泊松分布中参数的无偏估计

基于泊松分布,讨论未知参数θ与g(θ)无偏估计的区别和联系。得到当E(^θ)=θ时,不一定有E(g(^θ))=g(θ)。并给出了几个一般性结论。     

Skating

Technical evaluation in the sport of figure skating is characterized by a subjective marking system. Figure skating judges are responsible for quickly and accurately discerning the quality of technical elements as well as assigning a score to the overall aesthetic appearance of a performance. Traditionally, overall placement marks are assigned for the entire performance; however, the landing of a jump is widely acknowledged as one of the most critical elements of a skater's program. Therefore, our aims were to identify the biomechanical variables that contribute to technical success in executing landings and to establish whether landings rated as biomechanically optimal are also awarded high technical merit scores by judges. Ten nationally ranked competitive figure skaters were asked to execute on‐ice, double and triple revolution jumps and to try to land the jumps void of technical faults within a calibrated space. Data were collected at 60 Hz using standard three‐dimensional videography. Data reduction was done using the APAS system (Ariel Dynamics Inc). Concurrently, videotapes were viewed and evaluated by 42 accredited judges to determine the perceived technical quality of the landing performances. Judges were asked to evaluate the landing phase of each jump against a landing criteria document. A comparative criteria model was developed to facilitate an assessment of excellence in landing performances through both empirical and subjective analyses. Results of these analyses were twofold: a biomechanical profile of on‐ice landings was obtained, and on‐ice jump landing strategies rated by empirical evaluations were in agreement with judge's perceptions of the same performances.     

泊松方程的优化有限差分方法

本文基于Kreiss所建立的紧致差分公式,提出一种既简单又新颖的离散二维泊松方程的优化有限差分方法。首先将二维泊松方程转化成一维问题,再利用紧致差分直接离散一维方程,以此为基础,最终建立起九结点矩形网格下的求解二维泊松方程的优化差分格式。     

分组零膨胀泊松模型的半参数统计推断

泊松回归模型常常用于计数数据的研究中,然而在实际数据中零值的比例可能远远大于泊松分布中取零值的概率,而且这些零值通常都有其特殊含义.此外计数数据可能是分组数据,即观测到的数据不是确切值而只是已知其落在某一个区间范围之内;或者某些特定的数据,例如工资,要先对它进行人为的分组然后再进行分析.考虑一种零膨胀泊松半参数回归模型来处理上述分组计数数据.该模型中泊松分布的期望与协变量之间采用部分线性连接函数,而零值的概率与协变量之间采用线性连接函数.利用Sieve极大似然估计方法来估计该回归模型中参数和非参数函数,并提出了一种得分检验方法来检验是否存在零膨胀.在一定正则条件下,获得了Sieve极大似然估计的渐近性质,证明了参数部分的估计是强相合,渐近正态及渐近有效的;同时非参数函数的估计达到了最优收敛速度.模拟研究表明,估计和检验方法效果都比较好,最后将此模型和推断方法应用于一组公共卫生领域实际数据研究.     

基于Trilinos开发的并行复杂几何P oisson方程求解器

基于Trilinos程序包中的AztecOO和ML package开发了并行Poisson求解器。在非均匀的结构化网格上实现了复杂金属/电介质几何体的建模。 Poisson方程通过有限体积方法离散形成求解矩阵,然后利用Trilinos进行并行矩阵求解。并行测试表明,求解器的收敛表现良好,在典型情况下性能满足需求。这一求解器代码可以用于从等离子体模拟到传热过程等多种任务。     

用马尔可夫调制的泊松过程近似多分形突发流量研究

研究了用马尔可夫调制的泊松过程(MMPP)对Internet多分形流量突发行为进行近似建模的能力. MMPP可用于描述适当时间尺度范围内流量的变化以及相关性, 而且它可作为排队系统输入过程得到分析结果. 描述了刻画突发流量行为的重要统计量, 在此基础上给出了一个基于矩的MMPP参数估计方法. 除了对MMPP进行拟合优度检测以外, 本文通过将MMPP的样本过程和实际流量记录输入到排队系统模型中比较其输出结果来研究MMPP对排队性能的预测能力. 数值和仿真实验表明, MMPP能够较好地用于对多分形流量近似建模, 即可以准确地预测网络结点的排队性能.     

调查中零频数过多的统计分析方法

无论是在自然科学领域还是在人文社会科学领域,我们会遇到各种各样的计数数据.对于社会生活、生产、管理中的一些计数数据通常是用泊松分布以及泊松过程来描述具有非常好的拟合效果.然而实际环境中,由于受各种因素影响与制约,出现了很多频数为零的数据.此时对含零特别多的计数数据,我们仍用泊松回归模型拟合就有些不合适了[1],因此人们开始构造新的模型,其中对于这种数据拟合效果比较好的一种模型就是零过多泊松分布模型(Zero-Inflated Poisson Distribution)[3,5].     

Converse result on Szász-type operators

Szasz-type operators can be constructed by a Poisson process. The purpose of this paper is to derive the converse result in connection with Szasz-type operators by Steckin-Marchaud-type inequalities and new Ditzian modulus of continuity. The degree of approximation on deterministic signals is also given.     

The evolution of patent pools and patent application behavior against the

在技术标准大量引用技术专利的背景下,标准联盟以专利池运营其拥有的技术专利,专利池在标准创立及产业化中扮演着日益重要的角色。以典型专利池为研究样本,定量分析专利池中的专利数量变化与专利申请行为;研究表明,专利池创立前后是专利申请的高峰期,这些专利绝大部分为专利池的发起人所控制。对专利引用进行泊松回归,揭示出专利池中的专利质量随时间推移逐步降低,在专利池演进过程中,发起人存在策略性的专利申请行为,倾向于将低价值专利＂塞入＂专利池中。     

Updating a Classic: “The Poisson Distribution and the Supreme Court” Revisited

W.A. Wallis studied vacancies in the US Supreme Court over a 96‐year period (1837–1932) and found that the distribution of the number of vacancies per year could be characterized by a Poisson model. This note updates this classic study.