Top incomes in the UK over the 20th century

Summary.  Recent changes in the distribution of income need to be placed in historical context. The paper provides new evidence about the evolution of top incomes in the UK over the 20th century. Making use of published tabulations of the income tax statistics, and of microdata for recent years, we construct estimates of the shares of top income groups, giving for the first time an annual time series for gross incomes that spans more than 90 years. The paper pays particular attention to the problems of data construction and of the interpretation of tax-based evidence. The resulting statistics have evident limitations but throw light on periods, such as that between the First and Second World Wars, for which there is little other empirical material. The results bring out clearly how the major equalization of the first three-quarters of the century in the UK has been reversed, taking the shares of the top income groups back to levels of inequality found 50 years ago. A similar U-shaped pattern is found for the USA, but the post-war experience of France is different from that in the UK.     

Order Sampling Design with Prescribed Inclusion Probabilities

Order sampling with fixed distribution shape is a class of sampling schemes with inclusion probabilities approximately proportional to given size measures. In a recent article, methods were provided to compute the exact first and second order inclusion probabilities numerically when the distribution shape is of the Pareto type. In the same article, procedures were also provided for this case to adjust the parameters to get predetermined inclusion probabilities. In this paper we prove the existence and uniqueness of a solution for the latter problem, in general for any order sampling of fixed distribution shape.     

Estimation of the maximal moment exponent with censored data

Heavy-tailed distributions have been used to model phenomena in which extreme events occur with high probability. In these type of occurrences, it is likely that extreme events are not observable after a certain threshold. Appropriate estimators are needed to deal with this type of censored data. We show that the well-known Hill-Hall estimator is unable to deal with censored data and yields highly biased estimates. We propose and study an unbiased modified maximum likelihood estimator, as well as a truncated tail regression estimator. We assess the expected value and the variance of these estimators in the cases of stable- and Pareto-distributed data.     

A note on characterization based on shannon entropy of record statistics

In this note we compare the Shannon entropy of record statistics with the Shannon entropy of the original data and give an application to characterization of the generalized Pareto distribution,     

Pareto Sampling versus Sampford and Conditional Poisson Sampling

Abstract.  Pareto sampling was introduced by Rosén in the late 1990s. It is a simple method to get a fixed size π ps sample though with inclusion probabilities only approximately as desired. Sampford sampling, introduced by Sampford in 1967, gives the desired inclusion probabilities but it may take time to generate a sample. Using probability functions and Laplace approximations, we show that from a probabilistic point of view these two designs are very close to each other and asymptotically identical. A Sampford sample can rapidly be generated in all situations by letting a Pareto sample pass an acceptance–rejection filter. A new very efficient method to generate conditional Poisson ( CP ) samples appears as a byproduct. Further, it is shown how the inclusion probabilities of all orders for the Pareto design can be calculated from those of the CP design. A new explicit very accurate approximation of the second-order inclusion probabilities, valid for several designs, is presented and applied to get single sum type variance estimates of the Horvitz–Thompson estimator.     

高校双语教学的瓶颈及其突破途径

随着经济全球化和高等教育国际化趋势的日益加强,高校双语教学在我国也越来越为人们所重视.但作为一个新生事物,高校双语教学不可避免地面临许多新的挑战,存在诸多亟待解决的问题,其中教育者的双语教学能力欠缺以及受教育者的英语能力不强,更是成为制约高校双语教学发展的两大瓶颈.增强教师双语教学能力与提高学生双语学习能力,是突破这两大瓶颈、增强高校双语教学实效性的关键.     

因子分析精确模型的基本思想与方法

文章从统计思想、等价性的方法入手,给出了初始因子分析精确模型及解、因子分析精确模型及解、主成分分析与因子分析的关系式等结论。从基本思想、方法上完善了因子分析精确模型和理论。     

CHARACTERISATIONS OF SOME INCOME DISTRIBUTIONS BASED ON MULTIPLICATIVE DAMAGE MODELS

This paper characterises the Pareto and scaled beta distributions within the context of multiplicative damage and generating models. The results obtained allow the destructive or generating mechanism to have more general distributions on (0,1) than the beta(e, l) distribution considered by several authors, thus generalising some recent results. Errors in earlier work are mentioned.     

同步与圆圆映射

当一个生成三角波的回路同步失稳时,利用李亚普诺夫函数可以很容易证明系统实际上处于混沌态。对应于不同触发信号周期的混沌区宽度的实验数据与用计算机打出的相应图形作了比较。系统也可以用所谓“圆圆映射” 即一维自身分立圆映射来分析,分析表明,当波形改变时,对应于不同参数时的同步失稳电路可以分别具有周期、准周期和混沌解。     

基于供应链的合作促销与定价问题

本文针对供应链中厂商和销售商之间的合作促销问题,使用博弈论的方法主要就最优的合作促销费用投入和定价进行了研究。首先讨论了传统的厂商为领导者,销售商为跟随者的情形,接着考虑到如今销售商地位的提高,对此进行了拓展,讨论了销售商为领导者的情形。最后以前两种情形为参照,建立了厂商和销售商之间Pareto改进的合作促销模型,并利用Nash讨价还价和效用理论得出了Pareto改进情形下的最优结果。