小批量生产时的中位数控制图

设计总体服从正态分布的小批量生产中位数控制图的控制限,首先导出与中位数有关的统计量的分布,然后将中位数标准化,找出标准化中位数的分布和近似正态分布,最后分别基于标准差和极差给出小批量生产中位数控制图作出了讨论,给出了随着样本组数可变的控制界限.     

一类基于秩次的稳健线性回归估计与诊断方法

线性回归模型的误差项不服从正态分布或存在多个离群点时,可以将残差秩次的某些函数作为权重引入估计模型来减少离群点的不良影响。本文从参数估计、稳健性质、回归诊断等方面对基于残差秩次的一类稳健回归方法进行介绍.通过模拟研究和实例分析表明,R和GR估计是一种估计效率较高的稳健回归方法,其中GR估计可同时避免X与Y空间离群点,而高失效点HBR估计可通过控制某个参数在稳健性与估计效率之间进行折衷.     

误差服从多元t分布的一类线性模型下参数估计的若干注记

研究一类线性模型下参数估计的若干问题．这类模型包含了多个因变量线性模型、增长曲线模型、扩充的增长曲线模型、似乎不相关回归方程组、方差分量模型等常用模型．在这类线性模型下,证明了当误差服从多元t分布时与误差服从多元正态分布时,具有相同的完全统计量和无偏估计,且在后一种情况下的充分统计量必为前一种情况下的充分统计量．对于带有多种协方差结构的前述几种模型,把在误差服从多元正态分布下,相应的协方差阵及有关参数的一致最小风险无偏(UMRU)估计存在性的结论推广到了相应的误差服从多元t分布情形．此外,对于误差服从多元t分布的这类统一的线性模型,给出了回归系数的线性可估函数的无偏估计的协方差阵的C-R下界．     

上证指数周收益率分布的分段高斯性

以往的研究显示股票收益率往往有厚尾的特性,在本文中,我们假设收益率服从不同的分布,所以我们将数据分段,用两种方法对数据进行分段分布拟合.第一种方法是假设这三段数据服从相同均值,但不同方差的正态分布;第二种方法是假设这三段数据服从均值和方差均不相同的正态分布.在这两种假设下,对于每一小段,用最小二乘原理得到了相应分布的参数值.最后利用K-S检验进行验证.结果显示,上证指数周收益率服从分段正态分布.     

随机误差的分布机理

研究随机变量误差的分布函数,通过数理变形、推导证明此随机变量精确服从正态分布.     

上海股票市场收益率分布研究

股票市场的收益率从分布的角度看,并不服从标准的正态分布,而是呈现出一种"尖峰、厚尾"的特征。本文对上海股票市场进行分析,采用几种方法对股指对数收益率进行正态分布检验,发现收益率更加接近于一种混合正态分布,本文利用混合辨析的思想得到了收益率分布的具体形式。     

判定二维随机变量服从正态分布的一个充分条件

探讨了二维随机变量服从正态分布的一个充分条件.在两个不相关的随机变量的任意正整数线性组合都是正态随机变量的条件下,利用矩生成函数证明了它们分别服从正态分布,且联合分布也是二维正态分布.     

淮安市PM2.5的分布特征与灰色预测模型

研究对象是淮安市主要大气污染物中PM2.5在2013-2016年间的观测数据,从两个方面对PM2.5的浓度进行了研究.一方面,利用非参数假设检验中的卡方拟合检验与W检验等方法研究了PM2.5浓度的分布特征.研究发现,污染物PM2.5的日均浓度服从对数正态分布、月均浓度服从正态分布.另一方面,建立了PM2.5年均浓度的精度为一级可用于长期预测的GM(1,1)预测模型,利用预测模型对未来五年中PM2.5的浓度水平进行了预测.     

矩阵正态统计分布的一个性质

对于服从相同统计分布的两个 n维随机向量 X和 Y,若 X关于 Y的条件概论分布为多元正态分布Nn(ATy+ b,φ0 ) ,则由 X和 Y构成的 2 n维随机向量也服从多元正态分布 ,并且︳(A) <1;利用条件分布和特征函数的唯一性定理 ,证明了矩阵正态分布也存在类似结论 .     

基于MRS-GARCH模型的中国股市波动率估计与预测

基于误差项服从正态分布、t分布、广义误差分布的GARCH族模型和MRS-GARCH模型对中国股市波动的结构变化特征进行了实证研究。结果表明,中国股市存在显著的高、低波动状态,两种波动状态的ARCH和GARCH项系数存在较大差异;高、低波动状态均具有较长的持续时间,低波动状态的持续时间长于高波动状态的持续时间,且中国股市更易于从高波动状态转向低波动状态;MRS-GARCH模型预测效果总体上优于GARCH族模型,基于正态分布的MRS-GARCH模型短期预测效果较好。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].