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

Abstract：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.