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.

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 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.

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.

Nonequilibrium Statistical Nature of Intergranular Brittle Fracture in Polycrystal

The brittle fracture probability and reliability are obtained in terms of dislocation mechanism of microcrack evolution. The statistical distribution functions and statistical deviations of elongation, strength, plastic work, crack extension force, fracture foughness, critical and crack length, can be derived in a unified fashion.

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.

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.

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.

Statistical distribution of nonlinear random water wave surface elevation

This study deals with the development of statistical modeling for water wave surface elevation by using a method that combines a dynamic solution with random process statistics. Ocean wave data taken from four NOAA （National Oceanic and Atmospheric Administration） buoys moored in the northeast Pacific were used to validate the model. The results indicated that the nonlinear probability density distribution of ocean wave surface elevation derived from the model described the measurements much better than Gaussian distribution and Longuet-Higgins distribution.

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.

Numerical Prediction of Statistical Masonry Wall Fragment Distribution Induced by Blast Loading

The hazard caused by the fragments of damaged structures is usually significant in acci-dental explosions or hostile blast events.A reliable and efficient method to estimate probable fragment size,velocity and launch distance will be useful to assess and design countermeasures to mitigate the possible fragment hazards.This paper presents a numerical method for predicting the size and launch distance of the fragments caused by explosive damage of masonry wall.Numerical simulations with different scaled distances are carried out,and the statistical distribution functions of the fragment size and launch distance in terms of the scaled distance are derived.

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

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.

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.

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.

Distributed Estimator of Market Beta under Extreme Conditions

Market beta is a measure of the volatility or systematic risk of a security or portfolio compared to the market as a whole. This paper considers the distributed estimation of market beta in the case of massive data, and obtains the consistency and asymptotic normality of the estimator. Further, simulations show the finite sample properties of this estimator.

Experimental Study on the Effects of A Breakwater on Wave Field Characteristics

Studies on the possible effects of a detached breakwater on the characteristics of the wave field are carried out experimentally. A serpentine wave generator is used to generate both uni- and multi- directional waves. Characteristics of the wave fields analyzed here include the wave field directionality, and the probability distributions of surface elevations and of the wave heights. Owing to the presence of the breakwater. waves outside the harbour are Found to be reflected with, however, concentrated energy within the harbour entrance. In general. wave heights can be approximated with a Rayleigh distribution, with occasional deviations from the theory. This occurs more frequently for waves with higher peak frequency values than for those with lower values both for uni- and multi-directional waves. Surface elevations can be approximated with the Gaussian model, although the Edgeworth's form of the type A Gram- Charlier series expansions would yield better fits. Wave directionality is found to have no discernible effects on the statistical characteristics of the wave field.