Comparison of methods of estimation of parameters of the weibull distribution

The generalised least squares, maximum likelihood, Bain-Antle 1 and 2, and two mixed methods of estimating the parameters of the two-parameter Weibull distribution are compared. The comparison is made using (a) the observed relative efficiency of parameter estimates and (b) themean squared relative error in estimated quantiles, to summarize the results of 1000 simulated samples of sizes 10 and 25. The results are that: generalised least squares is the best method of estimating the shape parameter ß the best method of estimating the scale parameter a depends onthe size of ß for quantile estimation maximum likelihood is best Bain-Antle 2 is uniformly the worst of the methods.     

中国商业银行业实行分业经营的合理性分析

一、前言作为一种银行审慎经营管制手段 ,分业经营制度实质上是银行资产选择管制 ,隔离商业银行业务、投资银行业务与保险业务是其最主要的内容。除了资产选择管制 ,其它常用的审慎经营管制手段还有存款利率管制、资本充足性要求。世界各国都对银行业进行审慎经营管制的原因在于银行业不同于其他产业的特征 :首先 ,债务在银行资产结构中所占比重很大 ,且债权人极为分散 ;其次 ,除了可内部化的破产成本外 ,银行破产还存在高昂的社会成本。负债比重越大银行破产的概率越大 ,而债权人越分散债权人对银行资产运营监管能力和积极性越小。银行破产…     

Table of percentage points of ratios of linear combinations of order statistics of samples from exponential distributions

A form of the distribution function of ratios of linear combinations of order statistics of samples from an exponential distribution is given. From the distribution, tables of percentage points of the statistic for α = .05, .95, and n = 3(1)50, and for censoring up to five observations are presented. Use of the tables is made to find critical values of the most powerful scale and location invariant test of exponentiality against uniformity, and also to find critical values for a test of outliers in an exponential population.     

A comparison of estimators of the precision of two instruments

Three different estimators of the variance in errors of measurement, or the “imprecisions” of instruments, have been proposed (Hahn and Nelson, 1970; Maxwell, 1974; Hanumara: 1975) for the case where two measurements by one instrument and one measurement by a second instrument are available for each item. The estimators are compared by studying the probabilities of negative values, the biases, the variances, and the mean square errors. Based on these results, Hahn and Nelson's estimators for the variances in errors of measurement are recommended. Simultaneous confidence intervals of the imprecisions of instruments are also given.     

Simulation of extremes of diffusions

The authors consider the problem of simulating the times of events such as extremes and barrier crossings in diffusion processes. They develop a rejection sampler based on Shepp [Shepp, Journal of Applied Probability 1979; 16:423–427] for simulating an extreme of a Brownian motion and use it in a general recursive scheme for more complex simulations, including simultaneous simulation of the minimum and maximum and application to more general diffusions. They price exotic options that are difficult to price analytically: a knock‐out barrier option with a modified payoff function, a lookback option that includes discounting at the risk‐free interest rate, and a chooser option where the choice is made at the time of a barrier crossing. The Canadian Journal of Statistics 38: 738–755; 2010 © 2010 Statistical Society of Canada     

Comparison of dispersions of mixtures of ordered distributions

In the paper we consider mixtures of unknown stochastically ordered distribution functions according to known mixing distribution functions. We provide optimal lower and upper bounds on ratios of general dispersion measures of such mixtures. The bounds do not depend on the particular form of dispersion measure. We present applications of the results in reliability theory, insurance mathematics, Bayesian statistics, and regression analysis.     

论加强需求管理——对当前宏观经济形势的认识及其调控建议

１９９７年下半年开始,我国经济明显出现了居民消费需求不足,或者说,出现了供给相对过剩的发展态势。至１９９８年１２月已连续１５个月物价指数同比负增长,１９９８年商品零售价格下降２．６％,居民消费价格下降０．８％,可以认为这又是通货紧缩的重要征兆。出现需...     

A comparison of estimators of the degree of insect control

The current estimator of the degree of insect control by an insecticide in a field experiment laid out in randomized blocks is equal to one minus the cross-product ratio of a two way table of total insect counts over blocks. Since much work has been done on estimation of the common odds ratio of a number of strata in medical studies, a series of Monte Carlo studies was performed to investigate the possible use of these estimators and their standard errors in estimating the common degree of inject control of a number of blocks. Maximum likelihood, Mantel-Haenszel, and empirical logit estimators were evaluated and compared with back-transformed means over blocks, of cross-product ratios on the arithmetic, logarithmic, and arcsine scales. Maximum likelihood and Mantel-Haenszel estimators had the smallest mean squared errors, but their standard error estimates were only appropriate when sampling distributions were approximately Poisson and there was little heterogeneity among plots within blocks in the natural rates of population change.     

中国国债融资功能的反思

一、中国国债融资制度的产生在传统计划经济体制下 ,中国的经济资源分配方式是 ,首先由国家强制集中全社会的资本要素 ,然后再用行政手段进行分配。从融资体制角度看 ,国家在这里充当了资本流动的中介 ,国家是融资的主体 ,它把资本从所有者那里筹集起来 ,再分配给他所选择的企业经营者使用 ,这种计划经济下的融资体制被称之为国家融资 (张春霖 ,2 0 0 0 )。在过去的几十年中 ,这种融资体制主要采取了两种基本形式 ,即收入融资和债务融资。所谓收入融资是指国家通过低工资、工农产品剪刀差等途径 ,把城乡居民应得的收入中可以用于长期储蓄的…     

Estimation of variance of mean using known coefficient of variation

An optimum unbiased estimator of the variance of mean is given It is defined as a function of the mean and itscustomary unbiased variance estimator, utilizing known coefficient of variation, skewness and kurtosis of the underlying distributions. Exact results are obtained. Normal and large sample cases receive particular treatment. The proposed variance estimator is generally more efficient than the customary variance estimator; its relative efficiency becomes appreciably higher for smaller coefficient of variation, smaller sample (in the normal case at least), higher negative skewness, or higher positive skewness with sufficiently large kurtosis. The empirical findings are reassuring and supportive.     

SNA关于机构部门分类的修订与中国机构部门的调整研究

 本文对2008SNA关于机构部门分类的修订进行了梳理。对比了2008SNA和1993SNA在机构部门与机构单位内容上的主要区别,分析了中国国民经济核算体系关于机构部门分类所存在的问题,提出了机构部门相关核算方法的调整建议。     

SAS软件的应用——基于ARMA模型的商品销售额的预测分析

文章运用SAS软件系统中的一些时间序列建模方法及回归分析方法对某商品的月销售额作了预测分析,得到了较高的预测精度,在实际应用中预测值的准确对于指导商家的战略决策起着重要作用.     

Minutes of Committee of Presidents of Statistical Societies

The general approach to generating random variates through transformations with multiple roots is discussed. Multinomial probabilities are determined for the selection of the different roots. An application of the general result yields a new and simple technique for the generation of variates from the inverse Gaussian distribution.     

Isotonic estimation of survival under a misattribution of cause of death

Several authors have indicated that incorrectly classified cause of death for prostate cancer survivors may have played a role in the observed recent peak and decline of prostate cancer mortality. Motivated by the suggestion we studied a competing risks model where other cause of death may be misattributed as a death of interest. We first consider a na?ve approach using unconstrained nonparametric maximum likelihood estimation (NPMLE), and then present the constrained NPMLE where the survival function is forced to be monotonic. Surprising observations were made as we studied their small-sample and asymptotic properties in continuous and discrete situations. Contrary to the common belief that the non-monotonicity of a survival function NPMLE is a small-sample problem, the constrained NPMLE is asymptotically biased in the continuous setting. Other isotonic approaches, the supremum (SUP) method and the Pooled-Adjacent-Violators (PAV) algorithm, and the EM algorithm are also considered. We found that the EM algorithm is equivalent to the constrained NPMLE. Both SUP method and PAV algorithm deliver consistent and asymptotically unbiased estimator. All methods behave well asymptotically in the discrete time setting. Data from the Surveillance, Epidemiology and End Results (SEER) database are used to illustrate the proposed estimators.     

Estimation of an indicator of the representativeness of survey response

Nonresponse is a major source of estimation error in sample surveys. The response rate is widely used to measure survey quality associated with nonresponse, but is inadequate as an indicator because of its limited relation with nonresponse bias. Schouten et al. (2009) proposed an alternative indicator, which they refer to as an indicator of representativeness or R-indicator. This indicator measures the variability of the probabilities of response for units in the population. This paper develops methods for the estimation of this R-indicator assuming that values of a set of auxiliary variables are observed for both respondents and nonrespondents. We propose bias adjustments to the point estimator proposed by Schouten et al. (2009) and demonstrate the effectiveness of this adjustment in a simulation study where it is shown that the method is valid, especially for smaller sample sizes. We also propose linearization variance estimators which avoid the need for computer-intensive replication methods and show good coverage in the simulation study even when models are not fully specified. The use of the proposed procedures is also illustrated in an application to two business surveys at Statistics Netherlands.     

三分位数的意义及计算

统计中已有确定中位数、四分位数、十分位数等的方法,文章在此基础上提出三分位数的概念及其确定的方法。三分位数从另一个角度对总体的分布特征进行描绘,对于现象总体的内部构成,对于由不同组成部分、类型形成的总体的认识,对于分组时组间界限的确定,甚至对于分层抽样中层的划分,对于研究分析总体分布的离散程度都有一定的作用。同时对单项式设计的变量数列确定中位数、三分位数的方法也进行了一定的论述。     

Comparison of three estimators of the number of species

We consider estimation of the number of cells in a multinomial distribution. This is one version of the species problem: there are many applications, such as the estimation of the number of unobserved species of animals; estimation of vocabulary size, etc. We describe the results of a simulation comparison of three principal frequent-ist' procedures for estimating the number of cells (or species). The first procedure postulates a functional form for the cell probabilities; the second procedure approxi mates the distribution of the probabilities by a parametric probability density function; and the third procedure is based on an estimate of the sample coverage, i.e. the sum of the probabilities of the observed cells. Among the procedures studied, we find that the third (non-parametric) method is globally preferable; the second (functional parametric) method cannot be recommended; and that, when based on the inverse Gaussian density, the first method is competitive in some cases with the third method. We also discuss Sichel's recent generalized inverse Gaussian-based procedure which, with some refine ment, promises to perform at least as well as the non-parametric method in all cases.     

中国城镇居民消费需求分析

进入 2 0世纪 90年代后 ,随着社会体制改革的深入 ,中国城镇居民收入差距的显著加大。这在目前收入仍然是制约城镇居民消费的重要因素前提下 ,城镇居民收入差距的加大不仅导致居民消费选择行为的不同 ,而且加剧了各等级城镇居民消费的不均衡。本文将时间序列和截面数据结合起来建立panle -data模型 ,经验分析收入差距对中国城镇居民消费需求的影响。研究发现收入分配因素和时间预期因素对我国城镇居民消费支出影响显著 ;收入等级水平越高 ,居民消费结构变化越快 ,且消费等级越高变化就越平缓 ;收入差距的拉开 ,使居民消费的共振现象趋于淡化…     

Test of equality of normal means in the absence of independent estimator of variance

Let X_l,…,X_n be normally and independently distributed with means θ_l,…,θ_nand a cornmorl variance. Thus there are n observations and n+i unknwon parameters. A test of the null hypothesis that, the θ_i's are all zero and the alternative that the vector (θ_l,…,θ_n) lies in a convex cone with its vertex a.t the origin is connsidered in this paper. It is shown that under a mild condition the likelihood ratio test is possible. The ordinary one sided t - test belongs to the class of tests considered in this paper. The hypothesis of equality of means against the simple order alternative can be tested in certain cases .     

Automatic repeated-loess decomposition of data consisting of sums of oscillatory curves

Repeated loess is a nonparametric procedure that uses progressive smoothing and differencing to decompose data consisting of sums of curves. Smoothing is by locally weighted polynomial regression. Here the procedure was developed so that the decomposition into components was controlled automatically by the number of maxima in each component. The level of smoothing of each component was chosen to maximize the estimated probability of the observed number of maxima. No assumptions were made about the periodicity of components and only very weak assumptions about their shapes. The automatic procedure was applied to simulated data and to experimental data on human visual sensitivity to line orientation.An erratum to this article can be found at