The median of the poisson distribution

The purpose of this paper is twofold: first, to provide a closed form expression for the median of the Poisson distribution and, second, to improve the known estimates of the difference between the median and the mean of the Poisson distribution. We use elementary techniques based on the monotonicity of certain sequences involving tail probabilities of the Poisson distribution and the Central Limit TheoremReceived November 2002     

Bounds for the median of the negative binomial distribution

Summary Bounds are obtained for the median of the negative binomial distribution which are valid for all possible parameter values of the distribution when the median is defined as inf {x: P(X≤x)≥1/2}.     

Successive Sampling to Estimate Quantiles with P-Auxiliary Variables

The successive sampling is a known technique that can be used in longitudinal surveys to estimate population parameters and measurements of difference or change of a study variable. The paper discusses the estimation of quantiles for the current occasion based on sampling in two successive occasions and using p-auxiliary variables obtained of the previous occasion. A multivariate ratio estimator from the matched portion is used to provide the optimum estimate of a quantile by weighting the estimates inversely to derived optimum weights. Its properties are studied under large–sample approximation and the expressions of the variances are established. The behavior of these asymptotic variances is analyzed on the basis of data from natural populations. A simulation study is also used to measure the precision of the proposed estimator.     

On characterizations of distributions by expected values of order statistics and record values with gap

In this paper, we obtain some recurrence relationships for conditional expectations of nonadjacent order statistics and record values when the distribution function is absolutely continuous, and we prove that the distribution function is uniquely determined by the distribution of conditioned record values and by the expected values of these records. Further, different distributions are characterized by these relationships.     

Gamma-minimax estimation of a multivariate normal mean

Summary The mean vector of a multivariate normal distribution is to be estimated. A class Γ of priors is considered which consists of all priors whose vector of first moments and matrix of second moments satisfy some given restrictions. The Γ-minimax estimator under arbitrary squared error loss is characterized. The characterization follows from an application of a result of Browder and Karamardian published in Ichiishi (1983) which is a special version of a minimax inequality due to Ky Fan (1972). In particular, it is shown that within the set of all estimators a linear estimator is Γ-minimax. The authors would like to thank the Deutsche Forschungsgemeinschaft for financial support.     

A note on finite sample breakdown points of projection based multivariate location and scatter statistics

In this note, general results of finite sample breakdown point are obtained for two classes of projection based location and scatter statistics: the Stahel-Donoho statistics and the Maronna-Yohai statistics. It is shown that these projection based location and scatter statistics can achieve the maximum breakdown point of affine equivariant multivariate location and scatter statistics. General relationships between the finite sample breakdown point of these statistics and the uniform finite sample breakdown point of the sample median and a modified sample median absolute deviation are formally established. Received: May 1999     

温州中心城市功能重构

分析了温州中心城区的功能定位,提出应当培育三大核心功能:第一,构建制造业垂直分工体系,强化生产性服务功能;第二,发展独占性资源产业,提升流通服务功能;第三,培育知识密集型产业,增强流通服务功能.最后,结合温州的发展现状及区位优势,提出了建立区域协调机制,重构产业体系与构建综合交通体系等三点对策建议.     

Stability of characterizations of normal distributions based on the conditional expected values of the sample skewness and the sample kurtosis

Characterizations of normal distributions given by Nguyen and Dinh (1998) based on conditional expected values of the sample skewness and the sample kurtosis, given the sample mean and the sample variance, are shown to be stable. Received: September 1998     

Generalized piecewise linear histograms

We extend the concept of piecewise linear histogram introduced recently by Beirlant, Berlinet and Györfi. The disadvantage of that histogram is that in many models it takes on negative values with probability close to 1. We show that for a wide set of models, the extended class of estimates contains a bona fide density with probability tending to 1 as the sample size n increases to infinity. The mean integrated absolute error in the extended class of estimators decreases with the same rate n^–2/5 as in the original narrower class.     

利用微分方程求辅助函数证明中值定理

对于微分中值定理有关证明,"奇妙"的构造辅助函数问题。利用微分方程的求解,分析辅助函数的内在特征,给出一种构造方法。     

一个新数论函数及其均值

对任意正整数n,设h(kn)表示不大于n的最大k次幂,以及h(kn)=n-IK(kn),利用初等方法和解析方法,研究了新定义的数论函数h(kn)的均值性质;并给出了一个较强的均值渐近公式。     

加快咸宁市中心镇建设策略研究

中心镇介于城乡之间,是带动一定区域农村经济发展的中心。中心镇建设是实现工业化与城镇化的重要节点,要以产业建设作为中心镇建设的支柱,以生态建设作为中心镇建设的基础,以文化建设作为中心镇建设的灵魂,以功能建设作为中心镇建设的核心,以特色建设作为中心镇建设的根本。     

现代物流业与中心城市聚散功能

以分析中心城市聚散功能的基本作用规律为基础,深入分析了现代物流业强化中心城市聚散功能的具体途径.     

Non-Existence of the First Moment of the Adjusted Least Squares Estimator in Multivariate Errors-in-Variables Model

The linear normal multivariate errors-in-variables model is considered. The model involves an equation error. It is proved in both structural and functional cases that the first moment of the adjusted least squares estimator does not exist.     

Weighted least squares estimators in possibly misspecified nonlinear regression

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes the model itself close to nonparametric. We study the behavior of weighted least squares estimators both when the regression function is correctly specified, and when it is misspecified and also involves possible additional covariates.     

微分中值定理中辅助函数构造的方法

通过对微分中值定理的应用研究,发现在解决此类命题中,大多采用构造辅助函数的方法来证明,如何构造辅助函数成为证明此类问题的关键。本文给出了三类关于辅助函数的构造的方法和技巧,并给出例题并加以应用。