相依结构和边际分布对水文多变量概率分布的影响

Effects of Dependence Structure and Marginal Distribution on Hydrological Multivariate Probability Distribution

以Gumbel-logistic模型和阿基米德Copula族中的Gumbel-Hougard Copula模型为例研究了不同相关性描述方法和边际分布型式对多变量联合概率的影响。拟合优度检验结果表明,基于变量秩相关系数构建的Copula函数模型优于基于变量的线性相关关系而建立的其他各类模型,如Gumbe-llogistic模型等,其原因在于秩相关系数既可以度量变量的线性关系,又可以度量变量间非线性的相关关系,而线性相关系数仅能度量变量之间的线性相关关系。边际分布的优劣影响了联合概率分布模型结果的准确性,边际分布与数据的拟合效果越好,得到的联合概率也越准确。构建多变量概率分布模型时,需要准确描述变量之间相关关系,并选择适宜的边际分布型式,这是保证多变量概率分布模型准确性的重要基础。

The effects of dependence structure and marginal distribution on hydrological multivariate probability distribution are studied by taking the Gumbel-logistic model and Gumbel-Hougard Copula model as example, which are the representatives of traditional bivariate probability model and Copula function method respectively. The results of Goodness-of-fit test showed that the Copula model which are constructed based on rank correlation coefficient Kendall＇s have better Goodness-of-fit than the traditional bivariate probability model such as Gumbel-logistic model, bivariate lognormal distribution, Gumbel Mixed Model, etc, which are constructed based on linear correlation coefficient. The reason is that both the linear and nonlinear correlation between variables can be measured by rank correlation coefficient Kendall＇ s, while the linear correlation coefficient can only describe the linear correlation. The marginal distribution plays another important role in constructing multivariate probability model, which have obvious effects on ioint probability, and marginal distribution with better Goodness-of-fit obtained better multivariate probability model. The results showed that the dependence structure and marginal distribution are the two important factors which should be chosen carefully when constructing the multivariate probability distribution model.