Scaling in the distribution of intertrade durations of Chinese stocks

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.     

Extreme fluxes in solar energetic particle events: Methodological and physical limitations

In this study, all available data on the largest solar proton events (SPEs), or extreme solar energetic particle (SEP) events, for the period from 1561 up to now are analyzed. Under consideration are the observational, methodological and physical problems of energy-spectrum presentation for SEP fluxes (fluences) near the Earth's orbit. Special attention is paid to the study of the distribution function for extreme fluences of SEPs by their sizes. The authors present advances in at least three aspects: 1) a form of the distribution function that was previously obtained from the data for three cycles of solar activity has been completely confirmed by the data for 41 solar cycles; 2) early estimates of extremely large fluences in the past have been critically revised, and their values were found to be overestimated; and 3) extremely large SEP fluxes are shown to obey a probabilistic distribution, so the concept of an “upper limit flux” does not carry any strict physical sense although it serves as an important empirical restriction. SEP fluxes may only be characterized by the relative probabilities of their appearance, and there is a sharp break in the spectrum in the range of large fluences (or low probabilities). It is emphasized that modern observational data and methods of investigation do not allow, for the present, the precise resolution of the problem of the spectrum break or the estimation of the maximum potentialities of solar accelerator(s). This limitation considerably restricts the extrapolation of the obtained results to the past and future for application to the epochs with different levels of solar activity.     

New Estimators of the Bayes Factor for Models with High-Dimensional Parameter and/or Latent Variable Spaces

Formal Bayesian comparison of two competing models, based on the posterior odds ratio, amounts to estimation of the Bayes factor, which is equal to the ratio of respective two marginal data density values. In models with a large number of parameters and/or latent variables, they are expressed by high-dimensional integrals, which are often computationally infeasible. Therefore, other methods of evaluation of the Bayes factor are needed. In this paper, a new method of estimation of the Bayes factor is proposed. Simulation examples confirm good performance of the proposed estimators. Finally, these new estimators are used to formally compare different hybrid Multivariate Stochastic Volatility–Multivariate Generalized Autoregressive Conditional Heteroskedasticity (MSV-MGARCH) models which have a large number of latent variables. The empirical results show, among other things, that the validity of reduction of the hybrid MSV-MGARCH model to the MGARCH specification depends on the analyzed data set as well as on prior assumptions about model parameters.     

Hitting time distributions in financial markets

We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995-1998. We compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution. Specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold, we compare the probability density function (PDF) of three models, namely the geometric Brownian motion, the GARCH model and the Heston model with that obtained from real market data. We will present also some results of a generalized Heston model.     

混响室雷达地杂波统计特性模拟

为实现混响室中威布尔分布杂波的有效模拟,营造逼真的雷达电磁环境,基于广义平稳非相关散射电磁环境下混响室信道衰落特性,通过控制幅度调制信号对衰落系数进行补偿,提出一种基于时域波形设计的混响室地杂波模拟方法。通过调节输入信号序列中大、小幅度脉冲比例,改变混响室传统输入信号的零均值幅度特性,以实测地杂波统计特性为参考,最终得到与实测数据统计特性参数一致的混响室杂波电磁环境。用最大似然估计和KS检验法对实验数据作参数估计和假设检验,实测地杂波数据拟合于标准威布尔模型,混响室实验数据拟合于实测地杂波幅度统计模型,从而实现了实测地杂波起伏特性的混响室有效模拟。     

Lifshitz tails and long-time decay in random systems with arbitrary disorder

In random systems, the density of states of various linear problems, such as phonons, tight-binding electrons, or diffusion in a medium with traps, exhibits an exponentially small Liftshitz tail at band edges. When the distribution of the appropriate random variables (atomic masses, site energies, trap depths) has a delta function at its lower (upper) bound, the Lifshitz singularities are pure exponentials. We study in a quantitative way how these singularities are affected by a universal logarithmic correction for continuous distributions starting with a power law. We derive an asymptotic expansion of the Lifshitz tail to all orders in this logarithmic variable. For distributions starting with an essential singularity, the exponent of the Lifshitz singularity itself is modified. These results are obtained in the example of harmonic chains with random masses. It is argued that analogous results hoid in higher dimensions. Their implications for other models, such as the long-time decay in trapping problems, are also discussed.     

Predicting the long tail of book sales: Unearthing the power-law exponent

The concept of the long tail has recently been used to explain the phenomenon in e-commerce where the total volume of sales of the items in the tail is comparable to that of the most popular items. In the case of online book sales, the proportion of tail sales has been estimated using regression techniques on the assumption that the data obeys a power-law distribution. Here we propose a different technique for estimation based on a generative model of book sales that results in an asymptotic power-law distribution of sales, but which does not suffer from the problems related to power-law regression techniques. We show that the proportion of tail sales predicted is very sensitive to the estimated power-law exponent. In particular, if we assume that the power-law exponent of the cumulative distribution is closer to 1.1 rather than to 1.2 (estimates published in 2003, calculated using regression by two groups of researchers), then our computations suggest that the tail sales of Amazon.com, rather than being 40% as estimated by Brynjolfsson, Hu and Smith in 2003, are actually closer to 20%, the proportion estimated by its CEO.     

背景气体对金属原子二维平面蒸发过程的影响

在原子蒸气法激光分离同位素中,金属原子蒸气宏观物理性质的空间分布会直接影响到分离过程的电离率和原料利用率.本文从分离过程的实际需求出发,建立了双组分气体的Bhatnagar-Gross-Krook模型方程组,并利用数值计算方法对方程进行求解,研究了背景气体对二维平面蒸发过程中原子蒸气宏观物理性质和蒸发速率的影响.研究结果表明:随着背景气体密度的增加,远离蒸发源位置处的金属原子蒸气密度增大,速度减小,温度升高,而近蒸发源位置处原子蒸气的性质则几乎不受影响,因而蒸发速率基本上不随背景气体密度发生变化.另外,随着尾料板温度的升高和对原子蒸气吸收率的增加,金属原子蒸气宏观物理性质受背景气体的影响逐渐下降.理论计算的结果对于分离装置的真空设计和光斑分布设计有较为重要的参考意义.     

The role that conduction band tail states play in determining the optical response of hydrogenated amorphous silicon

We aim to explore the role that conduction band tail states play in shaping the optical response of hydrogenated amorphous silicon. We do so within the framework of an empirical model for the valence band and conduction band density of states functions, one that considers valence band band, valence band tail, conduction band band, and conduction band tail states. We examine the sensitivity of the joint density of states function to variations in the conduction band tail breadth, all other parameters being held fixed at their nominal hydrogenated amorphous silicon values. We find that when the conduction band tail is narrower than the valence band tail, its role in shaping the corresponding spectral dependence of the joint density of states function is relatively minor. This justifies the use of a simplified empirical model for the density of states functions that neglects the presence of the conduction band tail states in the characterization of the optical response of this material. Experimental data corresponding to hydrogenated amorphous silicon, demonstrating that the conduction band tail breadth is always less than the valence band tail breadth for this material, is then presented. Finally, fundamental reasons for the observed asymmetry in the band tail breadths are reviewed.     

Methods of estimation of equilibrium charge distribution of ions in solid and gaseous media

The new version of theoretical estimation of equilibrium charge distribution of ions passing through the matter is proposed. This estimation is based on the correction of charge exchange cross sections for gases taking into account the density effect. The results of calculations are compared with experimental data and with empirical estimation based on the averaging of experimental data for charge distributions of ions in gases and solids. The theoretical method describes the experimental oscillations of width of the charge distribution in contrast to the empirical method.     

Rare events in a log-Weibull scenario - Application to earthquake magnitude data

We discuss the pertinency of the log-Weibull model in the statistical understanding of energy release for earthquake magnitude data. This model has many interesting features, the most remarkable of which being: depending on the value of the deformation index of the source, it may present tails ranging from moderately heavy () to very heavy (with tail index zero as ), through hyperbolic (power law) for the critical value . Under this model (for which a precise tail study is supplied), the occurrence of power laws appears as a critical phenomenon: this reinforces the current trend predicting that some departure from the ideal (strictly scaling fractal) model may be ubiquitous. Having applied an affine transformation in the logarithmic scale, quantile estimation and the Kolmogorov-Smirnov statistics are used to fit the log-Weibull distribution to a realization of an iid sample. This enables to decide whether the upper tail of the phenomenon under study is light/heavy/very heavy. A comparative study of recorded French and Japanese earthquake magnitudes suggests that they exhibit comparable tail behaviour, albeit with different centrality and dispersion parameters. Received 15 March 1999 and Received in final form 20 May 1999     

双声道波导中低频环境噪声分布特性

针对北极冰下双声道波导的噪声分布特性研究,采用垂直阵对双声道波导内的噪声场进行了观测,北极冰下噪声物理模型使用混合加性噪声模型描述,统计分布模型使用α稳定分布描述.并将噪声划分为3个频段,按噪声来源分为背景噪声、冲击噪声以及航船噪声3种场景,分析其统计特性,给出了直方图统计、核函数估计与正态分布的比较结果,α稳定分布参数估计结果,峰度与偏度的计算结果以及累积分布函数检验结果。经分析讨论,给出结论:双声道波导中的噪声统计分布可用α稳定分布来描述,但上下表面声道的分布参数具有明显差别,上表面波导背景噪声明显偏离高斯分布而下表面声道的背景噪声接近于高斯分布;上下表面声道中不同频带的噪声分布差异也很明显,其中2~30 Hz差异性最大,30~100 Hz差异性较大,而100~500 Hz差异性相对较小,并且可以认为是对称α稳定分布.此外,上下表面声道中不同频带噪声α稳定特征参数变化也存在差异,上表面波导受冲击噪声影响α值变大,拖尾变薄;而下表面波导受冲击噪声影响α值则会变小,拖尾变重。      

Modeling and analysis of an agent-based model for Chinese stock market

We constructed an agent-based stock market model which concisely describe investors? heterogeneity and adaptability by introducing price sensitivity and feedback time. Under different parameters, the peak and fat-tail property of return distribution is produced and the obtained statistic values coincide with empirical results: the center peak exponents range from ?0.787 to ?0.661, and the tail exponents range from ?4.29 to ?2.37. Besides, long-term correlation in volatility is examined by DFA1 method, and the obtained exponent α is 0.803, which also coincides with the exponent of 0.78 found in real market.     

临近空间气象火箭探测资料精度的综合评估

为综合分析评估2004年11月在中国酒泉卫星发射中心的首次临近空间气象火箭探测资料精度, 分别利用经验预报模式资料和卫星遥感资料进行对比. 分析结果表明, 由于经验预报模式时空分辨率低, 同时缺乏中国区域平流层的中上部以上高度的探测数据, 在平流层中上部以上高度与气象火箭探测资料的偏差较大; 相比于经验预报模式, 气象火箭探测资料与卫星资料的偏差明显减小, 偏差主要由两者的系统性误差和对比点在时间及经纬度的差异造成的. 综合对比结果表明, 相比于经验预报模式资料和卫星遥感资料, 气象火箭探测资料的精度较高,具有较强的可信度, 可对其他方式的探测结果进行标定. 关键词： 临近空间 气象火箭 经验预报模式 精度评估     

Dependence of the density distribution of 208Pb on the occupation probabilities of shell-model orbits

An independent-particle model for the proton density distribution of ²⁰⁸Pb is constructed; it closely approximates the Hartree-Fock calculation of Dechargé and Gogny. We investigate the modifications which arise when one introduces a depletion of the Fermi sea of the amount suggested by analyses of recent electron scattering data and by nuclear-matter calculations. The main effect of the depletion is to flatten the density distribution in the nuclear interior. The calculated density is in good agreement with the empirical one near the nuclear centre but is too small in the vicinity of 5 fm. The main consequences of the depletion are shown to be largely independent of the details of the model. It is concluded that Hartree-Fock single-particle wave functions which yield good agreement with empirical density distributions are rather different from the natural orbitals. Accordingly they should not be expected to yield a good approximation to the off-diagonal elements of the one-body density matrix, e.g. to the momentum distribution.     

Evolutionary model of the personal income distribution

The aim of this work is to develop a qualitative picture of the personal income distribution. Treating an economy as a self-organized system the key idea of the model is that the income distribution contains competitive and non-competitive contributions. The presented model distinguishes between three main income classes. 1. Capital income from private firms is shown to be the result of an evolutionary competition between products. A direct consequence of this competition is Gibrat’s law suggesting a lognormal income distribution for small private firms. Taking into account an additional preferential attachment mechanism for large private firms the income distribution is supplemented by a power law (Pareto) tail. 2. Due to the division of labor a diversified labor market is seen as a non-competitive market. In this case wage income exhibits an exponential distribution. 3. Also included is income from a social insurance system. It can be approximated by a Gaussian peak. A consequence of this theory is that for short time intervals a fixed ratio of total labor (total capital) to net income exists (Cobb–Douglas relation). A comparison with empirical high resolution income data confirms this pattern of the total income distribution. The theory suggests that competition is the ultimate origin of the uneven income distribution.     

非球对称电离层掩星数据反演

电离层掩星数据的传统反演方法是电离层球对称假设下的Abel变换反演方法,但是实际的电离层电子密度分布不是球对称的,电离层的非球对称分布给电离层电子密度反演带来误差.发展了一种新的非球对称电离层掩星反演方法,利用国际参考电离层模型提供的三维电离层电子密度分布先验信息来修正掩星总电子含量 ,再通过球对称假设下的Abel变换反演出电离层电子密度.利用新方法反演了星座气象、电离层和气候观察系统掩星实测数据,并将得到的反演结果与电离层探测器资料进行了比较.结果表明,新方法能够较好地反演出电离层电子密度. 关键词： 电离层掩星 电子密度 国际参考电离层模型     

基于非参数方法的频率密度分布计算及其并行优化

跳频序列预测是信息对抗的关键问题之一。基于跳频序列具有的伪随机特性和数据之间连续分布的相似性,采用非参数密度估计方法计算并预测出频率的大概率分布区间,进而用于引导通信的梳状灵巧干扰。针对实际应用对实时性的要求,在多结点多核平台上实现了基于消息传递机制的可扩展计算。测试表明,并行程序计算结果正确,并且具有较好的可扩展性。     

面向对象分析的非结构化背景目标高光谱探测方法研究

针对非结构化背景探测器中背景协方差矩阵估计的局限性,提出了一种基于面向对象分析的高光谱小目标探测算法。首先对图像进行自适应迭代分割处理,将其划分为许多均质对象;然后进行正态最优分布选取,利用多元正态无偏检验选取最佳对象集;最后将此数据集合作为局部背景并结合GLR基准算法进行目标探测。该算法可以使局部背景最大化的服从正态分布,有效地将背景光谱信息和目标光谱信息分离开来,同时通过最优选取过程克服了目标信息“污染”问题。为了验证算法的有效性,利用真实的OMIS数据进行仿真实验,并与非结构化背景探测器GLR和基于K-Means聚类的改进GLR算法的检测结果比较,结果表明提出的算法具有良好的探测性能和较低的虚警概率。     

Living in an irrational society: Wealth distribution with correlations between risk and expected profits

Different models to study the wealth distribution in an artificial society have considered a transactional dynamics as the driving force. Those models include a risk aversion factor, but also a finite probability of favoring the poorer agent in a transaction. Here, we study the case where the partners in the transaction have a previous knowledge of the winning probability and adjust their risk aversion taking this information into consideration. The results indicate that a relatively equalitarian society is obtained when the agents risk in direct proportion to their winning probabilities. However, it is the opposite case that delivers wealth distribution curves and Gini indices closer to empirical data. This indicates that, at least for this very simple model, either agents have no knowledge of their winning probabilities, either they exhibit an “irrational” behavior risking more than reasonable.