二元Burr Ⅲ型分布的识别性和渐近独立性

本文讨论了二元Burr Ⅲ分布的识别性和尾部相关性,若已知可识最小值的分布密度时,所有参数皆可识别;另外,还计算了X,Y之间的尾部相关系数,证明了X,Y之间的渐近独立性.     

二元Lawrance-Lewis型指数分布的识别性及渐近不独立性

本文讨论了二元Lawrance-Lewis指数分布的识别性和渐近不独立性,若已知可识最小值的分布密度时,所有参数皆可识别;另外,还计算了X,Y之间的相关系数和尾部相关系数,证明了X,Y之间的渐近不独立性;且X,Y不相关当且仅当b=2时.     

二元一般指数分布的识别性及其参数估计

讨论了一般二元指数分布的识别性问题及参数估计问题.本文证明了两个结论:其一、当只有最大值随机变量的分布已知时,仅一个参数可识别;其二、当可识别最大值的分布已知时,所有参数皆可识别.进一步根据上述结论得到了所有参数的最大似然估计.     

二元Kundu-Gupta型二点分布参数的最大似然估计

讨论二元Kundu-Gupta型二点分布的识别性及参数估计,已知可识最小值的分布时,则参数可识别;由此得到了参数的最大似然估计;其中二个参数的估计量是无偏的,另外一个参数的估计量的期望不存在;模拟结果显示:估计值均稳定于真值参数.     

二元Arnold-Strauss型指数分布的条件指数性及渐近独立性

本文讨论二元Arnold-Strauss型指数分布的条件指数性及渐近独立性,证明了给定X关于Y的条件密度和给定Y关于X的条件密度都是指数分布密度,求出了用于预报的条件概率;并证明了X,Y之间的渐近独立性.另外,讨论了它的识别性,若已知可识最小值的分布密度时,所有参数皆可识别.     

例说基于可识最小值之识别性与参数估计及特征的关系

讨论基于可识最小值之识别性与参数估计及特征的关系,以二元Marshall-Olkin型Weibull分布为例,存在全部参数可估计且可识别且有识别特征的情形;以二元McKay型伽马分布为例,存在全部参数可估计且部分参数可识别且无识别特征而有其它分离特征的情形,若是基于可识最小值及差值,则是全部参数可估计且全部参数可识别且有识别特征的情形;以二元极值二点分布为例,存在部分参数可估计且部分参数可识别且有识别特征的情形.     

不同损失下Lomax分布形状参数的Bayes估计

本文研究了两参数Lomax分布形状参数的Bayes估计问题.当尺度参数已知时,给出了在几种不同损失函数下形状参数的Bayes估计表达式,并运用随机模拟方法对各个估计进行了比较.     

非平方损失函数下Gamma部件可靠性的Bayes估计

Lwin和Singh对部件寿命x服从Г(t,λ,k)分布,当形状参数k已知,尺度参数未知时对部件可靠性进行Bayes估计。考虑到实际问题的需要,对损失函数应加上测度不变性的要求,本文取损失函数在参数λ的先验分布分别为指数Beta分布和Gamma分布的情况下,讨论了Gamma部件各项可靠性指标的Bayes估计,且把Lwin和Singh所做的结果看作本文的特例。设部件的寿命x服从其中:t>0,λ>0,k>0为已知的形状参数,尺度参数λ未知。那么部件的可靠度函数与平均寿命分别为:     

一种可用于检测过程尺度参数的非参数控制图

传统的控制图多数是在已知过程分布的假设下构建的,这种控制图被称为参数控制图。然而,在实际应用中,大多数过程因为其数据的复杂性导致他们的精确分布往往难以确定。当预先指定的参数分布无效时,参数控制图的结果将不再可靠。为了解决这个问题,通常考虑非参数控制图,因为非参数控制图比参数控制图更加稳健。近年来对非参数控制图的研究越来越多,但大多数现有的控制图主要是用于检测位置参数的变化。本文提出一个新的非参数Shewhart控制图(称为LOG图),可用来检测未知连续过程分布的尺度参数。文中依据运行长度分布的均值,方差和分位数,分析了LOG图在过程受控和失控时的性能表现,并与其他非参数控制图进行比较。模拟结果表明,LOG图在不同过程分布下对检测尺度参数的漂移都具有很好的性能。最后用一个实例来说明LOG图在实际中的应用。     

一类条件最值问题的再研讨

1　问题的提出文 [1]在解决问题 (1) :“已知 x,y∈ R+ ,且 x+y= 1,求 1x+4y的最小值 .”时 ,采用了“用 1代换”的方法 ,在将该方法移植到解决问题 (2 ) :“已知 x ,y∈R+ ,且 x+y=1,求 1x2 +8y2 的最小值 .”时 ,思路受阻后 ,提出了在 (1x2 +8y2 )· (　 )中 ,括号中应配上什么式子才能解决问题的疑问 .由此利用柯西(Cauchy)不等式和待定系数法探求出了一个定理 :“已知 x,y∈ R+ ,且 x+y=1,若 λ>0 ,则当且仅当y:x=λ1n+ 1时 ,1xn+λyn (n>0 )取得最小值 ,最小值为(1+λ1n+ 1) n+ 1”.文 [1]的探索是有意义的 ,上述定理是正确的 ,读后…     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

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.     

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].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.