正态定限（Orthant）概率

本文采用不同以往的方法；对正态定限（Ｏｒｔｈａｎｔ）概率积分施行线性变换与极坐标变换；得到了一个新的递推公式，使积分重数至少降低了３重；并推导了四维正态定限概率的表达式，这对进行数值计算是十分有意义的．     

正态性检验的图示方法及其应用

用图示方法进行正态性检验，不需要作复杂的运算、简单直观、近年来，正态性的图示又有了许多发展，本文在这些发展的基础上，给出了一些图形的接受区间，提高了使用效率，排除了对图形解决的直观性，并且适合在计算机上作图，ＭｏｎｔｅＣａｒｌｏ模拟结果和两个实例也说明了这些方法是用的。     

高维正态概率积分的降维算法与L_1逼近

高维正态概率积分计算一直是统计学家关注的课题．早期工作已由Gupta（1963）[1]评价，并给出大量的参考文献．近期工作则可参考Tong（1990）[2]的专著．虽然有关的文献很多，但是除了二、三维问题已有较好的算法外（例如见Zhana－Yana，1993[3]），更高维问题尚无公认的有效算法．在维数m＞3的高维情形，多数文章常假设积分域或相关阵有特殊形式，否则只有使用MonteCarlo方法［4］或拟MonteCarlo方法（亦称数论网格方法，例如见Fang－Wang，1994[5]）．但即使是被认为较好的拟MonteCarlo方法，其收敛阶仅为O（n－2／m），因此对于真…     

一类Kaplan-Meier估计泛函的一些大样本性质

设F,G分别表示某寿命随机变量与删失随机变量的分布函数,在不假定F、G连续的情况下该文使用点过程鞅方法证明了Kaplan－Meier估计的一类泛函的渐近正态性,并建立了一个均方误差不等式和一个概率不等式．     

Hill统计量的渐近正态性

的正整数。此后,统计量γ_n的渐近性质被广泛地加以研究。Mason证明了γ_n是弱相容的,同时指出:如果k_n=[n~β],0<β<1,那末γ_n也是γ的强相容估计。[3]和[4]讨论了γ_n的渐近正态性;作为正则变化函数性质的一个应用,[5]中对此亦有讨论。本文将在d.f.F连续这一假定下,揭露γ_n的分布与一个条件iid的rv阵列行和的     

数理统计学小史9 社会统计(下)

魁特奈特的正态拟合 魁特奈特(A.Quetelet,1796-1874)是19世纪最有影响的统计学家之一.他的主要贡献,是倡导并身体力行将正态分布用于连续性数据的分析.他的这一努力使正态分布在19世纪统计应用中大为流行.有的学者说正态分布统治了19世纪的统计学,并造出了"魁特奈特主义"这个名词.     

James—Stein型置信椭球及其覆盖概率

本文构造了协方差阵具有非球型结构（未知）的多元正态分布均值的James-Stein型置信椭球,它能渐近一致改进通常置信椭球的覆盖概率,并给出了改进余项的一致阶,同时本质改进了文献中有关余项的一致阶。     

数理统计学小史

６误差分布：正态与偏态（上）上一章我们讲了最小二乘法及其相关的发展,在那里,这个方法是纯粹作为一个处理测量值的代数方法来讨论的,不涉及有关的统计推断问题,要研究这个问题,需要考虑到测量值有误差。这种误差（假定量测过程排除了可能的系统性因素的影响）是随...     

正态向量的函数与线性型之间的独立性

本文通过讨论正态向量X的函数f(X)与线性型AX之间的独立性，把已知的正态向量的二次型与线性型的独立性问题作了推广，并得出了一系列推论。     

关于独立同分布正态随机变量部分和尾概率的注(英文)

设{X,Xn,n≥1}是独立同分布正态随机变量序列,EX=0且EX2=σ2>0,Sn=sum (Xk) form k=1 to n,λ(ε) =sum form (P(|Sn|≥ nε)) form n=1 to ∞.在本文中,我们证明了存在正常数C1和C2,使得对足够小的ε>0,成立下列不等式C1ε3 ≤ε2λ(ε)-σ2+ε2 /2 ≤ C2ε3.     

Inference for a truncated positive normal distribution

The main object of this paper is to study an extension of the half normal distribution defined by adding a positive truncation to it. The new model is more flexible than the half-normal distribution and contains the half normal distribution as a special case. Properties of this distribution, such as moments, hazard function and entropy are studied and parameters estimation is dealt with by using moments and maximum likelihood. A real data application indicates good fit performance of the new model when compared to other competitors in literatures.     

A discussion on mean excess plots

The mean excess plot is a tool widely used in the study of risk, insurance and extreme values. One use is in validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot.     

基于空间滞后随机前沿模型技术效率的估计

为了刻画潜在的空间效应,本文提出了一类空间滞后随机前沿模型.在单边误差项分别服从半正态分布、指数分布及截尾正态分布的情况下,我们给出了模型的对数似然函数及迭代步骤.此外,应用JMLS方法给出了单边误差项的条件均值与条件众数,因而得到了相应的技术效率估计.     

A generalization of the half-normal distribution

In this paper we introduce an extension of the half-normal distribution in order to model a great variety of non-negative data. Its hazard rate function can be decreasing or increasing, depending on its parameters. Some properties of this new distribution are presented. For example, we give a general expression for the moments and a stochastic representation. Also, the cumulative distribution function, the hazard rate function, the survival function and the quantile function can be easily evaluated. Maximum likelihood estimators can be computed by using numerical procedures. Finally, a real-life dataset has been presented to illustrate its applicability.     

Two‐strata rotatability in split‐plot central composite designs

A rotatable design (Ann. Math. Stat. 1957; 28 :195–241) for k factors is one such that the prediction variance is purely a function of distance from the design center. Of special interest in this paper is the rotatable central composite design (CCD), which most software packages use as the typical default choice for a second‐order design. In many cases some factors are hard to change while others are easy to change, which creates a split‐plot experiment. This paper establishes that the split‐plot structure precludes the possibility of any second‐order design being rotatable in the traditional sense. As an alternative this paper proposes the two‐strata rotatable split‐plot CCD, where the resulting prediction variance is a function of the whole plot (WP) distance and the subplot (SP) distance separately instead of the sum of them. The resulting design is rotatable in the WP space when the SP factors are held fixed, and vice versa. In the special case where the WP variance component is zero, the two‐strata rotatable split‐plot CCD becomes the standard rotatable CCD. Copyright © 2009 John Wiley & Sons, Ltd.     

A strategy for analysing mixed and pooled exponentials

It is shown that a linear plot of the mean residual life on the failure rate characterizes the mixture of two exponentials. This plot is used to estimate the two components in the mixing distribution with the two largest mixing proportions. The EM algorithm is then used with these as initial values to obtain the MLE. Gradient plots are used to see if a higher-order fit is needed. A heuristic is given on how to use the gradient plots to identify components in the higher-order fit when this is the case. Graphs of an assignment function are then used to determine if the data are from a mixed model or simply the effect of pooling.     

Displaying Variation in Large Datasets: Plotting a Visual Summary of Effect Sizes

Displaying the component-wise between-group differences high-dimensional datasets is problematic because widely used plots such as Bland–Altman and Volcano plots do not show what they are colloquially believed to show. Thus, it is difficult for the experimentalist to grasp why the between-group difference of one component is “significant” while that of another component is not. Here, we propose a type of “Effect Plot” that displays between-group differences in relation to respective underlying variability for every component of a high-dimensional dataset. We use synthetic data to show that such a plot captures the essence of what determines “significance” for between-group differences in each component, and provide guidance in the interpretation of the plot. Supplementary online materials contain the code and data for this article and include simple R functions to produce an effect plot from suitable datasets.     

Extending the GGobi pipeline from R

This paper describes progress towards developing a platform for rapid prototyping of interactive data visualizations, using R, GGobi, rggobi and RGtk2. GGobi is a software tool for multivariate interactive graphics. At the core of GGobi is a data pipeline that incrementally transforms data through a series of stages into a plot and maps user interaction with the plot back to the data. The GGobi pipeline is extensible and mutable at runtime. The rggobi package, an interface from the R language to GGobi, has been augmented with a low-level interface that supports the customization of interactive data visualizations through the extension and manipulation of the GGobi pipeline. The large size of the GGobi API has motivated the use of the RGtk2 code generation system to create the low-level interface between R and GGobi. The software is demonstrated through an application to interactive network visualization.     

Control of chaos in laser plasma interaction

The chaotic dynamics originating from the equation governing the laser plasma interaction is studied. Our motivation is to show that it is possible to control this chaotic scenario either to a periodic state or to a totally steady state by adopting two different modes of control – one is the sinusoidal time variation of one parameter of the system and the other is the proportional pulse approach. Extensive use is made of Poincaré section, power spectrum analysis and phase space plot to prove the assertions. The observations can be of practical use in the simulation of plasma experiments.