Some Results and Recommendations on Bivariate Frequency Modeling in Hydrology

This paper deals with bivariate hydrological frequency modeling, which allows the study of two dependent hydrological variables X₁ and X₂, the marginal distributions of which are generally non symmetrical and do not belong to the same distribution family. The first type of bivariate models we consider is "copula-based", another is derived from "classical families of bivariate distributions" through variable transformation. We provide information on the joint, conditional and marginal distributions that are obtainable from these two types of bivariate models. We also consider parameter estimation and give graphical and numerical diagnostic tools for assessing the adequacy of a bivariate model and for choosing among different bivariate models. The analysis of a hydrological data set demonstrates how the proposed methodologies are implemented in practice.