法庭科学中检材和比对的统计检验问题

本文将法庭科学中检验检材和比对是否同一的问题转化为多元统计的假设检验问题，将多元统计的检验方法应用到法庭科学中，取得了初步成果．     

教学质量评估的统计分析法

教学评估是一项主观性很强的工作 ,因而是复杂的 ,其结果很可能偏离被评估对象的根本属性。为确保评估的公正、科学、准确 ,有必要对实测数据进行统计分析。本文首先采用稳定度检验和卡方检验来分析各项指标的评估结果是否具有可信性 ;其次 ,通过对各项指标评价结果的集中趋势进行统计分析 ,以检验量化误差是否在可接受的范围内 ;最后 ,运用符号秩次检验法对各项评估指标的权重是否合理进行统计分析。这些统计分析方法的应用 ,经实践证明是合理的 ,能够衡量评价结果的真实程度 ,从而保证了教学质量评估工作的顺利进行     

一种检验定性指标的有效方法

介绍了一种检验定性指标的有效方法,可用于确定产品的合格率和评价检验人员的检验水平。用该方法分析了某厂产品的一项实际指标,合格率为91 4%,还对该厂10名检验员的检验水平作了客观的评价。     

关于具有最小第二原子键连通性指标的单圈图

由Graovac和Ghorbani定义的另一种新的原子键连通性指标, 我们称之为第二原子键连通性指标(简记为$ABC_{2}$). 它为研究分子特征提供了方便, 且其极值问题是研究的重点. 本文通过分式比较, 给出了$n$个顶点的具有最小$ABC_2$指标的单圈图及其结构性质.     

一种新型粗糙集的指标筛选模型及实证分析

针对现有指标筛选方法不能将指标客观数据和指标实际含义同时处理的弊端,研究提出了一种新型粗糙集指标筛选方法,并对绿色经济下的社会可持续发展评价指标体系构建进行了实证分析.方法同时将粗糙集决策表的相对约简理论与信息表的属性约简理论相结合,既保证了筛选的客观性又兼顾了指标的实际含义,其主要做法一是通过布尔推理算法,保证了连续型指标离散化过程中候选断点的最优组合,为粗糙集约简提供了高准确率的信息表数据;二是考虑了指标的实际含义,通过对有因果关系的指标构成的决策表进行相对约简,删除了指标信息间的冗余指标;三是通过对无实际联系的指标构成的信息表进行属性约简,删除了研究指标客观数据中的冗余指标.     

单指标众数模型的统计诊断及在波士顿房价分析中的应用

在金融、经济、社会科学、气候科学、环境科学、工程技术和生物医学等领域,数据分布常常呈现出尖峰厚尾的特征,且密度分布是不对称的有偏分布。此时,单指标众数模型是刻画这些特征的一个重要方法。为此,非常有必要研究该模型下的统计诊断。本文将考虑单指标众数模型基于数据删除模型和众数漂移模型的统计诊断与局部影响分析。模拟研究和波士顿房价数据的结果表明所提出的方法是有效和可行的。     

单指标回归模型的若干检验问题

在参数和非参数回归模型中,关于异方差检验、一阶自相关存在性检验以及附加变量检验问题都有很多的研究.文中利用P-样条方法,研究了单指标模型的异方差、一阶自相关存在性及附加变量检验问题,分别得到了三种情况下的Score检验统计量,最后给出计算机模拟和实际例子,证实了文中所提出的方法的可行性和有效性,推广和发展了先前的工作.     

基于集值统计原理的多指标灰靶决策方法研究

针对区间数多指标群决策问题,提出一种基于集值统计模型的改进灰靶决策方法。首先利用集值统计模型对多专家的区间评价进行估计,得到符合可信度要求的决策指标样本矩阵。然后利用基于加权广义马氏距离的灰靶决策方法对决策方案进行排序,给出决策样本为区间数群决策矩阵形式的灰靶决策模型。最后通过一个具体的算例给出决策方法的过程,避免了马氏距离不存在的情况,克服了决策指标间的相关性、重要性差异和不同量纲对决策过程和决策结果的影响,方法的可行性与有效性得到验证。     

基于多层次分析模型的中国居民消费能力评估

建立了多层次统计分析模型来考察中国居民的消费能力.在模型中,分析了居民在消费过程中面临的内在冲击和外在冲击,并定量地测定了外在冲击和内在冲击对消费能力的影响.实证研究发现,中国农村消费能力不足来源于农村居民的绝对收入过低,农村居民主要面临外在消费冲击;中国城市居民消费能力相对较高.但面临着较大的消费波动.城市居民主要面临消费的内在冲击.     

探析习题教学中学生优良思维品质的培养

习题训练不仅可以加深学生对知识的理解,还可以加强学生的综合运用能力和信息获取能力．实践研究表明,思维能力是各种能力的基础,而只有具备了优良的思维品质,才可以具备较高程度的思维能力．本文将浅谈如何通过习题教学培养学生的思维品质．     

Principal components in the nonnormal case: The test of equality of Q roots

The limiting distribution of the likelihood ratio statistic W_q for testing the hypothesis of equality of q characteristic roots of a covariance matrix is studied in the case of nonnormal populations. It is shown, both theoretically and empirically, that the limiting distribution of W_q is not robust to departures from normality and that W_q cannot be used for nonnormal populations with long tails. For the class of elliptical populations the limiting distribution of W_q can be expressed in close form. A corrected test statistic, W_q^*, is proposed that can be used in principal component analysis when sampling from elliptical populations.     

New results for the Liebau phenomenon via fixed point index

We prove new results regarding the existence of positive solutions for a nonlinear periodic boundary value problem related to the Liebau phenomenon. As a consequence we obtain new sufficient conditions for the existence of a pump in a simple model. Our methodology relies on the use of classical fixed point index. Some examples are provided to illustrate our theory. We improve and complement previous results in the literature.     

Further results on atom-bond connectivity index of trees

The atom-bond connectivity (ABC) index of a graph G is defined as

     

教师对教学质量影响程度的单因素方差分析

用单因素方差分析的方法,对同年级26个班级数学期终考试成绩进行分组分析,并得到结论,教师在教学过程中起主导作用,但教师不是影响教学质量的首要因素.     

More accurate breakdown voltage estimation for the new step-up test method in the gumbel distribution model

The estimation problems for the conventional step-up method (the observed breakdown voltages are not given at all) and the new step-up method (some of the observed breakdown voltages are given) are analyzed when the underlying probability distribution (of breakdown voltage level) is assumed to be gumbel distributions for minima and maxima. The new step-up test method has advantages compared to the conventional method: (1) the confidence intervals of the estimates become smaller and (2) the estimates can be obtained with higher probability. In some case of real step-up breakdown voltage test, a fit of the gumbel distribution to the data case is found to be superior to that of the normal distribution, which suggests the usefulness of the gumbel distribution for the underlying distribution in the step-up breakdown voltage test.     

Use of the Szeged index and the revised Szeged index for measuring network bipartivity

We have revisited the Szeged index (Sz) and the revised Szeged index (Sz^∗), both of which represent a generalization of the Wiener number to cyclic structures. Unexpectedly we found that the quotient of the two indices offers a novel measure for characterization of the degree of bipartivity of networks, that is, offers a measure of the departure of a network, or a graph, from bipartite networks or bipartite graphs, respectively. This is because the two indices assume the same values for bipartite graphs and different values for non-bipartite graphs. We have proposed therefore the quotient Sz/Sz^∗ as a measure of bipartivity. In this note we report on some properties of the revised Szeged index and the quotient Sz/Sz^∗ illustrated on a number of smaller graphs as models of networks.     

学生体质评价模型的构建与分析

利用组合群验的理论和方法构建了学生体质评价数学模型,在这一模型基础上介绍了该模型的应用方法,为评价学生体质提供了新方法.     

Optimal decision indices for R&D project evaluation in the pharmaceutical industry: Pearson index versus Gittins index

This paper examines issues related to various decision-based analytic approaches to sequential choice of projects, with special motivation from and application in the pharmaceutical industry. In particular, the Pearson index and Gittins index are considered as key strategic decision-making tools for the selection of R&D projects. It presents a proof of optimality of the Pearson index based on the Neyman–Pearson lemma. Emphasis is also given to how a project manager may differentiate between the two indices based on concepts from statistical decision theory. This work demonstrates and justifies the correct use of the Pearson index.