CE模型下Weibull分布序加试验的Bayes分析

序进应力加速寿命试验是一种最为有效而经济的寿命试验方法,随着其理论的日趋成熟,在实践中开始得到应用和推广．本文给出了逆幂律模型下Weilbull分布定时和定数场合序进应力加速寿命试验的一种Bayes统计分析,并利用Gibbs抽样方法解决了分布的形状参数取为连续先验时各参数的Bayes估计．这种先验意义更明确,实例表明这是一种非常有效的方法．     

对数伽玛分布尺度参数的Bayes估计在LINEX与复合LINEX损失函数下的比较

在LINEX损失函数与复合LINEX损失函数下,研究对数伽玛分布尺度参数θ的Bayes估计、E-Bayes估计和多层Bayes估计.给出先验分布为伽玛分布和Jeffreys先验分布时的Bayes估计,进而给出先验分布为伽玛分布时的E-Bayes估计和多层贝叶斯估计.通过数据模拟检验参数的Bayes估计和E-Bayes估计的合理性及优良性,并且发现一些数据表中存在一定的规律.     

基于维纳过程步进应力加速退化试验的客观贝叶斯分析

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.     

具有竞争风险的步进应力加速寿命试验的最优设计和Bayes估计

讨论了渐进II型截尾数据中具有竞争风险的步进应力加速寿命试验的最优试验设计和参数估计.通过假定产品寿命服从Weibull分布,尺度参数对数是应力水平的线性函数基础上,利用KH模型采用极大似然方法和Bayes方法对模型参数进行了点估计和区间估计,而最优试验设计是使尺度参数对数的极大似然估计值在正常应力水平下的渐进方差达到最小.最后进行了仿真研究,结果显示提出的估计量具有良好的稳健性和有效性.     

幂函数模型下恒加寿命试验的非参数贝叶斯分析

线性加速模型常用于恒定应力加速寿命试验的统计分析,这与实际不完全相符.本文建立幂函数加速模型,给出了不同恒定加速应力水平间寿命分位数的关系,利用最小二乘法估计了加速模型的参数及特征标系数向量,从而实现不同应力水平间寿命数据的相互转换.采用Dirichlet过程先验,分别在完全数据情形和截尾数据情形下,得到可靠度函数的后验分布与非参数贝叶斯估计,并证明了后验估计的一致性.最后,通过一个金属氧化物半导体电容寿命实例说明了所建模型的效果.     

指数分布参数多层Bayes和E Bayes估计的性质

本文讨论无失效数据下指数分布参数多层Bayes估计和E Bayes估计的性质,在超参数分别取两种不同的先验分布下,证明参数的多层Bayes估计和E Bayes估计渐近相等,且多层Bayes估计值小于E Bayes估计值.     

Weibull分布恒定应力加速寿命试验的Bayes估计

对定时和定数截尾样本情形CE模型下Weibull分布场合恒定应力加速寿命试验进行了Bayes统计分析,利用Laplace方法给出了该模型的近似Bayes估计.最后通过模拟实例表明该Bayes估计是有效的.     

熵损失函数下两参数指数威布尔分布尺度参数的Bayes估计

本文给定一截尾样本，在熵损失函数下，研究了两参数指数威布尔分布尺度参数在先验伽玛分布下的Bayes估计，并给出了该参数的Bayes区间估计。     

双边定数截尾下Pareto分布的可靠性分析

基于双边定数截尾样本,选取未知参数的先验分布为无信息先验和Gamma分布,分别在平方损失和LINEX损失下,研究了Pareto分布的形状参数和可靠性指标(可靠度和失效率)的Bayes估计.为了研究估计的精度,采用Monte-Carlo模拟的方法给出了数值检验的例子.结果表明在LINEX损失下并选用Gamma先验分布时,参数的Bayes估计是最优的.     

双定数混合截尾下两参数Pareto分布的统计分析

在传统的定时和定数截尾试验的基础上,该文首次提出了一种新的截尾试验方案:双定数混合截尾.基于这类截尾数据求出了两参数Pareto分布参数的极大似然估计及θ的置信区间.当α已知时,取Gamma先验分布的情况下,求出了三种不同损失函数下参数θ、可靠度函数以及失效率函数的Bayes估计;当α,θ都未知时,分别取无信息先验分布...     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.