关于几何平均数的笔算法的改进

文章从几何平均数的定义出发，利用函数幂级数展开式，对几何平均数的笔算方法加以改进，并给出了误差估计公式。按改进后的方法计算几何平均数，简化了近似公式，使计算变得简便     

Z计分模型的改进及实证检验

文章结合我国上市公司的具体特点,以探索符合我国上市公司自身特点的财务预警模型,加入了现金流量这一财务指标,对Z计分模型做了改进,能更好地为企业财务预警机制服务.     

浅谈算术平均数与调和平均数的关系

关于算术平均数（简称“算均”）和调和平均数（简称“调均”）之间的区别和联系，统计界人士有不同的看法，其一认为“调均”是“算均”在资料条件及要求不同时的变形，其二认为“调均”有时是“算均”的变形，有时又是一种独立的计算形式，此时它的计算结果与“算均”不同，且恒小于“算均”。笔者同意前种看法。我们皆知，在同质总体中计算算术平均数的基本公式为：平均数一标志总量／总体总量，在计算过程中，不管资料条件如何受到限制，计算要求如何不同，但凡是符合这一计算公式的平均数，其实质总是“算均”。这是我们论述这一问题的…     

统计学中的算术平均数与几何平均数在量上可比吗

根据同一统计资料计算的算术平均数与几何平均数在量上比较缺乏可比性,在统计学中X≥G的关系不成立。     

强度相对数的再认识

强度相对数是一种应用十分广泛的相对数,要想正确发挥其作用,就必须对其定义及其公式有一个准确的理解。所谓准确理解,就是认为强度相对数的“分子、分母可以属于同一总体”。而强度相对数又有“平均”的含义,因此,对其与算术平均数的区别进行阐述非常必要。     

关于“算术平均数”的教学体会

算术平均数是平均数中最常见的形式,教师在讲授算术平均数这一统计学中的基本问题时应该引起高度重视,应该思考如何把算术平均数讲透,让学生能正确认识、计算和使用算术平均数。本文结合笔者多年的统计教育实践,谈谈算术平均数的一些教学体会。     

如何衡量几何平均数的代表性

与算术平均数一样,几何平均数也存在着其衡量代表性大小的问题。在实际应用中,对这一问题绝大多数仍是直接采用衡量算术平均数代表性大小的方法来加以解决,即采用和来作为衡量几何平均数代表性的指标。然而,笔者认为,这一做法是欠科学的,这是因为算术平均数和几何平均数两者在本质上存在着较大的差异。首先,两者在应用条件方面存在着差异。众所周知,当标志值总量等于各标志值的总和时,要反映其一般水平,应采用算术平均数的方法加以解决,如平均工资的计算等;而当标志值总量等于各标志值的连乘积时,要反映标志值的一般水平,应采…     

调和平均数归类之刍议

众所周知,现行统计教科书都将平均指标划分为算术平均数、调和平均数、几何平均数、中位数、众数并列的五种。这就是说,需计算平均指标的场合应有五种,以适应五种并列的平均数的计算。而实际上,只存在四种场合。一是需计算众数的场合——将出现次数最     

浅谈算术平均数的作用

一提到算术平均数,无论是否搞统计工作,大家都十分熟悉,因此似乎感到对算术平均数没有什么问题可探讨了。正是针对这种情况,引起了我们的思考,如何认识算术平均数的作用?在什么条件下应用算术平均数?它与已有某些方法以及几何平均数有什么关系?为了回答这些问题,我们拟写了这篇短文,仅供统计理论工作者和实践工作者参考。一、算术平均数对整体具有代表性对于给定顺序的观测数据ｘ1,ｘ2,……,ｘｎ,通常认为算术平均数最具有代表性,或者说用算术平均数去估计这个数据列从整体上讲犯的错误最小。算术平均数的这种作用,取决于算术平均数的一个有…     

A refinement of Hoeffding's inequality

In this paper, we present a refinement of Hoeffding's inequality which is of closed form and which significantly improves on this inequality in many cases. Some numerical comparisons are also presented.     

Some Improvements in Numerical Evaluation of Symmetric Stable Density and Its Derivatives

A new multivariate inverse Polya distribution of order k, type I, is derived by means of a generalized urn scheme and by compounding the multivariate negative binomial distribution of order k, type I, of Philippou, Antzoulakos and Tripsiannis (1988) with the Dirichlet distribution. It is noted that this new distribution includes as special cases a new multivariate inverse hypergeometric distribution of order k and a new multivariate negative inverse one of the same order. The mean and variance-covariance of the multivariate inverse Polya distribution of order k, type I, are derived, and two known distributions of the same order are shown to be limiting cases of it.     

带有流动性约束的投资组合模型及其应用

在考虑组合投资收益与风险受市场流动性影响等因素的条件下,提出了一种带有模糊流动性约束的投资组合模型,并利用可能性理论将其转化为二次规划模型,得到该模型的解。通过实例证明:在不确定的金融资本市场,投资者可根据此模型来选择自己的投资组合,使有限资源得到最大程度利用。     

Comparison of bootstrap estimation intervals to forecast arithmetic mean and median air passenger demand

The aim of this paper is to compare passenger (pax) demand between airports based on the arithmetic mean (MPD) and the median pax demand (MePD). A three phases approach is applied. First phase, we use bootstrap procedures to estimate the distribution of the arithmetic MPD and the MePD for each block of routes distance; second phase, we use percentile, standard, bias corrected, and bias corrected accelerated methods to calculate bootstrap confidence bands for the MPD and the MePD; and third phase, we implement Monte Carlo (MC) experiments to analyse the finite sample performance of the applied bootstrap. Our results conclude that it is more meaningful to use the estimation of MePD rather than the estimation of MPD in the air transport industry. By carrying out MC experiments, we demonstrate that the bootstrap methods produce coverages close to the nominal for the MPD and the MePD.     

A BLUP Synthetic Versus an EBLUP Estimator: An Empirical Study of a Small Area Estimation Problem

Model-based estimators are becoming very popular in statistical offices because Governments require accurate estimates for small domains that were not planned when the study was designed, as their inclusion would have produced an increase in the cost of the study. The sample sizes in these domains are very small or even zero; consequently, traditional direct design-based estimators lead to unacceptably large standard errors. In this regard, model-based estimators that 'borrow information' from related areas by using auxiliary information are appropriate. This paper reviews, under the model-based approach, a BLUP synthetic and an EBLUP estimator. The goal is to obtain estimators of domain totals when there are several domains with very small sample sizes or without sampled units. We also provide detailed expressions of the mean squared error at different levels of aggregation. The results are illustrated with real data from the Basque Country Business Survey.     

振奋精神，通力合作，开创学会工作新局面──中国统计学会第四次全体会员代表大会暨第七次全国统计科学讨论会侧记

振奋精神,通力合作,开创学会工作新局面──中国统计学会第四次全体会员代表大会暨第七次全国统计科学讨论会侧记中国统计学会第四次全体会员代表大会暨第七次全国统计科学讨论会于１９９３年１０月３０日在山东省泰安市召开。来自统计部门、科研机构、大专院校的１７０...     

Locally optimal test for simultaneously testing the mean and variance of a normal distribution

A generalization of the locally most powerful unbiased (LMPU) test for the single parameter case to the k-parameter case was proposed by SenGupta and Vermeire (1986). In particular we defined a locally most mean power unbiased (LMMPU) test based on the mean curvature of the power hypersurface. Compared to the type C tests of Neyman and Pearson and the type D tests (Isaacson, 1951), LMMPU tests possess better theoretical properties and enjoy ease of construction of critical regions. In this paper we present an interesting example of a two-parameter univariate normal population for which Isaacson (1951, p. 233) was unsuccessful in finding a type D test. For the case of one observation, we prove that no Type D region exists but the LMMPU test is obtained - it is an example of a test with singular Hessian matrix for its power but is nevertheless a strictly locally unbiased (LU) test.     

Estimation of the optimal portfolio weights by shrinking the mean vector towards a linear subspace

To obtain estimators of mean-variance optimal portfolio weights, Stein-type estimators of the mean vector that shrink a sample mean towards the grand mean have been applied. However, the dominance of these estimators has not been shown under the loss function used in the estimation problem of the mean-variance optimal portfolio weights, which is different than the quadratic function for the case in which the covariance matrix is unknown. We analytically give the conditions for Stein-type estimators that shrink towards the grand mean, or more generally, towards a linear subspace, to improve upon the classical estimators, which are obtained by simply plugging in sample estimates. We also show the dominance when there are linear constraints on portfolio weights.     

Estimation of a distribution function bounded by two known distribution functions

The problem of estimation of a cumulative distribution function (cdf), bounded by two known cdf's, is considered. An estimator satisfying the desired restriction has been obtained by suitably adjusting the empirical cdf. Consistency of the adjusted estimator has been established and its mean square error (MSE) has been shown to be smallerthan that of the empirical cdf. The new estimator has been comparedwith the empirical cdf for some special cases.     

模糊数据均值方法及应用研究

提出一种＂Zadeh＂式模糊数据,并探讨这种模糊数据的模糊样本均值及其统计检验问题,给出模糊等于、模糊属于的定义,提出离散型和连续型模糊总体均值检验方法,并利用一些实例阐述了此类统计方法的应用。