model

The estimation of parameters of the log normal distribution based on complete and censored samples are considered in the literature. In this article, the problem of estimating the parameters of log normal mixture model is considered. The Expectation Maximization algorithm is used to obtain maximum likelihood estimators for the parameters, as the likelihood equation does not yield closed form expression. The standard errors of the estimates are obtained. The methodology developed here is then illustrated through simulation studies. The confidence interval based on large-sample theory is obtained.

Distributed activation energy modelling for pyrolysis of forest waste using Gaussian distribution

Abstract The paper focuses on the influences of some factors significant to pyrolysis of forestry biomass on the asymptotic solution of the non-isothermal nth-order distribution energy model (DAEM) using Gaussian distribution. Investigated parameters are the integral upper limit, the frequency factor, and the heating rate parameters of the Gaussian distribution. The influence of these factors has been used for evaluating the kinetic parameters of the non-isothermal nth-order Gaussian distribution from thermogravimetric analysis of forest waste.

On Finding Geodesic Equation of Two Parameters Inverse Gaussian Distribution

The class of Inverse Gaussian distributions is quite commonly used as a life-time model in reliability studies. The books by Chhikara and Folks [1] and Seshadri [2] present extensive discussions on classical inference for the parameters of Inverse Gaussian distribution. However, in this paper, we switch our attention to find its geodesic equation. We applied two different algorithms to solve some partial differential equations, where these equations originated from the Inverse Gaussian distribution. As expected, the two algorithms yield the same result.

Bayesian analysis of generalized elliptical semi-parametric models

In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student-t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B-splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the function gesm().