模拟随机数统计性质比较

本文总结了几种历史上有影响的模拟随机数发生方法 ,并对线性同余法和取小数法进行了统计比较 ,从而肯定了取小数法的优良性能     

统计模拟在几何概率问题中应用的注解

设D为R²上的一个紧集, X 为D上的一个随机覆盖过程的统计量. 由于问题复杂, X的均 值、方差、分布函数均没有解析表达式. 统计模拟可以帮助我们找到它们的近似解. 为了在D上做统 计模拟, 需要D的代表点. 产生代表点的不同方法, 会影响统计模拟的结果. 若D不是一个矩形, 如 何选择合适的代表点至关重要. 文献中研究了一个在单位圆上的随机覆盖问题, 提出在单位圆上产生 代表点的四种方法, 并对这四种方法给予评估. 本文考虑两个随机圆的随机覆盖问题, 给出覆盖面积 的理论公式, 使比较四种产生代表点的方法有一个基准. 我们的研究结果和文献中的结论一致, 并发现 其中两种方法使覆盖面积均值的估计有偏, 且有较大的方差, 这是一个新的结果. 本文进一步指出覆 盖面积的分布可由 β 分布来拟合.     

两个回归函数相等的Bootstrap检验

两个回归参数相等性检验一直是统计界感兴趣的问题之一．在这篇文章中，四个检验统计量被用于度量两曲线的差异，在原假设下统计量的分布采用向量数据的重复抽样来逼近，并给出了—些模拟结果．     

基于“醉汉随机游走”问题的统计实验教学案例设计

为了提高学生在数据化时代的实践应用能力,本文基于"随机游走"问题设计统计实验教学案例.将蒙特卡洛随机模拟和回归分析应用于求解"随机游走"的平均距离,并找出平均距离与步数之间的关系,以深化学生对概率统计知识的理解和系统掌握,强化学生对统计软件的操作能力.     

统计视角下的结构突变检验设计及其应用

在结构突变检验中,针对参数统计检验需要依赖于严格假定的局限,本文创新性地提出了一套切实可行的非参数统计检验方法和检验程序。蒙特卡罗模拟表明,这套非参数统计组合设计具有较高的检验效力;结构突变前后样本量大小并不影响对截距与斜率双突变以及截距不变、斜率突变进行检验的检验效力,而对截距突变、斜率不变以及无结构突变检验影响较大。     

统计模拟中的数论方法

受现实生活的一个案例形成的随机覆盖问题之启发,我们在本文中讨论并比较了统计模拟中的几种方法,包括ELP网、NT网与其他网．我们给出的一些结果对统计模拟是有用的．     

随机数与模拟实验

在统计与概率学习中,最有效的教学途径是通过学生亲身实践、动手模拟,来体会统计思想和概率的意义．随机模拟试验需要大量随机数,用手工方法费时费力,而图形计算器可以快捷便利地实现,笔者以HP图形计算器为例,探讨利用图形计算器进行随机数与模拟实验教学的问题．     

熔融KCl中微观空洞及其分布的计算机模拟研究

以分子动力学计算机模拟所得KCl瞬态构型为原始数据，本文计算了不同温度的系统中存在的微观空洞并用径向分布函数描述微观空洞的统计分布，进而讨论了微观空洞的分布随温度变化的特点和不同半径的微观空洞的分布特点．我们也讨论了微观空洞的体积与系统自扩散系数、粘滞性之间的关系．     

几何体网对随机模拟的影响

随着计算机的迅速发展,统计模拟常用于解决实际问题.在几何概率问题中,代表几何体网的构造十分重要。本文考虑四种不同的产生网的方法对三种不同几何体(球带、圆饼、圆环)进行模拟试验,得到一些有用的结果,并推荐数论方法,特别是好格子点(GLP)方法。本文指出代表几何体的网十分重要,若选择不当,可能会导致有偏估计。     

一类虚拟寿命不完全维修模型的统计模拟分析

本文通过利用统计分析的方法分析了一类虚拟寿命不完全维修模型,在此类模型中,系统的报废时间由系统的虚拟寿命决定。由于在分析此类模型时,大多数情况下系统的运行时间之间相互不独立,直接导出相关的可靠性指标的计算公式比较困难,因此采用统计模拟的方法得出相关的可靠性指标。     

提示信息特征对秘书问题决策影响的仿真实验研究

针对具有提示信息的秘书问题,首先分析了提示信息特征变化对决策结果的可能影响.然后在此基础上,提出了在最大值标杆策略下研究提示信息的变化特征对决策结果的影响,接着阐述了仿真试验的理论假设和设计,通过仿真试验考察了提示信息的不同变化对仿真结果的影响;最后给出了对仿真结果的分析和探讨,仿真结果验证了理论假设的判断.     

基于遗传算法的车间作业计划仿真研究

将仿真技术和遗传算法相结合,根据生产车间的资源情况、优化目标等建立了生产调度仿真模型,然后对仿真输出结果进行统计,针对统计结果应用遗传算法对调度决策进行优化.仿真优化结果说明了该集成优化方法是有效性的.     

Simulation Model Development and Analysis in UNITY

We evaluate UNITY – a computational model, specification language and proof system defined by Chandy and Misra [5] for the development of parallel and distributed programs – as a platform for simulation model specification and analysis. We describe a UNITY-based methodology for the construction, analysis and execution of simulation models. The methodology starts with a simulation model specification in the form of a set of coupled state transition systems. Mechanical methods for mapping the transition systems first into a set of formal assertions, permitting formal verification of the transition systems, and second into an executable program are described. The methodology provides a means to independently verify the correctness of the transition systems: one can specify properties formally that the model should obey and prove them as theorems using the formal specification. The methodology is illustrated through generation of a simulation program solving the machine interference problem using the Time Warp protocol on a distributed memory parallel architecture.     

流通加工作业安排的建模及计算机模拟方法

论述了计算机模拟技术在流通加工安排中的应用问题,建立了相关模型及约束条件,对计算机模拟过程进行了较为详细的说明,对于解决流通加工作业排序问题,计算机模拟被认为是一种有效的方法.     

Simulating events of unknown probabilities via reverse time martingales

Let s∈(0,1) be uniquely determined but only its approximations can be obtained with a finite computational effort. Assume one aims to simulate an event of probability s. Such settings are often encountered in statistical simulations. We consider two specific examples. First, the exact simulation of non‐linear diffusions ([ 3 ]). Second, the celebrated Bernoulli factory problem ([ 10 , 13 ]) of generating an f(p)‐coin given a sequence X₁,X₂,… of independent tosses of a p‐coin (with known f and unknown p). We describe a general framework and provide algorithms where this kind of problems can be fitted and solved. The algorithms are straightforward to implement and thus allow for effective simulation of desired events of probability s. Our methodology links the simulation problem to existence and construction of unbiased estimators. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 38, 441–452, 2011     

Large scale nonlinear deterministic and stochastic optimization: Formulations involving simulation of subsurface contamination

Once subsurface water supplies become contaminated, designing cost-effective and reliable remediation schemes becomes a difficult task. The combination of finite element simulation of groundwater contaminant transport with nonlinear optimization is one approach to determine the best well selection and optimal fluid withdrawal and injection rates to contain and remove the contaminated water. Both deterministic and stochastic programming problems have been formulated and solved. These tend to be large scale problems, owing to the simulation component which serves as a portion of the constraint set. The overall problem of combined groundwater process simulation and nonlinear optimization is discussed along with example problems. Because the contaminant transport simulation models give highly uncertain results, quantifying their uncertainty and incorporating reliability into the remediation design results in a class of large stochastic nonlinear problems. The reliability problem is beginning to be addressed, and some strategies and formulations involving chance constraints and Monte Carlo methods are presented.     

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.     

赌博破产概率及其随机模拟试验

讨论了赌博问题中的最终破产概率,并给出了破产概率的随机模拟计算流程和一个具体例子的数值模拟结果.计算结果表明,由此方法得到破产概率的估计值与理论值的误差很小.最后,通过随机模拟给出游戏结束的平均次数.     

Multi-objective simulation-based evolutionary algorithm for an aircraft spare parts allocation problem

Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this study, we develop a solution framework which integrates multi-objective evolutionary algorithm (MOEA) with multi-objective computing budget allocation (MOCBA) method for the multi-objective simulation optimization problem. We apply it on a multi-objective aircraft spare parts allocation problem to find a set of non-dominated solutions. The problem has three features: huge search space, multi-objective, and high variability. To address these difficulties, the solution framework employs simulation to estimate the performance, MOEA to search for the more promising designs, and MOCBA algorithm to identify the non-dominated designs and efficiently allocate the simulation budget. Some computational experiments are carried out to test the effectiveness and performance of the proposed solution framework.     

Response surface methodology as a means for efficient data storage and retrieval

Managing the volume of experimental and/or simulation data required for large-scale design studies can be a significant problem. This paper describes a method for dealing with this problem, using response surface methodology. The method involves (1) determining a summary parameterization of the response of the underlying process mechanism generating the data, in order to characterize this response in terms of a manageable set of performance measures, and (2) deriving a model of the data, in order to summarize the dependence of the performance measures on selected predictor or design variables. The method is illustrated by its application to a problem in vehicle collision research.