基于离散枢轴量的泊松分布参数的精确最短置信区间

将泊松分布参数的充分统计量的离散型分布函数转化为生存伽马分布函数,以此为枢轴量构造了泊松分布参数的精确置信区间.通过数值模拟,选择合适的置信度组合,得到精确最短置信区间.讨论了大样本下泊松分布参数的近似置信区间的估计精度,验证了精确最短置信区间的计算结果.     

Kolmogorov统计量的精确分布及其在Bootstrap逼近中的应用

假设x₁,x_m iid服从分布F,当F连续时,Kolmogorov统计量的精确分布已由张里千(1956)获得.本文考虑在n个点上取概率为1/n的离散分布.得到的精确分布与张里千的结果有相同的形式.利用这个结果,得到Kolmogorov统计量分布的Bootstrap逼近的收敛速度为n^-1/2的阶.这是对统计量的极限分布形式复杂甚至未知的情况下Bootstrap逼近的收敛速度问题的一个初步的探讨.     

次序统计量线性组合之分布及其在可靠性统计中的应用

本文利用特征函数的方法,给出了来自于自由度为自然数r的Γ—分布的次序统计量线性组合之精确分布;并将其用于可靠性定数截尾试验中,得到了指数分布的似然比检验统计量之精确分布。     

基于联合II型删失数据的两总体指数模型的精确统计推断（英文）

在本文中,我们讨论两指数总体的位置参数和尺度参数的统计推断问题.利用极大似然方法,在联合II型删失数据的情形下给出参数的精确分布以及相关精确统计推断结果.将枢轴量表示为标准指数随机变量的线性函数,并且给出枢轴量的条件精确分布,这个条件精确分布的一个很大优点是计算比较简单.利用条件精确分布,可以获得枢轴量的精确分位数.为了说明本文方法的优劣,我们也提供Bootstrap方法构造参数置信区间的相关结果.最后将理论结果,进行了部分数值模拟实验,这些数值结果列在相应的表格里.     

多维Erlang混合的次序统计量及其在多生命理论中的应用（英文）

本文研究来自多维Erlang混合分布的具有相关性的随机变量的次序统计量并将相关结论应用到多生命理论中.利用熟知的数学归纳法推导出次序统计量分布密度函数的解析表达式并证明其分布为一维Erlang混合分布,寿险精算理论中常见的重要统计量可以算出精确解.这一结论将随机变量相互独立情形下的结果推广到变量存在相关性的情形.     

基于Beta分布形状的拟合优度检验

本文指出了拟合优度检验中选用经验频率公式时存在的误区,对顺序统计量失效概率分布进行了偏态和峰态分析,提出了一个基于Beta分布形状特征的经验分布函数,给出了精确值和近似值两种计算方法,在此基础上建立新的极值型检验统计量．利用Monte Carlo方法进行数值模拟,得到0．01、0．05、0．1显著度水平下检验统计量的临界值,并利用常用的分布模型进行检验功效比较,数值模拟结果表明基于分布形状的经验频率公式能更好地反映顺序统计量失效概率分布的集中趋势,证明了本文提出的两种检验统计量在中小样本条件下具有更优的检验功效．     

矩阵微分——推导精确分布的工具

在推导统计量的精确分布时,矩阵微分是一个既初等又方便的工具,这一工具是由许宝騄先生首先提出的,在30年代末期,用它导出了著名的正态样本协差阵特征根的联合分布。后来,1947年在北卡罗林纳(Noth Carolina)大学讲授多元分析一课时,他系统地发展了这一工具,得到了很多结果,有些结果后来也一直没有正式发表过。在Hotelling教授的倡议下,由W(?)L(?)Deemer和I(?)Olkin整理发表了其中矩阵微分的纯代数部分,     

线性模型中M检验原假设分布的随机加权逼近

在线性模型中M-方法可以用于线性假设检验, 其中M检验、Wald检验和Rao的计分型检验是最常用的检验准则. 但是在计算这些检验的临界值时都涉及到未知参数的估计. 在本文中我们利用随机加权的方法来逼近这些检验的原假设分布. 结果表明在原假设和局部对立假设之下随机加权统计量的渐近分布与原检验统计量在原假设之下的渐近分布相同. 因此我们不需要对冗余参数进行估计,利用随机加权的方法就可以得到这些检验的临界值. 而且在局部对立假设之下可以实现对功效的计算. 当取不同的误差分布和不同的随机权时, 我们对本文的方法进行了蒙特卡洛模拟. 结果表明用随机加权方法来逼近原假设分布是非常精确的.     

关于正态子样的峰度统计量的近似分布

峰度统计量b_2是正态性检验的重要统计量。然而,在一般情况下正态总体的峰度统计量的分布及分位点无法精确求得。本文提出了在与b_2具有相同的前四阶矩的几种类型的分布中,按照五阶矩、六阶矩与b_2最接近的原则寻找其近似分布和分位点的方法。     

基于随机加权的空间聚集性检验及其在基础教育师资均衡性评价中的应用

使用空间统计检验方法研究北京基础教育资源分配的均衡性问题.对于空间分布均匀性的检验,常用的统计量是Moran's I统计量.但基于Moran's I统计量做推断的时候,人们往往用渐进正态分布或者用Bootstrap反复抽样得到经验分布来进行.提出使用随机加权法进行统计量的经验检验.Jin和Lee(2014)文中得出基于Bootstrap的Moran's I统计量满足一致逼近和渐进正态等性质.采用类似的统计工具证明了基于随机加权得到的统计量的渐进分布也满足这些良好性质.填补了用随机加权法在空间统计量的推断中理论保证的空白.通过模拟研究,证明了所提算法的有效性.方法应用于北京基础教育的师资-适龄儿童数比例,师资-在校生数比例的空间聚集性检验中得到了良好的应用,并与其它检验方法所得结论进行比较.结论显示在不同相邻概念(地理相邻、政策空间相邻)下,方法得到的结论符合常理.     

求统计量极限分布的一个方法

一九四九年第一届Berkeley会议的论文集上刊印了一篇长达40多页的论文,在这篇论文(见[1])中,许宝騄先生用一个统一的方法,一举解决了一元、多元统计分析中近20个统计量的极限分布。这一方法的想法是非常明确的,它充分利用了数理统计的特点:样本是一组独立同分布的随机变量(或随机向量)。可惜的是后来的许多教科书和专著中,都没有把这一方法给以介绍和展开,其实,现在新提出的某些统计量,它们的极限分布是可以用这一方法求出的,因此,籍助几个重要的例子来说明这一方法还是值得的,本文就是为此目的而写的。     

Exact multiplicity and global structure of solutions for a class of semilinear elliptic equations

In this paper, we establish an exact multiplicity result of solutions for a class of semilinear elliptic equation. We also obtain a precise global bifurcation diagram of the solution set. As a result, an open problem presented by C.-H. Hsu and Y.-W. Shih [C.-H. Hsu, Y.-W. Shih, Solutions of semilinear elliptic equations with asymptotic linear nonlinearity, Nonlinear Anal. 50 (2002) 275-283] is completely solved. Our argument is mainly based on bifurcation theory and continuation method.     

关于一个非中心多元F阵特根的渐近联合分布的一点注记

In P.L.Hsu(1941),the proof of the basic Lemma 3 is basedon Lemma 1 which is wrong.The aim of this note is to correct the proof ofLemma 3,consequently,to ensure the main theorem in P.L.Hsu(1941).     

关于一类随机矩阵特征根极限分布的注记

一 引言 考虑k个p维总体X_1,X_2,…,X_k。假定它们都服从正态分布,其均值向量分别是(ξ_(1i),ξ_(2i),…,ξ_(pi)),i=1,2,…,k,且具有共同的协方差矩阵∑=(σ_(ij)),i,j=1,2,…,p。考虑矩阵     

The continuous-time triangular Pólya process

We study poissonized triangular (reducible) urns on two colors, which we take to be white and blue. We analyze the number of white and blue balls after a certain period of time has elapsed. We show that for balanced processes in this class, a different scaling is needed for each color to produce nontrivial limits, contrary to the distributions in the usual irreducible urns which only require the same scaling for both colors. The limit distributions (of the scaled variables) underlying triangular urns are Gamma. The technique we use couples partial differential equations with the method of moments applied in a bootstrapped manner to produce exact and asymptotic moments. For the dominant color, we get exact moments, while relaxing the balance condition. The exact moments include alternating signs and Stirling numbers of the second kind.     

Direct construction of code loops

Code loops were introduced by R.L. Griess Jr. [Code loops, J. Algebra 100 (1) (1986) 224-234] and T. Hsu [Explicit constructions of code loops as centrally twisted products, Math. Proc. Cambridge Philos. Soc. 128 (2) (2000) 223-232] gave methods to construct the corresponding code loop from any given doubly even binary code; both these methods used some kind of induction. In this paper, we present a global construction of the loop, where we apply the correspondence between the concepts of Moufang loops and groups with triality.     

Distributions of numbers of runs and scans on directed acyclic graphs with generation

In this paper, we introduce a class of a directed acyclic graph on the assumption that the collection of random variables indexed by the vertices has a Markov property. We present a flexible approach for the study of the exact distributions of runs and scans on the directed acyclic graph by extending the method of conditional probability generating functions. The results presented here provide a wide framework for developing the exact distribution theory of runs and scans on the graphical models. We also show that our theoretical results can easily be carried out through some computer algebra systems and give some numerical examples in order to demonstrate the feasibility of our theoretical results. As applications, two special reliability systems are considered, which are closely related to our general results. Finally, we address the parameter estimation in the distributions of runs and scans.     

An algorithm to construct Monte Carlo confidence intervals for an arbitrary function of probability distribution parameters

We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the parameter or a function of the parameter of one-parameter continuous distributions. After appropriate heuristic modifications of the algorithm we use it to obtain approximate confidence intervals for a parameter or a function of parameters for multi-parameter continuous distributions. The advantage of the algorithm is that it is general and gives a fast approximation of an exact confidence interval. Some asymptotic (analytical) results are shown which validate the use of the method under certain regularity conditions. In addition, numerical results of the method compare well with those obtained by other known methods of the literature on the exponential, the normal, the gamma and the Weibull distribution.     

Likelihood Inference under Generalized Hybrid Censoring Scheme with Comp eting Risks

Statistical inference is developed for the analysis of generalized type-II hybrid censoring data under exponential competing risks model. In order to solve the problem that approximate methods make unsatisfactory performances in the case of small sample size, we establish the exact conditional distributions of estimators for parameters by conditional moment generating function(CMGF). Furthermore, confidence intervals(CIs) are constructed by exact distributions, approximate distributions as well as bootstrap method respectively, and their performances are evaluated by Monte Carlo simulations. And finally, a real data set is analyzed to illustrate all the methods developed here.