圆内二维均匀分布的参数估计

研究了圆内二维均匀分布的参数估计,利用次序统计量得到了圆的半径的估计量与置信区间.     

关于凸像共形映照的掩蔽性质

<正> 1.设G是复数W平面上的一个凸形区域.假如通过G的一个境界点有一个圆周把G合在它的内部,那末这个圆周是 G 在此境界点的支持圆周.设在 G 的每一个境界点都有一个半径不超过ρ(ρ>0)的支持圆周,并且有一个点,其支持圆周的半径不能小于ρ,那末称 G 是一由半径为ρ的圆所支持的凸形区域.我们又简称这种区域为支持半径为ρ的区域.当ρ=∞时圆周化成直线,每一凸形区域都为一个半平面所支持.     

Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

平面Bonnesen型不等式

将用积分几何方法给出平面等周不等式以及Bonnesen型不等式,平面区域D的面积、周长、最大内接园半径及最小外接园半径的一些几何不等式的简单证明.     

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本文利用广义p值和广义置信区间理论,研究了两独立服从双参数指数分布产品平均寿命比率的统计推断问题.给出了平均寿命比率的广义置信区间,并对该区间的覆盖率和区间长度进行了数据模拟,模拟结果与已有文献中的近似置信区间进行了比较,结果显示本文给出的广义置信区间的区间覆盖率和区间长度都要优于近似置信区间,特别是在小样本的情况下.     

单峰分布枢轴量的等尾与等高置信区间的比较

对枢轴量G的分布具有单峰密度函数的情形,证明了G的最短置信区间是满足置信区间端点密度函数值"等高"条件的置信区间.还对枢轴量分布为正态分布、t分布、卡方分布、F分布、伽玛分布和对数正态分布情形下,在Excel中进行了搜索式数值计算,并列表比较了"等尾"和"等高"情形下置信区间的长度,验证了上述分析结论.另外,还讨论了枢轴量的最短置信区间与枢轴量中所含参数的最短置信区间的关系.     

置信区间的随机加权估计

用随机加权法建立了分位点ｑ的置信区间，又用后向临界点导出了更实用的置信区间。导出的置信区间是非参数的且和原置信区间长度相同。     

单个多元正态总体均值向量联合置信区间的比较

单个多元正态总体均值向量的Bonferroni和Scheff\'{e}联合置信区间在实际中经常用到,本文主要采用解析的办法比较这两个置信区间的长短, 证明了当均值向量的维数$2\le p\le 12$时, Bonferroni联合置信区间比Scheff\'{e}联合置信区间短.     

条件密度置信区间的覆盖精度

本文用经验似然方法讨论了条件密度的置信区间的构造. 通过对覆盖概率的Edgeworth展开得到了经验似然置信区间的覆盖精度, 同时证明了条件密度的经验似然置信区间的Bartlett可修正性     

指数分布抽样基本定理及在指数分布参数统计推断中的应用

发现指数分布抽样基本定理,应用到指数分布参数的统计推断中,得到了指数分布参数的一致最小方差无偏估计;并且得到了单总体指数分布参数的置信区间及联合置信区间,以及双总体指数分布参数比值及差的置信区间.     

n维球内均匀分布的参数估计

研究了n维球内均匀分布的参数的点估计与区间估计,利用次序统计量得到了球半径的最大似然估计,在此基础上构造了球半径的无偏估计,并且证明了该无偏估计的相合性.利用构造枢轴量的方法得到了球半径的最短置信区间.     

A new confidence interval for all characteristic roots of a covariance matrix

Confidence intervals for all of the characteristic roots of a sample covariance matrix are derived. Using a perturbation expansion, we obtain a new confidence interval for these roots. Then, we propose another confidence interval based on the results of Monte Carlo simulations. Since it is based on simulations, this new confidence interval is both narrower and more accurate than others when the difference between the largest and smallest characteristic roots of the population covariance matrix is large.     

线性混合模型中方差分量的广义推断

本文考虑了线性混合模型中方差分量的假设检验和区间估计问题.基于广义P-值和广义置信区间的概念,构造了对应于随机效应的单个方差分量的精确检验和置信区间.所构造的广义p-值和广义置信区间是最小充分统计量的函数.对于两个独立线性混合模型中对应于随机效应的方差分量的比较,建立了精确检验和置信区间.进-步,研究了所给检验和置信区间的统计性质,给出了这些检验方法与文献中已有方法的功效比较的模拟结果.模拟结果表明,新检验在功效方面有显著的改进.最后,通过-个实例来演示本文方怯.     

关于均匀分布区间长度的区间估计

给出了均匀分布区间长度的估计量以及概率密度,并给出了区间长度的区间估计.     

均匀分布区间长度的估计

给出了均匀分布区间长度的估计量以及概率密度,并给出了区间长度的区间估计.     

Consensus formation of two-level opinion dynamics

Opinion dynamics have received significant attention in recent years. This paper proposes a bounded confidence opinion model for a group of agents with two different confidence levels. Each agent in the population is endowed with a confidence interval around her opinion with radius αd or (1-α)d, where α ∈ (0,1/2] represents the differentiation of confidence levels. We analytically derived the critical confidence bound d_c = 1/(4α) for the two-level opinion dynamics on ?. A single opinion cluster is formed with probability 1 above this critical value regardless of the ratio p of agents with high/low confidence. Extensive numerical simulations are performed to illustrate our theoretical results. Noticed is a clear impact of p on the collective behavior: more agents with high confidence lead to harder agreement. It is also experimentally revealed that the sharpness of the threshold d_c increases with α but does not depend on p.     

Fuzzy confidence interval for pH titration curve

In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.     

On the Radius of Spatial Analyticity for the Inviscid Boussinesq Equations

In this paper, we study the problem of analyticity of smooth solutions of the inviscid Boussinesq equations. If the initial datum is real-analytic, the solution remains real-analytic on the existence interval. By an inductive method we can obtain a lower bound on the radius of spatial analyticity of the smooth solution.     

Ricci Flow of Regions with Curvature Bounded Below in Dimension Three

We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has sectional curvature bounded from below by ?1, then we prove estimates which show that compactly contained subregions of this ball will be smoothed out by the Ricci flow for a short but well-defined time interval. The estimates we obtain depend only on the initial volume of the ball and the distance from the compact region to the boundary of the initial ball. Versions of these estimates for balls of radius r follow using scaling arguments.