Behrens-Fisher问题的正态逼近

 本文提出用基于得分检验的正态逼近方法来解决Behrens-Fisher问题,即比较方差比未知时两正态总体的均值。模拟结果显示：在所有的研究情况下,我们的方法都能很好地控制第一类错误,检验功效也不差;而最常用的Welch近似t检验在样本量不等时大多数情况都不能控制第一类错误。     

关于分层累计抽样的几个问题

一、分层累计抽样 所谓分层累计抽样技术就是对抽样框进行以下技术处理: 1.等距分层。将各单位按有关标志进行分层。 2.将各层并排起来,分层进行累计。即把等分后的各层(层内各单位原排队次序不变)按首尾相并的方法排列起来,再对各单位的值按由上至下的方向,分层进行累计。 3.绘制抽样框图。对按一定次序排列起来的各层,按照同一比例绘制成一定长度     

分层累计抽样技术中抽样框图的绘制

对称等距抽样是我国社会经济抽样凋查中的一种主要方法。但其确定样本点的计算公式比较复杂难记,从而限制了这种方法的推广和应用。用分层累计抽样技术来实施对称等距抽样,技术简便,容易操作。抽样框图是分层累计抽样技术的关键一步,笔者在实践中摸索出了一种绘制抽样框图的简便方法,并由计算机来完成,使得分层累计抽样技术更完善,易于推广、应用。一、分层累计抽样技术设总体有N个单位,分别用A_1,A_2,…,A_N表示,各单位的有关标志值分别用X_1,X_2,…,X_N表示,辅助标志值分别用     

“全国农产量抽样方案”理论基础探讨

一、国家统计局全国农产量抽样调查抽样程序 第一步,以省一级行政区为单位,省内所有的县组成一个抽样总体,抽取约35％的县。 第二步,以抽中的县为单位,县内所有的行政村组成抽样子总体,抽取15-20个村。 第三步,以抽中的村为单位,抽取农作物地块。 上述的每一步都采用有关标识排队等距抽样的方法。以省抽县为例,具体步骤如下: 1.设X_i、S_1分别代表第i号县的前三年平均亩产、面积。根据X_i的大小将所有的县进行排序。经排序后得到X_1 ≤X_j(i>j)。     

基尼系数的抽样估计

The paper discusses the properties of statistics and precision of estimation when the sample statistics are used to estimate Gini Coefficient.     

统计数据中异常值的检验方法

一、异常值的两种理解统计数据质量问题一直困扰着我国统计界 ,也为社会各界所关注。所以近年来对其理论上的研究探讨始络保持热点。但研究的重点主要是在健全统计法律制度和完善工作程序等方面。毫无疑问 ,这些确实是提高统计数据质量的重要方面。但统计数据质量问题本质上是误差问题。即所提供的统计数据与客观的社会经济现象实际的数量特征之间的差距问题。如果数据中混进了异常值 ,就会使相应统计分析误差增大 ,小则出差错 ,大则发生事故 ,甚至导致宏观决策上的失误。因此 ,在利用统计数据进行统计分析之前 ,有必要对其进行异常数据的检…     

南宋秦九韶的抽样检验法

秦九韶(1202—1261,南宋数学家,字道古,普州安岳(今四川省安岳县)人。著有《数书九章》。全书共十八卷八十一题,分为九大类。第一,大衍类,阐述一次同余式组的解法,包括著卦发微,古易会积,推记土功,推库额钱等;第二,天时类,是关于历法推算,降雨量测量;第三,田域类,是土地面积的丈量和计地容民等问题;第四,测量类,是测算目的物高远方法;第五,赋役类,是租税徭役的计算方法;第六,钱谷类,是征购粮     

成数抽样的比率估计

成数抽样的比率估计李金昌ＡＢＳＴＲＡＣＴＴｈｅｐａｐｅｒｄｉｓｃｕｓｓｅｓｔｈｅｉｓｕｅｏｆｒａｔｉｏｅｓｔｉｍａｔｉｏｎｉｎｓａｍｐｌｅｓｕｒｖｅｙｏｆｐｒｏｐｏｒ－ｔｉｏｎａｌｎｕｍｂｅｒｓ．Ｔｈｅｅｓｔｉｍｅｔｏｒａｎｄｖａｒｉａｎｃｅｏｆｓａ...     

The Discrete Normal Distribution

Abstract

The normal distribution has been playing a key role in stochastic modeling for a continuous setup. But its distribution function does not have an analytical form. Moreover, the distribution of a complex multicomponent system made of normal variates occasionally poses derivational difficulties. It may be worth exploring the possibility of developing a discrete version of the normal distribution so that the same can be used for modeling discrete data. Keeping in mind the above requirement we propose a discrete version of the continuous normal distribution. The Increasing Failure Rate property in the discrete setup has been ensured. Characterization results have also been made to establish a direct link between the discrete normal distribution and its continuous counterpart. The corresponding concept of a discrete approximator for the normal deviate has been suggested. An application of the discrete normal distributions for evaluating the reliability of complex systems has been elaborated as an alternative to simulation methods.     

Exact Bayesian Variable Sampling Plans for the Exponential Distribution Based on Type-I and Type-II Hybrid Censored Samples

A sampling plan with a polynomial loss function for the exponential distribution is considered. From the distribution of the maximum likelihood estimator of the mean of an exponential distribution based on Type-I and Type-II hybrid censored samples, we obtain an explicit expression for the Bayes risk of a sampling plan with a quadratic loss function. Some numerical examples and comparisons are given to illustrate the effectiveness of the proposed method, and a robustness study reveals that the proposed optimal sampling plans are quite robust.     

The Mean-shift Outlier Model under Skew Normal Distribution

Asymmetric models have been extensively studied in recent years, in situations where the normality assumption is not satisfied due to lack of symmetry of the data. Techniques for assessing the quality of fit and diagnostic analysis are important for model validation. This paper presents a study of the mean-shift method for detecting outliers in asymmetric normal regression models. Analytical solutions for the estimators of the parameters are obtained using the algorithm. Simulation studies and application to real data are presented, showing the efficiency of the method in detecting outliers.     

The Slippage Problem for the Circular Normal Distribution

The slippage problem occurs when an unspecified observation in a given random sample is from a distribution other than that for all the remaining observations. This paper studies the problem in terms of the 'slip' in the mean direction of a circular normal distribution. The slippage problem is first treated as a multiple decision problem with a prior which is invariant under the permutations of the hypotheses. The probabilities of accepting the various hypotheses for the Bayes rule with respect to this prior are explicitly obtained. The likelihood ratio tests for this slippage problem, for the cases when the mean directions are both known and unknown, are shown to be easily computable. The tests are illustrated through two well-known datasets. The performances of a range of tests are compared using extensive simulation.     

Misspecifications of the Normal Distribution

Incorrect statements about the normal distribution are discussed and illustrated with counterexamples.     

Alpha正态分布及其在环境污染中的应用

目前,对实际数据的处理常采用一些对称分布,如正态分布和t分布等,而这种对称分布所给出的结果往往并不能令人满意。偏分布常用来处理有偏重尾数据,基于传统正态分布,提出一种处理偏态和重尾数据的alpha正态分布,并研究其参数估计方法及基本性质。将所提分布应用于环境污染数据,通过拟合检验alpha正态分布给出了很好的结果。     

The Multivariate Split Normal Distribution and Asymmetric Principal Components Analysis

The multivariate split normal distribution extends the usual multivariate normal distribution by a set of parameters which allows for skewness in the form of contraction/dilation along a subset of the principal axes. This article derives some properties for this distribution, including its moment generating function, multivariate skewness, and kurtosis, and discusses its role as a population model for asymmetric principal components analysis. Maximum likelihood estimators and a complete Bayesian analysis, including inference on the number of skewed dimensions and their directions, are presented.     

关于期望寿命的估计

一、引言期望寿命又叫平均剩余寿命。设寿命 (或生存时间 )为Ｘ ,则在Ｘ >ｔ的条件下Ｘ -ｔ的期望ｅ =Ｅ(Ｘ -ｔ|Ｘ >ｔ)是期望寿命。设Ｘ的分布函数Ｆ(ｘ)是未知的 ,如何估计ｅｔ,这是保险精算、可靠性工程及生存分析等实际工作中很关心的问题。随机考察ｎ个个体 ,这些个体的寿命分别是ｘ1 ,ｘ2 ,… ,ｘｎ,他们被看作随机变量 ,相互独立 ,有相同的分布函数Ｆ(ｘ)。我们分别在一列时刻ａ0 =0 <ａ1<ａ2 <… <ａｍ 观测其寿命。令ａｍ + 1 =∞ ,Ｉｋ=(ａｋ,ａｋ + 1 ](ｋ =0 ,1,2 ,… ,ｍ)。考虑等距分组 ,即每个区间的长度都为ｈ ,ｈ =ａｋ +…     

The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables

Abstract

An expression for the exact cumulative distribution function of a ratio of quadratic forms in noncentral normal variable is derived in terms of infinite series of top order invariant polynomials.