Application of PSO Method for Archimedean Copula Parameter Estimation in Flood (Rain) and Tide Joint Distribution Analysis

Abstract

Archimedean copulas are the most popular class of copulas used in hydrological statistical models. Parameter estimation of copulas is an open and complex task. A faster and computationally easier estimation procedure is needed. In this study, a particle swarm optimization (PSO) method is proposed to obtain the parameters of copulas and their corresponding marginal distributions. The proposed PSO method is illustrated on hydrological variables (i.e., flood discharge, rainfall, tide level) of four gauging sites located in Jiangsu province and Shenzhen city, China. Five commonly used marginal distributions (including Pearson Type III, lognormal, gamma, Weibull, and generalized extreme value), three symmetric Archimedean copulas (including Clayton copula, Gumbel–Hougaard copula, Frank copula), and six asymmetric Archimedean copulas are used to construct the joint distributions of selected hydrological variables. The best parameters of copulas and marginal distributions are estimated based on PSO, and the most appropriate copulas and marginal distributions are selected based on the goodness of fit between empirical and theoretical distributions. The results show that the proposed PSO-based parameter estimation method is effective in this case study.