试论调和平均数代表性大小的测定及其应用

调和平均数是社会经济统计中常用的一个平均指标，其在实际中已得到了广泛的应用。但在调和平均数的长期使用过程中，往往忽视了其作为一个平均指标所需进行的代表性大小测定的问题，从而使其在深入统计分析研究中受到了很大的限制。本文拟从调和平均数的特点出发，论述调和平均数代表性大小的测定及其在深入统计分析中的应用。一、调和平均数R其基本特征调和平均数是变量值的倒数的平均数的倒数，其在实际应用中可分为两种情况：第一，为算术平均数的变形。在实际中，由于掌握的资料不同，不能直接利用算术平均数X一计算，而需改用调和平…     

再论统计平均数大小关系的证明及其推广

一、引言统计平均数是统计分析和一般经济分析中广泛运用的指标形式,在统计学中有重要的地位。统计平均数按代表意义和计算方式的不同,可以分为数值平均数和位置平均数,其中常用的数值平均数有算术平均数(-X)、几何平均数(G)和调和平均数(H),三者源于同一个家族———幂平均数(     

平均数指数与综合评价

平均数指数与综合评价山西大学刘锦雯在统计综合评价领域，平均数指数方法得到了广泛的应用。然而，对于平均数指数为何能起到综合评价的作用，它的机理是什么，它和统计综合评价方法之间有何内在联系等问题，还需要进一步从理论上加以探讨。统计指数产生于资本主义商品经...     

谈中位数和众数计算公式推导

谈中位数和众数计算公式推导南昌高等专科学校刘太平平均指标是统计指标的一种重要表现形式，在实际工作中应用极为广泛。常用的平均指标主要有：算术平均数、调和平均数、几何平均数、中位数和众数。前三种平均数属于数值平均数，其数值要受每一个变量值大小影响，所以，...     

物价统计中不宜采用“掐头去尾”平均法

李朝鲜和王心赤同志在《统计》1988年第4期上发表了“物价统计中运用掐头去尾平均法的探讨”一文,认为“掐头去尾平均数是有广泛的适应性,……因其方差最小,而充分体现其优越性.……它在物价统计中有广泛的应用前景.”我们认为这个问题还值得探讨.     

慎用和善用统计平均指标

统计平均指标也称之为统计平均数,是我们最熟悉并且在进行统计分析、评价与决策以及日常管理工作中应用最为广泛的指标之一.然而,人们在应用平均指标时,却经常出现一些使用和理解上的错误.     

均值方差可互补 管理水平能提高

统计的核心是均值与方差。不论我们使用什么统计方法，对现象进行统计分析时，实际上都是在它们的平均数和标准差上做文章。因为平均数和标准差是现象变化的统计规律的两个方面。平均数反映的是现象的集中趋势，是现象的一致性结果；而标准差是现象的离中趋势，反映现象差异性的变化。这两个指标从不同角度描述了现实中事物的对立和统一，即矛盾又一致的情景。因此，对指导现实社会有非常大的作用。在学习统计中，只要充分掌握和理解了平均数和标准差，对统计的其他方法，也就不难理解了。 在现实经济社会中，应用平均数和标准差的领域也…     

浅谈统计预测中权数的应用问题

浅谈统计预测中权数的应用问题沈阳工业高等专科学校刘柏霞在统计中，由于分组而使各组标志值出现的次数不同，而次数的多少对算术平均数的影响有权衡轻重的作用，所以标志值出现的次数又称之为权数，它有绝对数形式和相对数形式两种。权数在统计实践中应用得极为广泛，权...     

平均数不等式的若干证明方法

平均数是统计分析和一般经济分析中广泛运用的指标形式,在统计学中占有重要地位.统计平均数的作用主要表现在,它可以概括的表征各种统计数列的基本数值特征,借以显示数列的一般水平或分布的集中趋势,进行各种对比分析.     

浅谈统计平均指标的应用

平均指标是统计研究中的基本指标之一,它反映总体在一定时间。地点、条件下所达到的一般水平。在研究总体水平,总体水平的变动以及两个总体水平之间存在的差别时,都要利用平均指标进行研究。例如,研究两个企业职工的工资水平状况时,要计算两个企业职工的平均工资进行比较,哪个企业职工的平均工资高说明哪个企业职工工资水平高。可以看出,统计平均指标是社会经济统计分析中广泛应用的一种综合指标。 平均指标就其计算方法不同,分为算数平均数,调和平均数和几何平均数。 一、算数平均数与调和平均数 以前就有对统计中是否应有调和平…     

Sample size and the probability of a successful trial

This paper describes the distinction between the concept of statistical power and the probability of getting a successful trial. While one can choose a very high statistical power to detect a certain treatment effect, the high statistical power does not necessarily translate to a high success probability if the treatment effect to detect is based on the perceived ability of the drug candidate. The crucial factor hinges on our knowledge of the drug's ability to deliver the effect used to power the study. The paper discusses a framework to calculate the 'average success probability' and demonstrates how uncertainty about the treatment effect could affect the average success probability for a confirmatory trial. It complements an earlier work by O'Hagan et al. (Pharmaceutical Statistics 2005; 4:187-201) published in this journal. Computer codes to calculate the average success probability are included.     

Some Uses for Distribution-Fitting Software in Teaching Statistics

Statistics courses now make extensive use of menu-driven, interactive computer software. This article presents some insight as to how a new class of PC-based statistical software, called “distribution-fitting” software, can be used in teaching various courses in statistics.     

Detecting Randomness: A Review of Existing Tests with New Comparisons

In this article we review and compare a number of existing tests for detecting randomness in time series data, with emphasis on stock market index data. By comparing variance ratio tests with traditional statistical tests, we have the most extensive simulation comparison of such procedures. The investigated tests are compared over a diverse group of distributions, models, and stock market applications. In our stock market data analysis, the choice of data transformation can have a noticeable effect on test results. This study provides the reader with a guide as to which test and transformation is most appropriate for their use.     

Exchange Rates and Markov Switching Dynamics

This article presents a systematic and extensive empirical study on the presence of Markov switching dynamics in three dollar-based exchange rates. A Monte Carlo approach is adopted to circumvent the statistical inference problem inherent to the test of regime-switching behavior. Two data frequencies, two sample periods, and various specifications are considered. Quarterly data yield inconclusive evidence; the test rejects neither random walk nor Markov switching. Monthly data, on the other hand, offer unambiguous evidence of the presence of Markov switching dynamics. The results suggest that data frequency, in addition to sample size, is crucial for determining the number of regimes.     

A New GWMA Control Chart for Monitoring Process Mean and Variability

In this article, we extend a single exponentially weighted moving average semicircle (EWMA-SC) chart to a single generally weighted moving average (GWMA) chart. This new control chart can effectively combine the features of the SC chart with GWMA techniques, and can easily indicate the source and direction of a change. We perform simulations to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the GWMA-SC and EWMA-SC charts. An extensive comparison shows that the GWMA-SC control chart is more sensitive than the EWMA-SC chart for detecting small shifts in the process mean and/or variability.     

中国企业统计能力评价方法研究

企业统计能力是国家统计能力的重要组成部分，企业统计能力的提高直接影响到国家统计能力的建设。从统计能力建设问题入手，讨论中国企业统计能力的内涵及其与政府统计能力的区别，提出了企业统计能力评价的系统结构，并从个体评价和总体评价两个角度对企业统计能力的评价方法进行了研究。     

The Generally Weighted Moving Average Variance Chart

This article extends the generally weighted moving average (GWMA) technique for detecting changes in process variance. The proposed chart is called the generally weighted moving average variance (GWMAV) chart. Simulation is employed to evaluate the average run length (ARL) characteristics of the GWMAV and EWMA control charts. An extensive comparison of these control charts reveals that the GWMAV chart is more sensitive than the EWMA control charts for detecting small shifts in the variance of a process when the shifts are below 1.35 standard deviations. Additionally, the GWMAV control chart performs little better when the variance shifts are between 1.35 and 1.5 standard deviation, and the 2 charts performs similar when the variance shifts are above 1.5 standard deviation. The design of the GWMAV chart is also discussed.     

A Comparison of Multiple Outlier Detection Methods for Regression Data

The problem of outliers in statistical data has attracted many researchers for a long time. Consequently, numerous outlier detection methods have been proposed in the statistical literature. However, no consensus has emerged as to which method is uniformly better than the others or which one is recommended for use in practical situations. In this article, we perform an extensive comparative Monte Carlo simulation study to assess the performance of the multiple outlier detection methods that are either recently proposed or frequently cited in the outlier detection literature. Our simulation experiments include a wide variety of realistic and challenging regression scenarios. We give recommendations on which method is superior to others under what conditions.     

Monitoring the coefficient of variation using a variable sample size and sampling interval control chart

This article proposes a CV chart by using the variable sample size and sampling interval (VSSI) feature to improve the performance of the basic CV chart, for detecting small and moderate shifts in the CV. The proposed VSSI CV chart is designed by allowing the sample size and the sampling interval to vary. The VSSI CV chart's statistical performance is measured by using the average time to signal (ATS) and expected average time to signal (EATS) criteria and is compared with that of existing CV charts. The Markov chain approach is employed in the design of the chart.     

Exponentially weighted moving average charts for correlated multivariate Poisson processes

In this article, we study exponentially weighted moving average (EWMA) control schemes to monitor the multivariate Poisson distribution with a general covariance structure, so that the practitioner can simultaneously monitor multiple correlated attribute processes more effectively. The statistical performance of the charts is assessed in terms of the run length properties and compared against other mainstream attribute control schemes. The application of the proposed methods to real-life and simulated datasets is demonstrated.