多维正态分布函数的表示

在许多金融问题的研究中,如金融衍生产品定价、金融风险度量与管理等领域,经常用到多维正态分布函数.在概率论与数理统计文献中只给出了一维标准正态分布表,而多维正态分布函数的计算问题没有给出具体的算法.本文给出了多维正态分布函数与一维标准正态分布函数的关系式,从而解决了多维正态分布函数的计算问题.     

基于涨跌幅限制的双边截断正态分布期权定价模型

标准Black Scholes期权定价公式假设股票价格服从对数正态分布,没有考虑股票价格涨跌幅的限制带来的影响.放松该假设条件,假设股票价格服从双边截断对数正态分布,考虑中国股票市场的涨跌幅限制,得到一个新的B-S期权定价公式来表达股价行为.双边截断正态分布假设下收益率的波动率要要比正态分布下的波动率小,所以新B-S公式计算出的期权价格就会比标准B-S公式计算出的价格低.     

正态分布的近似表达式

本文给出了标准正态分布的两个简便、实用,且特别适宜于用袖珍计算器进行计算的近似表达式.     

常见连续型统计分布的一点注记

正态分布是概率论与数理统计中最重要的一个分布,本文讨论了常见的连续型统计分布与标准正态分布间的关系,结果表明:几乎所有的常见连续型统计分布都是标准正态分布的函数.     

正态随机变量的非线性函数具有正态性的两个例子

设 X是一个服从标准正态分布的随机变量 ,即 X～N(0 ,1) ,本文给出两类非线性函数 f(x) ,使得 f (X )仍然服从标准正态分布 .     

有偏总体的极差控制图

根据加权标准差方法建立有偏总体的极差控制图,它基于有偏总体来计算对应于正态分布的控制图常数,根据样本数据的偏度来计算上下控制限,对于总体是对称分布,该控制图退化为标准的休哈特控制图.最后,用蒙特卡洛方法给出了改进的控制图常数.     

对数正态分布的参数估计

给出对数正态分布的数字特征,分别计算了对数正态分布参数的矩估计、极大似然估计和贝叶斯估计,并讨论了参数的区间估计.     

上海股票市场收益率分布研究

股票市场的收益率从分布的角度看,并不服从标准的正态分布,而是呈现出一种"尖峰、厚尾"的特征。本文对上海股票市场进行分析,采用几种方法对股指对数收益率进行正态分布检验,发现收益率更加接近于一种混合正态分布,本文利用混合辨析的思想得到了收益率分布的具体形式。     

二维和三维正态分布的一种近似计算

<正> 在数理统计中,正态分布有特殊重要的地位.因此已制作了不少一维正态分布表,以供实际使用.多维正态分布也是经常要遇到的问题,比如在讨论多指标问题的综合评定时,就以多维正态分布的计算为一种手法.二维正态分布在经过标准化之后,可表为     

例谈正态分布的应用

正态分布是自然界中最常见的一种分布,例如测量的误差,人的生理特征的某些数据,学生的考试成绩等等.它广泛存在于自然现象及科学技术的许多领域中.在实际应用中,当给定一个标准的正态分布N(0,1)以后,设P(ξ相似文献   

Accelerating the convergence in the single-source and multi-source Weber problems

The modified Weiszfeld method [Y. Vardi, C.H. Zhang, A modified Weiszfeld algorithm for the Fermat-Weber location problem, Mathematical Programming 90 (2001) 559-566] is perhaps the most widely-used algorithm for the single-source Weber problem (SWP). In this paper, in order to accelerate the efficiency for solving SWP, a new numerical method, called Weiszfeld-Newton method, is developed by combining the modified Weiszfeld method with the well-known Newton method. Global convergence of the new Weiszfeld-Newton method is proved under mild assumptions. For the multi-source Weber problem (MWP), a new location-allocation heuristic, Cooper-Weiszfeld-Newton method, is presented in the spirit of Cooper algorithm [L. Cooper, Heuristic methods for location-allocation problems, SIAM Review 6 (1964) 37-53], using the new Weiszfeld-Newton method in the location phase to locate facilities and adopting the nearest center reclassification algorithm (NCRA) in the allocation phase to allocate the customers. Preliminary numerical results are reported to verify the evident effectiveness of Weiszfeld-Newton method for SWP and Cooper-Weiszfeld-Newton method for MWP.     

复合材料旋转壳非线性稳定性分析计算

利用前屈曲一致理论和能量变分法分析计算了复合材料旋转壳非线性稳定性.前屈曲应变-位移关系采用非线性的卡门方程,能量积分采用数值积分,用势能最小原理求解前屈曲位移和内力,提出了求解临界载荷的实用计算方法,用FORTRAN语言编制了相应的计算机程序,并给出了算例.     

On the accuracy of the projection computation of the collision integral

The accuracy of the projection method as applied to the computation of the collision integral is analyzed. It is shown that the method has an error of the second order of smallness with respect to the mesh size. An optimal method for choosing additional nodes that minimizes the computational error is found. The theoretical conclusions and the optimality of the method are confirmed in a series of numerical experiments.     

The estimation of the strength of the heat source in the heat conduction problems

A general method is proposed to determine the strength of the heat source in the Fourier and non-Fourier heat conduction problems. A finite difference method, the concept of the future time and a modified Newton–Raphson method are adopted in the problem. The undetermined heat source at each time step is formulated as an unknown variable in a set of equations from the measured temperature and the calculated temperature. Then, an iterative process is used to solve the set of equations. No selected function is needed to represent the undetermined function in advance. Three examples are used to demonstrate the characteristics of the proposed method. The validity of the proposed method is confirmed by the numerical results. The results show that the proposed method is an accurate and stable method to determine the strength of the heat source in the inverse hyperbolic heat conduction problems. Furthermore, the result shows that more future times are needed in the hyperbolic equation than that of parabolic equation. Moreover, the robustness and the accuracy of the estimated results in the non-Fourier problem are not as well as those of the Fourier problem.     

Implicit difference approximation for the time fractional heat equation with the nonlocal condition

In this work, a method for solving inhomogeneous nonlocal fractional heat equations is proposed. The method is based on the modified Gauss elimination method. It is proved by using matrix stability approach that the method is unconditionally stable. Numerical results are provided to illustrate the accuracy and efficiency of the proposed method.     

On the regularizing properties of the GMRES method

Summary. The GMRES method is a popular iterative method for the solution of large linear systems of equations with a nonsymmetric nonsingular matrix. However, little is known about the behavior of this method when it is applied to the solution of nonsymmetric linear ill-posed problems with a right-hand side that is contaminated by errors. We show that when the associated error-free right-hand side lies in a finite-dimensional Krylov subspace, the GMRES method is a regularization method. The iterations are terminated by a stopping rule based on the discrepancy principle. Received November 10, 2000 / Revised version received April 11, 2001 / Published online October 17, 2001     

混凝土构件检测样本容量的确定方法

混凝土构件检测时,一般采用百分比抽样的方式.以回弹法中对混凝土强度进行检测时采用百分比抽样的抽样方式为例,从绝对误差限和相对误差限的角度分析了不同构件总量均采用此方法抽取样本的不合理性,并提出在不同混凝土强度等级、不同构件总数的情况下,通过控制一定的误差限来确定样本数量的方法.通过理论和实例分析,提出在抽样过程中,采用分层抽样技术对检测构件进行合理分层,降低总体方差,可减少样本数量.这种方法也适用于其它检测问题的样本容量的确定.     

On the convergence of the UOBYQA method

We analyze the convergence properties of Powell's UOBYQA method. A distinguished feature of the method is its use of two trust region radii. We first study the convergence of the method when the objective function is quadratic. We then prove that it is globally convergent for general objective functions when the second trust region radius ρ converges to zero. This gives a justification for the use of ρ as a stopping criterion. Finally, we show that a variant of this method is superlinearly convergent when the objective function is strictly convex at the solution.     

On the accelerated iterative method for estimating the optimum overrelaxation parameter

This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.     

关于边界层方法

本文指出传统的边界层方法(包括匹配法和Vi?ik—Lyusternik方法)的不足:不能作出边界层项的渐近展开式.提出多重尺度构造边界层项的方法,得到符合实情的结果.又与Levinson所用的方法比较,本方法能更简单地导出后一方法给出的边界层项的渐近展开式.又应用此方法研究现有的关于奇异摄动的某些成果,指出这些成果的局限性,并在一般情况下作出解的渐近展开式.