The Effect of Prior Probability on Skill in Two-Group Discriminant Analysis

Although the weights in a discriminant function (both linear and quadratic) are independent of group prior probabilities, the performance of the classifier (on the training and validation data) is sensitively dependent on these often unknown probabilities. After reviewing some defects of a popular measure of performance in the situation where the group sizes are naturally disproportionate, three alternative measures of performance (or association) are considered and it is shown that the behavior of the measures as a function of group prior probability is different between measures. Consequently, the optimum choice of the group prior probability depends on the specific measure of performance. Among the measures considered, only two measures - the index of mean square contingency and the Heidke Skill Statistic - are found to be well defined in the disparate-group size situation, and are, therefore, recommended. An empirical data set, dealing with delinquency among high school students is employed to illustrate all of the findings.     

统计效力和效应量的估计方法与应用

如果假设检验不能告诉我们差异的大小与犯β错误的概率,应将统计效力和效应量作为补充文章介绍了统计效力和效应量的含义、估计方法与应用。     

控制多元质量特性的方法

介绍了工序中同时控制多个相关质量特性均值向量的T2控制图方法。该方法用T2作为统计量,可简捷地画出控制图,监控工序有无失控现象。给出了计算公式及计算实例。     

Multivariate t and beta distributions associated with the multivariate F distribution

Relationships between F, skew t and beta distributions in the univariate case are in this paper extended in a natural way to the multivariate case. The result is two new distributions: a multivariate t/skew t distribution (on ℜ^m) and a multivariate beta distribution (on (0,1)^m). A special case of the former distribution is a new multivariate symmetric t distribution. The new distributions have a natural relationship to the standard multivariate F distribution (on (ℜ⁺)^m) and many of their properties run in parallel. We look at: joint distributions, mathematically and graphically; marginal and conditional distributions; moments; correlations; local dependence; and some limiting cases. Received: March 2001     

粗骨料级配对普通和高强度等级机制砂混凝土性能的影响

粗骨料对混凝土的工作性能、力学性能和耐久性具有很大影响,因此,选择粗骨料级配非常重要。本文将三种粒度粗骨料按不同比例进行混合,研究了粗骨料级配对普通和高强度等级机制砂混凝土的性能影响。结果表明:三级配粗骨料制备的普通强度等级混凝土的强度最高;对高强度等级混凝土而言,两级配粗骨料制备的混凝土强度最高。粗骨料比表面积对普通强度等级混凝土性能影响较大,而粗骨料堆积空隙率对高强度等级混凝土性能影响较大。     

The Effect of Sample Size on the Mean Efficiency in DEA with an Application to Electricity Distribution in Australia,Sweden and New Zealand

This study examines the effect of sample size on the mean productive efficiency of firms when the efficiency is evaluated using the non-parametric approach of Data Envelopment Analysis. By employing Monte Carlo simulation, we show how the mean efficiency is related to the sample size. The paper discusses the implications for international comparisons. As an application, we investigate the efficiency of the electricity distribution industries in Australia, Sweden and New Zealand.     

膨胀土土体抗剪强度参数测定试样尺寸效应

文章在大量试验资料的基础上,论述测定膨胀土抗剪强度时试样尺寸对抗剪强度参数的影响,从而指出测定膨胀土抗剪强度时的合理试样直径及C、Φ值的确定方法。     

Multivariate L1 mean

The center of a univariate data set {x ₁,…,x _n} can be defined as the point μ that minimizes the norm of the vector of distances y′=(|x ₁−μ|,…,|x _n−μ|). As the median and the mean are the minimizers of respectively the L ₁- and the L ₂-norm of y, they are two alternatives to describe the center of a univariate data set. The center μ of a multivariate data set {x ₁,…,x _n} can also be defined as minimizer of the norm of a vector of distances. In multivariate situations however, there are several kinds of distances. In this note, we consider the vector of L ₁-distances y′₁=(∥x ₁- μ∥₁,…,∥x _n- μ∥₁) and the vector of L ₂-distances y′₂=(∥x ₁- μ∥₂,…,∥x _n-μ∥₂). We define the L ₁-median and the L ₁-mean as the minimizers of respectively the L ₁- and the L ₂-norm of y ₁; and then the L ₂-median and the L ₂-mean as the minimizers of respectively the L ₁- and the L ₂-norm of y ₂. In doing so, we obtain four alternatives to describe the center of a multivariate data set. While three of them have been already investigated in the statistical literature, the L ₁-mean appears to be a new concept. Received January 1999     

Limit theorems for multivariate discrete distributions

According to the usual law of small numbers a multivariate Poisson distribution is derived by defining an appropriate model for multivariate Binomial distributions and examining their behaviour for large numbers of trials and small probabilities of marginal and simultaneous successes. The weak limit law is a generalization of Poisson's distribution to larger finite dimensions with arbitrary dependence structure. Compounding this multivariate Poisson distribution by a Gamma distribution results in a multivariate Pascal distribution which is again asymptotically multivariate Poisson. These Pascal distributions contain a class of multivariate geometric distributions. Finally the bivariate Binomial distribution is shown to be the limit law of appropriate bivariate hypergeometric distributions. Proving the limit theorems mentioned here as well as understanding the corresponding limit distributions becomes feasible by using probability generating functions.     

有关企业规模界定的评析

各国对企业规模界定采用的划分指标主要有两类:定量指标与定性指标.我国一直以定量划分为主.在操作性方面存在不足.针对市场经济发展实际和参与国际竞争的需要,2003年我国又调整了企业规模界定的标准.作者认为,无论采用什么标准,对企业规模的界定都不能只停留在对企业经营活动的表层描述上.企业规模的选择取决于企业在市场中的竞争行为,是企业适应市场竞争需要、市场规则自然选择的结果,故企业单纯做大或做小都是不适宜的.     

The Effect of Sample Size on the Mean Efficiency in DEA: Comment

Zhang and Bartels (1998) show formallyhow DEA efficiency scores are affected by sample size. They demonstratethat comparing measures of structural inefficiency between samplesof different sizes leads to biased results. This note arguesthat this type of sample size bias has much wider implicationsthan suggested by their example. Models which implicitly restrictthe comparison set like some models for non-discretionary variableslead to biased efficiency scores as well. A reanalysis of theBanker and Morey (1986b) data shows that the efficiency scoresderived there are significantly influenced by the variation insample size implicit in their model.     

Percentage Points of the Multivariate t Distribution

The known methods for computing percentage points of multivariate t distributions are reviewed. We believe that this review will serve as an important reference and encourage further research activities in the area.     

GIS支持下的昆明市中小学分布及其影响因素研究

本文分析了城市中小学存在的问题及影响学校分布的因素,运用GIS空间分析方法,对昆明市中小学分布进行了研究,提出布局调整建议,为优化城市中小学空间布局提供参考。     

基于多元统计分析的葡萄酒及其理化指标评价研究

文中以2012年大学生数学建模竞赛A题为背景,针对我国葡萄酒业内缺乏利用理化指标对葡萄酒进行评级的现状,特别根据已知的葡萄酒质量评定结果、对应的酿酒葡萄和葡萄酒的理化指标以及芳香物质,进行多元统计分析,讨论通过理化指标控制葡萄酒质量的可行性问题,通过运算验证解决了评酒员可靠与否以及理化指标与葡萄酒质量之间关联程度的相关问题。     

On subset selection from logistic populations

Some distributional results are derived for subset selection from logistic populations, differing only in their location parameter. The probability of correct selection is given. Exact and numerical results concerning the expected subset size are presented.     

Multivariate stable ARMA processes with time dependent coefficients

This paper considers the class of m-variate autoregressive moving average (ARMA) processes with stable innovations and time dependent coefficients. A set of suitable AR and MA regularity conditions is given to ensure existence and uniqueness of valid solutions. A simple form of the above solution is expressed in terms of one sided Green's matrix functions associated with the AR operator. We solve the prediction problem arising in this class of models. A few examples are added to support the general theory.     

基于分形理论谈安徽沿江环湖城市群的建立

简要介绍了分形理论的原理,运用分形理论,借助于罗特卡公式分析安徽省城市体系规模分布的分形特征,发现安徽省城市体系规模分布符合位序—规模率,存在城市体系规模分布过于均衡及首位城市、大城市规模过小的问题。提出建立安徽省沿江环湖城市群规模体系的发展对策。     

Corporate Governance and Performance of Indian Firms: The Effect of Board Size and Ownership

The paper reviews international literature on corporate governance and firm performance and investigates the relationship in the Indian context, taking into account the endogeneity in the relationship. Governance parameters include board size, directors’ shareholding, institutional and foreign shareholding, while the fragmentation in shareholding is captured by public shareholding. A simultaneous equation regression model for Tobin’s Q, as a measure of firm performance, is attempted using these variables, while controlling for industry effects and other non-governance variables. The data corresponds to a panel of 340 large, listed Indian firms for the period 1997–2001 spread across 24 industry groups.