对时期数和时点数的再思考

在统计学原理中,绝对指标根据指标反映的时间不同将其分为时期指标和时点指标。一般认为:时期指标反映的是社会经济现象在一定时期内达到的总数量,是一个流量,如年产量、销售额等。时期指标对某一变量的具体数值就是时期数。时点指标反映的是社会经济现象在某一时点(时刻)上达到的规模或者水平,是一个存量,如年末人口数、商品库存量等。同样,时点指标对某一变量的具体数值就是时点数。     

《统计基础知识》辅导思考题及答案

第一章总论（一）名词解释；（略）1、总体2、总体单位3、标志4、指标5、变异6、变量（二）填空题：1、统计资料是通过统计工作取得，用来反映社会经济现象的数字资料的总称．2、统计的特点为数量性、总体性、具体性、社会性。3、总体单位是构成总体的个别事物，它是总体的基本单位。4、统计总体中所包括的单位数是有限的，则称有限总体，反之是无限总体．5、标志是说明总体单位的特征的名称，标志分为品质标志和数量标志．6、品质标志表示总体单位的品质属性的待征，是不能用数值来表示的．7、数量标志是表示总体单位的数量的特征，只能用…     

平均数与强度相对数的区别

平均数与强度相对数是初学者很容易混淆的两种指标,其实它们的性质和作用是根本不同的。1．性质不同。平均数反映同一总体内各单位数量标志的一般水平,它是同质总体的标志总量与总体单位数之比。不同总体的数值是不能平均的。而强度相对数则是一个表明现象之间的数量对比关系的相对指标,它反映两个相互联系的总体之间的对比关系。     

对三大数值平均数之关系成立的条件补充

大多数《统计学原理》教科书把平均数分成两大类 :一类是数值平均数 ,包括算术平均数、调和平均数和几何平均数 ;另一类是位置平均数 ,包括众数、中位数等。而且都认为 ,对同一数列计算的三大数值平均数之间存在这样的数量关系 ,即几何平均数大于调和平均数而小于算术平均数 ,只有当所有的变量值相同时 ,三大平均数才相等。用数学公式表示 ,它们之间的关系式为 : Ｘ≥Ｇ≥Ｈ笔者以为 ,上述三大数值平均数之关系成立的条件是 :数列中的各个变量值都为正数 ,不能为负数和零。现举例说明 ,在数列中 ,若有负数和零 ,上述关系不能成立。例一 ,甲…     

统计理念与统计思维的培养

统计学不仅仅是一种方法与手段，而且是一种意识和理念。在国外一些发达国家，对统计尤为重视，从中学甚至从小学，就开设介绍统计方法和知识的课程。因为学习统计学可以提高学生的综合素质，其中包括对实际问题进行调查、分析和研究的能力，也有利于培养学生发现问题、分析问题和解决问题的能力。统计学不论是数理统计或社会经济统计，它们具有两大共性，一是总体性，二是数量性。总体性告诉人们要从全面看问题、整体看问题，防止以点代面、认识片面。数量性启示人们要重视数量研究，掌握事物的数量特征和数量关系，做到心中有“数”。这两…     

论回归分析中的两类误差

一、问题的提出回归分析是利用回归方程（函数）研究总体变量间依存关系的一种专门方法。由于研究总体的大量性所决定，实践中，回归分析一般是依据样本资料进行的，是一个以样本观察的数量关系──样本回归函数（SRF，或称经骏函数）去推断总体真实的数量关系──总体回归函数（PRF）的抽样推断过程。以一元线性回归为例，设：总体回归模型（2）（X1，Y1），（X2，Y2）……（Xn，Yn）为取自总体的一个样本，拟合得：SRF：（3）回归分析的过程实质上就是用（3）式估计（2）式，从而对总体进行经济预测、结构分析、政策评价等。显然，…     

对强度相对数中有关问题的研究

文章对统计学中强度相对数的概念及其与算术平均数、结构相对数、比例相对数的区别作了研究，探讨了“性质不同”与“强度”的含义。认为强度相对数是两个相关联的不具有同一总体的标志总量与单位总量关系或从属关系或可加关系的非同类指标值对比，用以说明相关联的非同类事物事（或现象）之间相互作用力的对比度（包括分布密度、普遍化程度、相互影响程度和对比关联程度）的综合指标     

基于工作抽样的生产线平衡的实证研究

一、工作抽样原理工作抽样是根据数理统计的理论,以概率法则作为基础的方法,从母集团(总体)中随机地取样本,如果这个样本足够大,则从样本的性质可以推断出母集团(总体)的状态。由于它不是全数调查,所以就会产生误差,这又取决于抽样的数量(即观测次数)。抽样数越多可靠性就越高;反之,可靠性就越低。但是抽样次数多,人力、物力、财力的消耗将增加。因此就必须考虑可靠度与精度的问题。     

加强对经济现象结构的研究

现代系统理论认为,任何一个具体的系统整体都由三个因素决定,即构成要素的性质、数量和结构。构成要素的结构称为系统的序。任何事物都是质、量、序的统一体,当事物的量变或序变达到一定限度后,都会引起事物的质变。这一思想对发展我国的社会经济统计很有启发。目前的统计理论仅仅从质与量的统一上把握社会经济现象的数量变化,忽视了对事物结构的认识,这不利于对社会经     

我国经济周期波动的统计特征

统计学具有两大特征:一是总体性,二是数量性。总体性是研究社会经济现象发展变化的总趋势和本质属性,以消除偶然因素的影响,达到正确认识社会经济现象本质的目的。数量性则是从数量上观察、研究社会经济现象的属性表现,寻找其发展变化规律,在质与量的统一中全面认识社会经济现象的本质。用统计学的这两大特征研究我国经济的周期波动,既具有全面性,又具有深刻性。一、我国经济周期波动的总体性近年来,我国经济理论工作者在进行大量实证分析的基础上,对我国经济周期波动产生的原因进行了深入的分析,并形成了以下几种主要观点:1)我国的经济周期波动属于货币推动型,因为国家对货币供应量的宏观调控松紧有度,因此国民经济的总体运行随着市场上资金流量的多少涨跌起伏。2)我国的经济周期波动属于消费拉动型,社会主义生产     

平均数是非评说

近十年来,随着我国统计打假力度的加大,统计体制改革步伐的加快,统计数字和统计计算分析方法透明度和公开度的提高,人们对官方和有关部门发布的统计数字的关注程度,监督力度、参与意识加强,鉴别力提高。人们不但敢于公开揭露虚假瞒报的统计数字,而且敢于公开质疑一些政府部门和媒体上发表的统计数字的准确性和可信     

Inferences on the Number of Unseen Species and the Number of Abundant/Rare Species

This paper focuses on estimating the number of species and the number of abundant species in a specific geographic region and, consequently, draw inferences on the number of rare species. The word 'species' is generic referring to any objects in a population that can be categorized. In the areas of biology, ecology, literature, etc, the species frequency distributions are usually severely skewed, in which case the population contains a few very abundant species and many rare ones. To model a such situation, we develop an asymmetric multinomial-Dirichlet probability model using species frequency data. Posterior distributions on the number of species and the number of abundant species are obtained and posterior inferences are induced using MCMC simulations. Simulations are used to demonstrate and evaluate the developed methodology. We apply the method to a DNA segment data set and a butterfly data set. Comparisons among different approaches to inferring the number of species are also discussed in this paper.     

Sum of a Random Number of Correlated Random Variables that Depend on the Number of Summands

The mean and variance of a sum of a random number of random variables are well known when the number of summands is independent of each summand and when the summands are independent and identically distributed (iid), or when all summands are identical. In scientific and financial applications, the preceding conditions are often too restrictive. Here, we calculate the mean and variance of a sum of a random number of random summands when the mean and variance of each summand depend on the number of summands and when every pair of summands has the same correlation. This article shows that the variance increases with the correlation between summands and equals the variance in the iid or identical cases when the correlation is zero or one.     

文字与数字的学问

有所谓<文字的学问>,一直是人类文明重要的宝藏,扮演着举足轻重的角色;亦有所谓<数字的学问>,在人类历史的洪流中常被轻忽.早期文官体系选用人才,以咱们中国老祖宗的科举制度为例,比的是文字的学问;历史上无论是脍炙人口或是震古铄今的巨著,以及那些能名留千古的人,亦以文学大师居多;即使在今日,联合国所谓世界各国的文化水平,主要亦以<识字率>做为衡量的指标,而此识字率即意指文字的能力;相形之下,数字学问并未受到同等的重视.虽然我们口中一直强调数学为科学之母.科技的进步和数字的水平确实有密切关系,但吾等身为数字教育者当扪心自问,数字学问受重视的程度能与文字学问相提并论吗?翻开历史文献,文字墨宝处处可见,而数字学问则多半归列在旁门左道、奇门遁甲中.显然地,数字工作者在起跑点上就已落后一大截,也因此有更大的空间待吾等努力改进.     

Zero Acceptance Number Chained Quick Switching System

Zero acceptance number sampling inspection plans are commonly employed for compliance sampling and audit inspection purposes. The discriminatory power of zero acceptance number sampling plans is rather poor. This article remedies this disadvantage by chaining past lot results within a quick switching system.     

Estimating the Basic Reproductive Number in the General Epidemic Model with an Unknown Initial Number of Susceptible Individuals

Abstract. In any epidemic, there may exist an unidentified subpopulation which might be naturally immune or isolated and who will not be involved in the transmission of the disease. Estimation of key parameters, for example, the basic reproductive number, without accounting for this possibility would underestimate the severity of the epidemics. Here, we propose a procedure to estimate the basic reproductive number ( R ₀ ) in an epidemic model with an unknown initial number of susceptibles. The infection process is usually not completely observed, but is reconstructed by a kernel‐smoothing method under a counting process framework. Simulation is used to evaluate the performance of the estimators for major epidemics. We illustrate the procedure using the Abakaliki smallpox data.     

基于区间灰数与离散灰数双重异构序列的预测建模方法研究

系统变化的复杂性导致了系统行为数据的不确定性与异构性,面向多源信息的数据集结导致了表征系统变化规律的灰色异构时序数据的产生。对面向区间灰数与离散灰数的双重异构数据序列预测建模方法展开研究,通过对区间灰数均匀分割处理,得到与离散灰数灰元数量相等的次级区间灰数,进而实现了灰色异构数据的"同质化"转换;在此基础上构建了面向异构数据序列的灰色预测模型,并应用该模型实现了大桥沉降量的有效模拟与准确预测。研究成果对拓展灰色预测模型应用范围具有积极意义。     

On Exact K-optimal Designs Minimizing the Condition Number

A new design criterion based on the condition number of an information matrix is proposed to construct optimal designs for linear models, and the resulting designs are called K-optimal designs. The relationship between exact and asymptotic K-optimal designs is derived. Since it is usually hard to find exact optimal designs analytically, we apply a simulated annealing algorithm to compute K-optimal design points on continuous design spaces. Specific issues are addressed to make the algorithm effective. Through exact designs, we can examine some properties of the K-optimal designs such as symmetry and the number of support points. Examples and results are given for polynomial regression models and linear models for fractional factorial experiments. In addition, K-optimal designs are compared with A-optimal and D-optimal designs for polynomial regression models, showing that K-optimal designs are quite similar to A-optimal designs.     

Lot Sampling Distributions for Bounded Number of Nonconformities

Attributes sampling is an important inspection tool in areas like product quality control, service quality control or auditing. The classical item quality scheme of attributes sampling distinguishes between conforming and nonconforming items, and measures lot quality by the lot fraction nonconforming. A more refined quality scheme rates item quality by the number of nonconformities occurring on the item, e.g., the number of defective components in a composite product or the number of erroneous entries in an accounting record, where lot quality is measured by the average number of nonconformities occurring on items in the lot. Statistical models of sampling for nonconformities rest on the idealizing assumption that the number of nonconformities on an item is unbounded. In most real cases, however, the number of nonconformities on an item has an upper bound, e.g., the number of product components or the number of entries in an accounting record. The present study develops two statistical models of sampling lots for nonconformities in the presence of an upper bound a for the number of nonconformities on each single item. For both models, the statistical properties of the sample statistics and the operating characteristics of single sampling plans are investigated. A broad numerical study compares single sampling plans with prescribed statistical properties under the bounded and unbounded quality schemes. In a large number of cases, the sample sizes for the realistic bounded models are smaller than the sample sizes for the idealizing unbounded model.