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多维正态分布函数的表示
引用本文:周圣武,张艳,韩苗,索新丽.多维正态分布函数的表示[J].大学数学,2011,27(4):142-145.
作者姓名:周圣武  张艳  韩苗  索新丽
作者单位:中国矿业大学理学院,江苏徐州,221116
基金项目:中央高校基本科研业务费专项资金,国家自然科学基金
摘    要: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.

关 键 词:正态分布  分布函数  协方差矩阵  正定矩阵

Expressions of Multi-dimensional Normal Distribution Function
ZHOU Sheng-wu,ZHANG Yan,HAN Miao,SUO Xin-li.Expressions of Multi-dimensional Normal Distribution Function[J].College Mathematics,2011,27(4):142-145.
Authors:ZHOU Sheng-wu  ZHANG Yan  HAN Miao  SUO Xin-li
Institution:ZHOU Sheng-wu,ZHANG Yan,HAN Miao,SUO Xin-li(College of Science,China University of Mining & Technology,Xuzhou 221116,China)
Abstract:In many researches of the financial problems,such as derivative securities pricing theory,financial risk measure and management and so on,multi-dimensional normal distribution functions are often used.But in the references of Probability and Statistics,the only one-dimensional standard normal distribution table was given and there's no specific algorithm about multi-dimensional normal distribution functions.In this paper,the relational expression between multi-dimensional normal distribution function and one-dimensional standard normal distribution function was given.Thus the computational problems about multi-dimensional normal distribution function can be solved.
Keywords:normal distribution  dsistribution function  covariance matrix  positive-definite matrix
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