Generation of irregular particle packing with prescribed statistical distribution, spatial arrangement, and volume fraction

A method for packing irregular particles with a prescribed volume fraction is proposed.Furthermore,the generated granular material adheres to the prescribed statistical distribution and satisfies the desired complex spatial arrangement.First,the irregular geometries of the realistic particles were obtained from the original particle images.Second,the Minkowski sum was used to check the overlap between irregular particles and place an irregular particle in contact with other particles.Third,the optimised advance front method(OAFM)generated irregular particle packing with the prescribed statistical dis-tribution and volume fraction based on the Minkowski sum.Moreover,the signed distance function was introduced to pack the particles in accordance with the desired spatial arrangement.Finally,seven biaxial tests were performed using the UDEC software,which demonstrated the accuracy and potential usefulness of the proposed method.It can model granular material efficiently and reflect the meso-structural characteristics of complex granular materials.This method has a wide range of applications where discrete modelling of granular media is necessary.

Statistical Distributions of Ambient Air Pollutants in Shanghai, China

Objective To determine the best statistical distribution of concentration data of major air pollutants in Shanghai. Methods Four types of theoretic distributions (lognormal, gamma, Pearson V and extreme value) were chosen to fit daily average concentration data of PM10, SO2 and NO2 from June 1, 2000 to May 31, 2003 in Shanghai by using the maximum likelihood method. The fit results were evaluated by Chi-square test. Results The best-fit distributions for PM10,SO2 and NO2 concentrations in Shanghai were lognormal, Pearson V, and extreme value distributions, respectively. Conclusion The results can be further applied to local air pollution prediction and control, e.g., the probabilities exceeding the air quality standard and emission source reduction of air pollutant concentration to meet the standard.

Application of Statistical Distribution of PM_(10) Concentration in Air Quality Management in 5 Representative Cities of China

Objective To estimate the frequency of daily average PM10 concentrations exceeding the air quality standard （AQS） and the reduction of particulate matter emission to meet the AQS from the statistical properties （probability density functions） of air pollutant concentration. Methods The daily PM10 average concentration in Beijing, Shanghai, Guangzhou, Wuhan, and Xi＇an was measured from 1 January 2004 to 31 December 2008. The PM10 concentration distribution was simulated by using the Iognormal, Weibull and Gamma distributions and the best statistical distribution of PM10 concentration in the 5 cities was detected using to the maximum likelihood method. Results The daily PM10 average concentration in the 5 cities was fitted using the Iognormal distribution. The exceeding duration was predicted, and the estimated PMlo emission source reductions in the 5 cities need to be 56.58%, 93.40%, 80.17%, 82.40%, and 79.80%, respectively to meet the AO, S. Conclusion Air pollutant concentration can be predicted by using the PM10 concentration distribution, which can be further applied in air quality management and related policy making.

EVOLUTION OF STATISTICAL DISTRIBUTION OF PIT GEOMETRIC PARAMETERS UNDER FATIGUE LOADING

The pits and pit-associated fatigue crack initiation of the offshore structure steel A537cLl have been investigated under salt water spray condition.The tests were interrupted on sched- ule to make plastic replica of corroded specimen surface on which many randomly distributed pits can be found.The development of the geometric parameters of pits was obtained and the statistical distributions of these parameters were determined.Instead of depth,the ratio of depth to width is the most dominant parameter in relation to crack initiation.Also,the pitting was enhanced when low frequency or high stress range was applied and although stress range has no effect on the nucleation of pits,it can accelerate the initiation of cracks from pits.

A statistical distribution of quad-pol X-band sea clutter time series acquired at a grazing angle

Although the complex Wishart distribution has been widely used to analyze the statistic properties of quad-pol SAR spatial data, the applicability of this complex distribution to the time series of sea clutter is rarely discussed.The measured data of the quad-pol X-band marine radar demonstrate that the time series of the sea echoes are also satisfied the circular Gaussian distributions if the low intensity signals, which are mainly dominated by a radar noise, in the shadow regions of the large-scale waves are removed. On the basis of this fact, the probability density functions（PDFs） of the intensity as well as the phase, the real and the imaginary parts of the sea echoes obtained by the marine radar have been derived, and the theoretical models are all expressed in closed forms. In order to validate the theoretical results, the PDFs are compared with the experimental data collected by the Mc Master IPIX radar. And the comparisons show that the PDF models are in good agreement with the experimental data.

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Statistical Distributions of Wavelengths

The statistical distribution of wavelength is directly derived from a two-dimensional and spatially homogeneous Gaussian wave field. The present result differs from both the result of Rayleigh distribution and Sun's result (1988b) which is transformed through the period distribution derived from a two-dimensional and stationary Gaussian wave field. A laboratory experiment shows that the present result is more consistent with the observations in the wave tank than the others.

The Statistical Distribution of the Horizontal Velocities of Water Particles at Wave Surface Maxima

On the basis of the linear model of random sea waves presented by Longuet-Higgins, the statistical distribution of the horizontal velocities of water particles at wave surface maxima is derived theoretically. The derived distribution is similar to that of wave surface maxima, and a new spectral width epsilon(u), which is defined as (1 - m(3)(2)/m(2)m(4))(1/2), is introduced in the distribution. When epsilon(u) tends to zero, the distribution is reduced to Rayleigh distribution and it is reduced to the normal distribution when epsilon(u) tends to unity. For a narrow spectrum, it is proved that epsilon is equal to 1/2 epsilon, where epsilon is (1 - m(2)(2)/m(0)m(4))(1/2) and is the commonly used spectral width.

Statistical distribution based detector response function of a Si(PIN) detector for K_α and K_β X-ray

A semi-empirical detector response function （DRF） model of Si （PIN） detector is proposed to fit element Kα and Kβ X-ray spectra, which is based on statistical distribution analytic （SDA） method. The model for each single peak contains a step function, a Gaussian function and an exponential tail function. Parameters in the model are obtained by weighted nonlinear least-squares fitting method. In the application, six kinds of elements＇ characteristic X-ray spectra are obtained by Si （PIN） detector, and fitted out by the established DRF model. Reduced chi-square values are at the interval of 1.11-1.25. Other applications of the method are also discussed.

A statistical distribution texton feature for synthetic aperture radar image classification

We propose a novel statistical distribution texton(s-texton) feature for synthetic aperture radar(SAR) image classification. Motivated by the traditional texton feature, the framework of texture analysis, and the importance of statistical distribution in SAR images, the s-texton feature is developed based on the idea that parameter estimation of the statistical distribution can replace the filtering operation in the traditional texture analysis of SAR images. In the process of extracting the s-texton feature, several strategies are adopted, including pre-processing, spatial gridding, parameter estimation, texton clustering, and histogram statistics. Experimental results on Terra SAR data demonstrate the effectiveness of the proposed s-texton feature.

THE RAMANUJAN'S Q-EXTENSION FOR THE EXPONENTIAL FUNCTION AND STATISTICAL DISTRIBUTIONS

In this paper. we shall propose a q-extension for the exponential function and develop q-analogs for families of statistical distribution, such as,the normal, and Poisson distribution etc.Many properties of these families will be studied.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.

Appropriateness of Reduced Modified Three-Parameter Weibull Distribution Function for Predicting Gold Production in Ghana

Forecasting mine production is pertinent to gold mining as it serves as production goals for investors. It is therefore important to identify the exact distribution that gold production as a response variable naturally follows. It is even more appropriate to have a model(s) with few predictor variables. This paper seeks to identify appropriate statistical distribution functions for fitting gold production in Ghana. The empirical paper relied mainly on quarterly secondary datasets on gold production between the years 2009 and 2022 secured from the Minerals Commission of Ghana, Accra. Several known statistical distributions including Weibull, Log-Normal, Generalized Extreme Value (GEV) were explored with Maximum Likelihood Estimation (MLE) and evaluated using model selection criteria as AIC, AICc and BIC. Goodness of Fits were evaluated using Kolmogorov-Smirnov Test (K-S), Cramer-Von Mises Statistic and Anderson-Darling Statistic. Based on the analysis conducted, the reduced modified 3-parameter Weibull distribution provided the best fit for gold production in Ghana. Though the reduced modified Weibull function is proposed, it is important however to recognize that other external factors can influence production levels. Also, the average quarterly fitted gold production is 1000334.8918 ± 75,327.080 (±7.5%) [i.e., 925,007.812 – 1,075,661.972]. This indicates that the average annually fitted gold production lies between 3700031.248 and 4302647.888 ounces at 99.9% confidence level. Therefore, the predicted gold production for the year 2022 is 3.7million ounces at 99.9% confidence level.

Reply to 'Statistical testing and distribution for lead chloride toxicity'

We are very grateful for the letter written by Dr Lange,and indeed apologize for the mistakes noted in the word-ing of our text regarding statistical analysis.This wasdue to changes carried out while revising the manuscriptat the request of reviewers,whom we thank for,point-ing out several issues that were actually similar to thosenoted by Dr.Lange.Unfortunately,we were unable todescribe and discuss our findings properly in the context

Distribution and segregation of dissolved elements in pipeline slab

The chemical composition in a cross section of a high grade pipeline slab was measured point by point （in a scale of 1 μm） using original position statistic distribution analysis （OPA）. The result indicated that negative segregation strips of Si, Mn, Mo, Ni, Cr, Nb, Cu, Ti, and V exist in the two sides 24 mm away from the central line, with a width of 8-12 mm, Negative segregation inside the central line is more severe than that outside the central line, and the highest positive segregation of the elements appears closely by the inner sides of the negative segregation strips. No obvious negative segregation strip of S and P is found. Segregation of the elements in the central area is higher than that in the outer and inner arc areas. The segregation of C, Ti, S, and P is high and that of Cr, Cu, Si, and Mn is low in the slab.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.

Wave Energy Estimation by Using A Statistical Analysis and Wave Buoy Data near the Southern Caspian Sea

Statistical analysis was done on simultaneous wave and wind using data recorded by discus-shape wave buoy. The area is located in the southern Caspian Sea near the Anzali Port. Recorded wave data were obtained through directional spectrum wave analysis. Recorded wind direction and wind speed were obtained through the related time series as well. For 12-month measurements（May 25 2007-2008）, statistical calculations were done to specify the value of nonlinear auto-correlation of wave and wind using the probability distribution function of wave characteristics and statistical analysis in various time periods. The paper also presents and analyzes the amount of wave energy for the area mentioned on the basis of available database. Analyses showed a suitable comparison between the amounts of wave energy in different seasons. As a result, the best period for the largest amount of wave energy was known. Results showed that in the research period, the mean wave and wind auto correlation were about three hours. Among the probability distribution functions, i.e Weibull, Normal, Lognormal and Rayleigh, ＂Weibull＂ had the best consistency with experimental distribution function shown in different diagrams for each season. Results also showed that the mean wave energy in the research period was about 49.88 k W/m and the maximum density of wave energy was found in February and March, 2010.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

Stability analysis of CO_(2)gas shielded welding short-circuit transition process based on GMAW dynamic model

Base on the arc phase and short-circuit phase and their relationship, the paper considers the changes of the extension of wire, the arc length, liquid bridge resistance and mass of liquid bridge, combines the improved “mass-spring” model with the loop model of welding power system, puts forward the critical judgment condition of droplet transition, and establishes a more accurate dynamic model for describing the short-circuit transition process. The dynamic changes of short-circuit transfer frequency, welding current and voltage, contact droplet and residual droplet equivalent radius and droplet equivalent radius at different wire feeding speeds were calculated and analyzed, and compared with the experimental results. It shows that the fluctuation of droplet displacement, velocity and wire extension length at the optimal arc starting point is the smallest. The smaller the initial liquid bridge curvature radius is, the better the stability of short-circuit transfer is.