Author(s): Lan Zhang; Vijay P. Singh
Linked Author(s): Vijay Singh
Keywords: Streamflow; Bivariate frequency; Shannon entropy; Copul
Abstract: Fundamental to risk assessment in hydrology is modeling the dependence of correlated hydrological variables. In recent years, the copula theory has been extensively applied to model the dependence structure and the theory has been shown to be more robust than traditional statistical methods for deriving bivariate (multivariate) joint distributions (e. g., bivariate (multivariate) normal and Students’ T distributions). The copula parameters have been estimated either non-parametrically from the rank correlation coefficient (e. g., Kendall’s τ or Spearman’s ρ) or parametrically using the Maximum Likelihood Estimation (MLE). This paper also applies the copula theory but proposes to estimate the parameters using the entropy theory and thus obtains the entropic copula. The method involves two steps. First, the marginals follow the uniform (0, 1) distribution according to the copula theory. Second, the measure of association is equal to the corresponding rank correlation coefficient. To validate the proposed method, copulas are identified using the entropy theory and these are then compared with the commonly applied Gumbel-Houggard copula (i. e., the parameter is estimated based on MLE) using streamflow datasets of experimental watersheds in the U. S.