Ein BASIC-Programm zur statistischen Auswertung von mikroskopischen Partikelzählungen

In many biological counting problems it is known that under ideal conditions repeated counts follow a Poisson distribution. This is true, for example, for counts of bacteria in a number of equal volumes from a well-mixed suspension. In order to indicate whether counts show more variability than can usually be expected from a Poisson distribution it is customary to use the index of dispersion. A BASIC-program written for personal computers is given which allows a rapid statistical evaluation of count data by means of the dispersion index. The program can be used, moreover, for some other tasks, too, such as the computation of confidence bounds, the testing of hypotheses and the planning of counting processes.     

On the relationship between the index of dispersion and Allan factor and their power for testing the Poisson assumption

Several statistical tests are available for testing the Poisson hypothesis and/or the equidispersion of a point process. The capability to discriminate between the Poissonian behaviour and more complex processes is fundamental in many areas of research including earthquake analysis, hydrology, ecology, biology, signal analysis and sociology. This study investigates the relationship between two indices often used for detecting departures from equidispersion, namely, the index of dispersion (ID) and the Allan factor (AF). Since an approximation of the sampling distribution of AF for Poisson data has been recently proposed in the literature, we perform a detailed analysis of its properties and its relationship with the asymptotic sampling distribution of ID. Moreover, the statistical power of the AF for testing the Poisson hypothesis is assessed by using an extensive Monte Carlo simulation, and the performances of AF and ID are compared. We propose a simplified version of the AF sampling distribution that does not depend on the rate of occurrence keeping the maximum errors of extreme percentiles always smaller than 2–3 %. The power study highlights that ID systematically outperforms AF for discriminating between equidispersed and under/over dispersed data. Both indices show the same lack of power for distinguishing between data drawn from equidispersed non-Poissonian distribution functions. Therefore, even though AF is a useful statistical tool for detecting the possible fractal behaviour of point processes, ID should be preferred when the analysis aims at assessing equidispersion. The lack of power for a small sample size confirms the difficulty of identifying the true nature of the occurrence process of rare events.     

Theoretical and Practical Investigations on the Heterogeneous Distribution of Plankton in the Main Basin of the Saidenbach Storage Reservoir

To detect spatial heterogeneous distributions it is necessary to delimitate quantitatively the sum of all errors caused by methods from sampling to counting. This is possible by the coefficient of variation, since it constitutes also a measure of the counting error and since its dependence on the counted number or the mean density of the population is clearly defined. In the investigations the error caused by methods (reproducibility of sampling and counting) does not exceed the theoretically permitted maximum counting error (at p = 0.05). Accordingly, all results of investigations for which the coefficient of variation lies above this counting error limit can be interpreted as actual spatial heterogeneous distributions. During the full circulations of autumn and spring as well as the summer stagnation period, in the Saidenbach storage reservoir no significant differences of the phytoplankton were observed within the range of horizontal distances of appr. 100m for 50% of the cases. For zooplankton. 45% of the investigations indicated a homogeneous distribution. The evaluation of data by the patchiness-index according to Lloyd (L), the Morisita index (M) as well as the graphical comparison between variance and mean value (8²/x) do not show any remarkably different results.     

Derivation of streamflow statistics based on a filtered point process

This work presents the derivation of general streamflow cumulants from daily rainfall time series. The general streamflow cumulants can be used to compute basic streamflow statistics such as mean, variance, coefficient of skewness, and correlation coefficient. Streamflow is considered as a filtered point process where the input is a daily rainfall time series assumed to be a marked point process. The marks of the process are the daily rainfall amounts which are assumed independent and identically distributed. The number of rainfall occurrences is a counting process represented by either the binomial, the Poisson, or the negative binomial probability distribution depending on its ratio of mean to variance. The first three cumulants and the covariance function of J-day averaged streamflows are deduced based on the characteristic function of a filtered point process. These cumulants are functions of the stochastic properties of the daily rainfall process and the basin-response function representing the causal relationship between rainfall and runoff.     

水平层状介质中基阶瑞利面波椭圆极化特征数值分析与研究

近年来的工程实践表明,以速度频散特性为理论基础的传统瑞利面波法的实际应用存在场地限制的瓶颈问题.为克服该困难,本文从面波的基础理论着手,在前人建立的水平层状介质中瑞利面波速度频散方程的基础上,推导了水平层状介质中瑞利面波质点位移的解析解公式.以工程中常见的几种典型的水平层状地层模型为例,结合地脉动单点谱比法(HVSR,Horizontal to Vertical Spectral Ratio),对基阶瑞利面波的椭圆极化特征进行了数值模拟研究.研究结果表明:与瑞利面波的速度频散特性类似,其椭圆极化同样具有频散特性,且椭圆极化时的质点位移水平分量与垂直分量的频谱比与地层泊松比结构有关.瑞利面波的这种椭圆极化特性展示了利用单点瑞利面波的多分量评价地层泊松比结构的理论可行性.     

Electron velocity distribution function in a plasma with temperature gradient and in the presence of suprathermal electrons: application to incoherent-scatter plasma lines

The plasma dispersion function and the reduced velocity distribution function are calculated numerically for any arbitrary velocity distribution function with cylindrical symmetry along the magnetic field. The electron velocity distribution is separated into two distributions representing the distribution of the ambient electrons and the suprathermal electrons. The velocity distribution function of the ambient electrons is modelled by a near-Maxwellian distribution function in presence of a temperature gradient and a potential electric field. The velocity distribution function of the suprathermal electrons is derived from a numerical model of the angular energy flux spectrum obtained by solving the transport equation of electrons. The numerical method used to calculate the plasma dispersion function and the reduced velocity distribution is described. The numerical code is used with simulated data to evaluate the Doppler frequency asymmetry between the up- and downshifted plasma lines of the incoherent-scatter plasma lines at different wave vectors. It is shown that the observed Doppler asymmetry is more dependent on deviation from the Maxwellian through the thermal part for high-frequency radars, while for low-frequency radars the Doppler asymmetry depends more on the presence of a suprathermal population. It is also seen that the full evaluation of the plasma dispersion function gives larger Doppler asymmetry than the heat flow approximation for Langmuir waves with phase velocity about three to six times the mean thermal velocity. For such waves the moment expansion of the dispersion function is not fully valid and the full calculation of the dispersion function is needed.     

Generic boundary conditions for lattice Boltzmann models and their application to advection and anisotropic dispersion equations

We address a “multi-reflection” approach to model Dirichlet and Neumann time-dependent boundary conditions in lattice Boltzmann methods for arbitrarily shaped surfaces. The multi-reflection condition for an incoming population represents a linear combination of the known population solutions. The closure relations are first established for symmetric and anti-symmetric parts of the equilibrium functions, independently of the nature of the problem. The symmetric part is tuned to build second- and third-order accurate Dirichlet boundary conditions for the scalar function specified by the equilibrium distribution. The focus is on two approaches to advection and anisotropic-dispersion equations (AADE): the equilibrium technique when the coefficients of the expanded equilibrium functions match the coefficients of the transformed dispersion tensor, and the eigenvalue technique when the coefficients of the dispersion tensor are built as linear combinations of the eigenvalue functions associated with the link-type collision operator. As a particular local boundary technique, the “anti-bounce-back” condition is analyzed. The anti-symmetric part of the generic closure relation allows to specify normal flux conditions without inversion of the diffusion tensor. Normal and tangential constraints are derived for bounce-back and specular reflections. The bounce-back closure relation is released from the non-physical tangential flux restriction at leading orders. Solutions for the Poisson equation and for convection–diffusion equations are presented for isotropic/anisotropic configurations with specified Dirichlet and Neumann boundary conditions.     

A nonhomogeneous Poisson process geostatistical model

This paper introduces a new geostatistical model for counting data under a space-time approach using nonhomogeneous Poisson processes, where the random intensity process has an additive formulation with two components: a Gaussian spatial component and a component accounting for the temporal effect. Inferences of interest for the proposed model are obtained under the Bayesian paradigm. To illustrate the usefulness of the proposed model, we first develop a simulation study to test the efficacy of the Markov Chain Monte Carlo (MCMC) method to generate samples for the joint posterior distribution of the model’s parameters. This study shows that the convergence of the MCMC algorithm used to simulate samples for the joint posterior distribution of interest is easily obtained for different scenarios. As a second illustration, the proposed model is applied to a real data set related to ozone air pollution collected in 22 monitoring stations in Mexico City in the 2010 year. The proposed geostatistical model has good performance in the data analysis, in terms of fit to the data and in the identification of the regions with the highest pollution levels, that is, the southwest, the central and the northwest regions of Mexico City.     

On the shot-noise streamflow model and its applications

In this paper we consider the shot-noise model of streamflow series. We show how design discharge can be obtained by the stochastic intensity of thinned Poisson processes describing the peaks over a threshold. The main result concerns the stationary distribution of peaks. We derive an explicit expression for this limit distribution in terms of its Laplace transform. Approximation formulas are developed making use of the saddle point method for the asymptotic evaluation of contour integrals and the Post-Widder formula for inversion of Laplace transforms. We illustrate this methods on the case of Gamma-distributed shots. The stationary peak distribution is used to approximate the maximum value distribution for larger time intervals.     

Brittleness characteristics of tight oil siltstones

Rock brittleness directly affects reservoir fracturing and its evaluation is essential for establishing fracturing conditions prior to reservoir reforming. Dynamic and static brittleness data were collected from siltstones of the Qingshankou Formation in Songliao Basin. The brittle–plastic transition was investigated based on the stress–strain relation. The results suggest that the brittleness indices calculated by static elastic parameters are negatively correlated with the stress drop coefficient and the brittleness index B₂, defined as the average of the normalized Young’s modulus and Poisson’s ratio, is strongly correlated with the stress drop. The brittleness index B₂, Young’s modulus, and Poisson’s ratio correlate with the brittle minerals content; that is, quartz, carbonates, and pyrite. We also investigated the correlation between pore fluid and porosity and dynamic brittle characteristic based on index B₂. Pore fluid increases the plasticity of rock and reduces brittleness; moreover, with increasing porosity, rock brittleness decreases. The gas-saturated siltstone brittleness index is higher than that in oil- or water-saturated siltstone; the difference in the brittleness indices of oil- and water-saturated siltstone is very small. By comparing the rock mechanics and ultrasonic experiments, we find that the brittleness index obtained from the rock mechanics experiments is smaller than that obtained from the ultrasonic experiments; nevertheless, both decrease with increasing porosity as well as their differences. Ultrasonic waves propagate through the rock specimens without affecting them, whereas rock mechanics experiments are destructive and induce microcracking and porosity increases; consequently, the brittleness of low-porosity rocks is affected by the formation of internal microcrack systems.     

A model to consider the spatial variability of rainfall partitioning within deciduous canopy. I. Model description

In this first paper of two, a numerical simulation model capable of simulating the spatial variability of rainfall partitioning within a canopy is presented. The second paper details how the model is parameterized, and some testing of its capabilities. The first stage of the model is to derive the mature canopy structure. This is achieved through simplified individual tree structures and a random placement routine based on a modified Poisson distribution. Following this the spatial discretization for throughfall is attained as a series of layers of triangles with a tree trunk at every apex. The number of layers is derived from the leaf area index through a modified Poisson distribution. Seasonal variation in the deciduous canopy is simulated through a time vector routine. The rainfall partitioning section of the model is based upon the Rutter model which has been modified to each individual triangle layer. The main feature of this model is that it offers a method of simulating rainfall partitioning at a scale that is a function of the size of the elementary physical components (tree and leaf scale). This can be used to investigate soil moisture variations under a canopy, or to study the variations within the forest hydrological processes themselves. © 1997 John Wiley & Sons, Ltd.     

两种新参数在银川—河套和祁连山—六盘山地震带地震预报中的应用研究

采用极值理论求得岗贝尔分布b值,可以克服目前广泛使用的求b值的方法对资料要求高的弱点。根据中强地震发生前小震出现偏离泊松分布的现象,构造泊松分布符合度Yn值。将这两种参数具体应用于银川-河套地震带和祁连山-六盘山地震带进行预测检验。结果表明在两个区域岗贝尔分布b值和泊松分布符合度Yn值对中强地震映震效果均较好。     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

Observed advantage for negative binomial over Poisson distribution in partial duration series

The goodness of fit of the negative binomial and the Poisson distributions to partial duration series of runoff events is tested. The data have been recorded by eight hydrometric stations located on ephemeral rivers in Isreal. For each station, a number of threshold discharges are considered, by that series of nested subsamples are formed. Owing to size limitations, a Chi-square test is conducted on samples associated with low to moderate threshold discharges. Positive results, at a 5% significance level, are obtained in 30 out of the 53 tests of the Poisson distribution, and in 22 out of the 28 tests of the negative binomial distribution. The fit of the Poisson distribution to samples of conventionally recommended sizes (of 2 to 3 events per year) is found positive for five rivers and negative for the three other rivers The fit of the negative binomial distribution to these samples is found positive for six rivers, inconclusive for one river and short of data for the eighth river. Mixed results are obtained as the threshold level is raised. Therefore, no direct extrapolation is possible to samples associated with high thresholds.An indirect extrapolation is drawn through a comparison of the actual properties of the samples with those expected under a perfect fit of the distribution functions. Ranges of such properties are defined with respect to the properties of the tested samples and to the test results. The actual properties of nine of the eleven samples associated with high thresholds (i.e. mean number of events <-0.1year ^–1) are found within these ranges. This provides a hint for a probable good fit of either distribution, and particularly the negative binomial, to the occurrence frequency of high events.     

中国大陆地震空间分布模型检验

本文以中国大陆地震目录为基础资料,以泊松模型为零假设模型,并将Neyman-Scott空间丛集过程的各子模型设为检验模型,采用K-function点过程分析法和最大似然估计法计算各模型参数,并以AIC准侧判定模型的拟合优度,来检验中国大陆地震空间分布模型.检验结果表明:泊松模型的拟合优度最差,说明地震在空间的分布不是完全随机的;广义Thomas模型的拟合优度最好,说明地震的空间分布是丛集的,可用由两个高斯核组成的广义Thomas模型较好地描述.研究结果还表明,同一研究区内,采用不同时段具有不同最小完整起始震级的地震目录计算得到的地震空间分布的丛集尺度几乎不变,这意味着地震空间丛集尺度不受小地震的控制,且可能与研究区的断层规模有关.     

Estimation of the dispersion coefficient in rivers with riparian vegetation

The study of the transport processes in the riparian environment is currently a subject of great interest. In this context, the evaluation of longitudinal dispersion is a fundamental issue. Although it plays an important role in the transport of chemicals, nutrients, and wood debris, few works have studied the effects of riparian vegetation on the dispersion coefficient in transversally non-uniform streams. Here, a quasi two-dimensional model is proposed to evaluate the transverse profile of the depth-averaged velocity in the presence of any vegetation distribution along the riparian transect. Once velocity profile is obtained, the dispersion coefficient is evaluated and the remarkable role of vegetation is shown. Both the velocity profile and the dispersion coefficient have been validated using our new experimental results and literature data. The work highlights the importance of taking into account the presence of vegetation along river banks. The estimation of the longitudinal dispersion in vegetated rivers can be affected by as much as 70–100% compared to the case without vegetation.     

辽宁地区5级以上地震复发间隔及地震概率预测模型研究

详细分析了辽宁地区三个震级档的地震复发间隔分布;基于Poisson分布,构建了辽宁地区5．0、5．5和6．0级三个震级档的Poisson概率预测模型及具有概率水平指标的三级预测预警指标。     

The first and the second e of the extreme value distribution,EV1

In the peak over threshold model resulting in the Extreme-value distribution, type I, (EV1) the firste of the distribution function is based on the Poisson number of exceedances, and the seconde arises from the Exponentially distributed magnitudes.This paper, on the one hand, generalises the Poisson model to the (positive and negative) Binomial distribution, and, on the other hand, the Exponential distribution is generalised to the Generalised Pareto distribution. Lack of fit with respect to the Poisson and Exponential distribution is measured by statistics derived from those which would be locally most powerful if the estimates of the location and scale parameter were equal to the true parameter values. Ways of combining both statistics are discussed.