The Tale of Cochran's Rule: My Contingency Table has so Many Expected Values Smaller than 5, What Am I to Do?

In an informal way, some dilemmas in connection with hypothesis testing in contingency tables are discussed. The body of the article concerns the numerical evaluation of Cochran's Rule about the minimum expected value in r × c contingency tables with fixed margins when testing independence with Pearson's X² statistic using the χ² distribution.     

C2C 环境中顾客重复购买行为的实证与建模

通过分析C2C 商家的交易记录, 发现单个商家的顾客重复购买次数呈幂律分布, 这与重复购买理论以往得到的购买次数为负二项分布的结论不同. 基于C2C 交易的实际情况, 建立了具有购买强化效应的购买概率模型, 模型很好的解释了顾客重复购买率呈幂律分布的现象.实证和模型表明, C2C 环境中, 顾客购买次数的分布具有很长的尾部, 大量顾客有低的购买次数, 而少数顾客有很高的重复购买次数;模型还揭示了巨大的潜在顾客数量和顾客多次购买的强化效应是造成重复购买分布呈幂律形式的重要原因.     

蒙古语科尔沁土语词汇研究二题

蒙古书面语mal＂牲畜＂与üker＂牛＂,在科尔沁土语中的语义演变与蒙古书面语ar＂犍牛＂在科尔沁土语中的消失有关。科尔沁土语的xurγb＂绵羊羔＂是蒙古书面语quraγa＂绵羊羔＂在科尔沁土语中元音屈折演变的形式。     

约瑟夫·奈的软权力理论在中国的流行和命运

约瑟夫·奈的软权力学说提出了与硬权力相对的软权力的概念,阐述了它的主要内容及其在国际事务中的作用。奈的软权力学说有其自身的理论缺陷,而中国也出现了对其生吞活剥地解读的倾向,因此,有必要对奈的软权力学说的认识进行审视和整理。     

文化时代的文化力和企业文化力

人类经历了政治时代、经济时代和文化时代。在一切时代,人类的发展都依赖生产力的发展。在政治时代,生产力主要借助政治力而发生作用;在经济时代,生产力主要借助经济力而发生作用。在文化时代,生产力主要借助文化力而发生作用。文化时代的文化力,又突出表现为企业文化力。企业文化力极大地放大了企业创造现代社会生活的能力,成为生产力的关键能力,使企业大大提高了自由、自觉活动的能力。企业文化力的培育,成为企业追求的一个目标;企业文化力的大小,成为企业活动能力的标志。     

Performance characteristics of the adjusted r2 algorithm for determining the start of the terminal disposition phase and comparison with a simple r2 algorithm and a visual inspection method

The adjusted r² algorithm is a popular automated method for selecting the start time of the terminal disposition phase (t_z) when conducting a noncompartmental pharmacokinetic data analysis. Using simulated data, the performance of the algorithm was assessed in relation to the ratio of the slopes of the preterminal and terminal disposition phases, the point of intercept of the terminal disposition phase with the preterminal disposition phase, the length of the terminal disposition phase captured in the concentration‐time profile, the number of data points present in the terminal disposition phase, and the level of variability in concentration measurement. The adjusted r² algorithm was unable to identify t_z accurately when there were more than three data points present in a profile's terminal disposition phase. The terminal disposition phase rate constant (λ_z) calculated based on the value of t_z selected by the algorithm had a positive bias in all simulation data conditions. Tolerable levels of bias (median bias less than 5%) were achieved under conditions of low measurement variability. When measurement variability was high, tolerable levels of bias were attained only when the terminal phase time span was 4 multiples of t_1/2 or longer. A comparison of the performance of the adjusted r² algorithm, a simple r² algorithm, and t_z selection by visual inspection was conducted using a subset of the simulation data. In the comparison, the simple r² algorithm performed as well as the adjusted r² algorithm and the visual inspection method outperformed both algorithms. Recommendations concerning the use of the various t_z selection methods are presented.     

新农村建设背景下的农村中小学布局调整

农村中小学布局调整对于减轻贫困农民负担、节约教育经费、优化教育资源等起到了一定的积极作用。但与此同时也涌现出了一系列社会问题，尤其是在经济落后的农村地区，这些问题更为突出。从新农村建设的背景出发，对布局调整以后农村出现的问题进行了分析，以期对新农村建设与农村的现实基础达到一个认识。     

与四阶矩阵特征问题相关的约束流与完全可积系统

主要讨论与四阶矩阵特征值问题相联系的孤子方程及其Lax上,利用位势函数与特征函数之间的Bargmann约束,将四阶特征值问题及相应的伴随特征值问题非线性化,获得新的有限维Hamilton系统,并应用r-矩阵理论证明了新的有限维Hamilton系统在Liouville意义下的完全可积性。最后借助于在Liouville意义下完全可积Hamilton系统的对合解得到孤子方程族解的对合表示。     

Recurrence relations for the minimum variance unbiased estimator of the probability function of the R distribution

We obtain a new technique to calculate the value of the minimum variance unbiased estimator (MVUE) of the probability function (p.f.) of the R distribution. This technique is based on an investigation of the ratios of r numbers. A recurrence relation for the MVUE of the p.f. of the R distribution is derived. It is interesting that the derived relation does not depend on the r numbers but depends on the ratios of the r numbers. The new method is efficient, convenient and accurate.     

Seasonality Tests

This article modifies and extends the test against nonstationary stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for structural breaks, or by the inclusion of regressors with nonseasonal unit roots. A parametric version of the test is proposed, and its performance is compared with that of the nonparametric test using Monte Carlo experiments. A test that allows for breaks in the seasonal pattern is then derived. It is shown that its asymptotic distribution is independent of the break point, and its use is illustrated with a series on U.K. marriages. A general test against any form of permanent seasonality, deterministic or stochastic, is suggested and compared with a Wald test for the significance of fixed seasonal dummies. It is noted that tests constructed in a similar way can be used to detect trading-day effects. An appealing feature of the proposed test statistics is that under the null hypothesis, they all have asymptotic distributions belonging to the Cramér–von Mises family.