指数分布2/3(G)表决系统产品的统计分析

针对指数分布2/3(G)表决系统产品,本文给出了系统的寿命分布及数字特征,并在全样本场合下给出了参数的矩估计、极大似然估计和逆矩估计,通过大量Monte-Carlo模拟比较了三种点估计的精度。此外,还给出了求参数区间估计的两种方法,并通过大量Monte-Carlo模拟考察了区间估计的精度,得到参数的精确区间估计优于近似区间估计。     

指数分布冷贮备系统产品的统计分析——转换开关指数型的情形

给出了全样本场合下指数分布冷贮备系统产品寿命分布中参数θ≠λ时的矩估计和极大似然估计,通过Monte-Carlo给出了参数矩估计的精度,考察了1000次满足条件时所需要的模拟次数,随着样本量的增大,矩估计存在的比率逐渐增大,而极大似然估计的结果与样本有关.同时给出了参数θ=λ时的矩估计、极大似然估计和逆矩估计,通过Monte-Carlo模拟考察了参数点估计精度,认为矩估计比较优.文章还给出了求参数区间估计的两种方法——精确方法和近似方法,通过Monte-Carlo模拟认为精确方法精度较高.     

定时截尾场合指数分布表决系统产品的统计分析

本文针对指数分布2/3(G)表决系统产品,在截尾样本场合下给出了参数的拟矩估计、极大似然估计和近似区间估计,并通过大量的Monte-Carlo模拟分别考察了点估计和区间估计的精度。     

Statistical Analysis of Series System for Masked Data under Successive Censored Life Test

In this paper, considering series system of masked data under simple successive censored and multiple successive censored life test, the likelihood function and maximum likelihood estimate are respectively proposed for series system composed of two units under two kinds of situations. One is the series system composed of two units with constant failure rate, and the other is the series system composed of two units with linear failure rate through the origin. The approximate interval estimates of parameters are given by using the method of likelihood ratio. Besides, the examples show the feasibility of the methods through Monte-Carlo simulations.     

指数分布串—并联混合系统产品的统计分析

给出单元寿命服从同一指数分布的串-并联混合系统产品参数的矩估计和极大似然估计,并通过大量Monte-Carlo模拟比较了估计的精度,得到在样本容量小于35时矩估计优于极大似然估计,而样本容量不小于35时极大似然估计优于矩估计.另外,还给出了参数的精确区间估计与近似区间估计,并通过大量Monte-Carlo模拟考察了区间估计的精度.     

Null Controllability for Some Systems of Two Backward Stochastic Heat Equations with One Control Force

The authors establish the null controllability for some systems coupled by two backward stochastic heat equations. The desired controllability result is obtained by means of proving a suitable observability estimate for the dual system of the controlled system.     

平衡随机模型中方差分量的非负估计

众所周知, 对于平衡随机模型, 方差分量的方差分析估计为一致最小方差无偏估计. 本文基于方差分量的方差分析估计, 构造了一个二次不变估计类, 它包含了一些常用重要估计. 证明了该估计类在一定条件下在均方误差意义下一致优于方差分析估计, 并在此估计类基础上, 给出了方差分量的两种非负估计, 它们在均方误差意义下分别一致优于方差分析估计和限制极大似然估计, 且有显式解、容易计算.     

On dynamics of the system of two coupled nonlinear Schrödinger in

In this paper, we give a new proof of the scattering and blow‐up theory of the two coupled nonlinear Schrödinger system via establishing the corresponding interaction Morawetz estimate and scattering criterion. The method of this paper simplifies the proof in Xu, and the result of the paper improves the result in Xu.     

认购证发行总数的估计

利用发行的认购证有编号１，２，……，Ｎ，，本文通过随机抽取的几个认购证号码，给出了认购证发行总数的最大似然估计，一致最小方差无偏估计和Ｂａｙｅｓ估计。     

Estimating the instantaneous volatility and covariance of risky assets

Using the Mihlstein approximation for solutions to stochastic differential equations and the stochastic calculus an estimate for the volatility is obtained. The estimate is also valid for stochastic, Markov, volatilities. If the process has jumps, these reduce the previous estimate. The instantaneous covariance of two risky assets is also calculated.     

关于两个均匀分布总体标准差比的估计

考虑取两个均匀分布总体样本数不同时,两个均匀分布总体标准差比的估计,给出了两个均匀分布总体标准差比的区间估计.     

艾拉姆咖分布参数的Bayes估计及检验

首先给出了艾拉姆咖分布在定数截尾场合下参数的极大似然估计;其次由"平均剩余寿命"的概念得到了参数的拟矩估计;然后取共轭先验分布给出了参数的经验Bayes估计、区间估计及假设检验;最后通过实例给出了不同截尾样本下参数的点估计和区间估计.     

A positive solution for some critical p-Laplacian systems

This paper deals with the existence of a positive solution for two classes of critical quasilinear system. We prove these results by a variant of mountain pass lemma, combining two convergence theorems and two estimate results. Here we avoid the usual compactness arguments(e.g., Palais–Smale condition or Cerami condition) and reveal the potential of some energy level estimates for the existence of nontrivial solutions.     

方差分量的广义谱分解估计

对于随机效应部分为一般平衡多向分类的线性混合模型,将王松桂(2002)提出的一种称之为谱分解估计的参数估计新方法推广到随机效应设计阵为任意矩阵的含两个方差分量的线性混合模型,给出了方差分量的广义谱分解估计方法,并证明了所得估计的一些统计性质。另外,还就广义谱分解估计类中某些特殊估计和对应的方差分析估计进行了比较,得到了它们相等的充分必要条件。     

A new method of spectral decomposition of covariance matrix in mixed effects models and its applications

For the mixed effects models with balanced data, a new ordering of design matrices of random effects is defined, and then a simple formula of the spectral decomposition of covariance matrix is obtained. To compare with the two methods in literature, the decomposition can not only give the actual number of all distinct eigenvalues and their expression, but also show clearly the relationship between the design matrices of random effects and the decomposition. These results can be applied to the problems for testifying the analysis of the variance estimate being a minimum variance unbiased under all random effects models and some mixed effects models with balanced data, for finding the explicit solution of maximum likelihood equations for the general mixed effects model and for showing the relationship between the spectral decomposition estimate and the analysis of variance estimate.     

��ʱ��β������ƽ�������ȹ����о�

本文讨论了相互独立且寿命服从单参数 指数分布的两产品在定时截尾寿命试验中的平均寿命比估计, 并给出了该估计量的渐近正态性和置信区间. 如果某一种(或某一类)产品与另一种(或某一类)产品平均寿命比率显著大于1, 那么该种产品就具有耐用优势, 这在投资决策中有重大意义. 通过数值模拟还进一步验证了该比估计量和估计方法的有效性.     

两个均匀分布总体标准差比的区间估计

考虑取两个均匀分布总体样本数不等时,两个均匀分布总体标准差比的估计,给出了两个均匀分布总体标准差比的区间估计.     

Lipschitz stability in determining density and two Lamé coefficients

We consider an inverse problem of determining spatially varying density and two Lamé coefficients in a non-stationary isotropic elastic equation by a single measurement of data on the whole lateral boundary. We prove the Lipschitz stability provided that initial data are suitably chosen. The proof is based on a Carleman estimate which can be obtained by the decomposition of the Lamé system into the rotation and the divergence components.     

On Two-stage Estimate Based on Independent Estimate of Covariance Matrix

When an independent estimate of covariance matrix is available, we often prefer two-stage estimate （TSE）. Expressions of exact covarianee matrix of the TSE obtained by using all and some covariables in eovariance adjustment approach are given, and a necessary and sufficient condition for the TSE to be superior to the least square estimate and related large sample test is also established. Furthermore the TSE, by using some covariables, is expressed as weighted least square estimate. Basing on this fact, a necessary and sufficient condition for the TSE by using some covariables to be superior to the TSE by using all eovariables is obtained. These results give us some insight into the selection of covariables in the TSE and its application.     

含随机效应GCM中回归参数阵两步估计的计算及其无偏性

首先给出了含随机效应增长曲线模型中回归参数阵两步估计的一个较为简单的计算方法;然后给出了回归参数阵的可估函数的两步估计具有无偏性的一个基本结论,并证明了两种常见两步估计均具有无偏性;最后给出了一个牙齿生长数据的实例模拟.