一种求解相关随机变量联合累积分布函数的方法

A method for solving cumulative distribution function of dependent random variables

在结构可靠性、水文、金融等多个领域中,对数据的分析必须考虑其相关性.Copula函数为求解联合累积分布函数的一般方法,在此基础上,提出了一种利用乘积生成元构造多参数Copula函数并拟合求解随机变量的联合累积分布函数的新方法.该方法首先参照普通生成元构造阿基米德Copula函数的方式,利用乘积生成元构造了一种含有未知参数的隐式Copula函数.其次以数据点处的边缘经验分布函数及联合经验分布函数分别代替边缘累积分布函数和联合累积分布函数,并以此作为拟合样本集.然后采用正交距离曲线拟合法确定未知参数,从而得到联合累积分布函数.最后,在K-S拟合优度检验以及OLS准则、AIC准则下,通过与常用的三类阿基米德Copula函数进行结果对比,表明了该方法是一种可以根据已有样本数据求解联合累积分布函数的直接、有效的方法.

Correlation needs to be taken into consideration when analyzing data In the fields of structural reliability,hydrology,and finance.This paper first introduces the general method of solving cumulative distribution function with Copula function.Then a new method for solving cumulative distribution function is proposed,which constructs the implicit function Copula with multiple parameters for fitting.Firstly,an implicit Copula function with unknown parameters is constructed by using the product generator,which imitates the way generators generate the Archimedes Copula function.Secondly,the edge empirical distribution function and the joint empirical distribution function at the data point are used to replace the edge cumulative distribution function and cumulative distribution function,and thus use it as a fitted sample set.Then the ODR algorithm are used to determine the unknown parameters,and cumulative distribution function is obtained.Finally,under the K-S goodness-of-fit test and the OLS criterion and AIC criterion,the results are compared with the results obtained by useing three types of Archimedes Copula function.The findings shows that the method is direct and efficient.