Parameter estimation of copula functions using an optimization-based method

Application of the copulas can be useful for the accurate multivariate frequency analysis of hydrological phenomena. There are many copula functions and some methods were proposed for estimating the copula parameters. Since the copula functions are mathematically complicated, estimating of the copula parameter is an effortful work. In the present study, an optimization-based method (OBM) is proposed to obtain the parameters of copulas. The usefulness of the proposed method is illustrated on drought events. For this purpose, three commonly used copulas of Archimedean family, namely, Clayton, Frank, and Gumbel copulas are used to construct the joint probability distribution of drought characteristics of 60 gauging sites located in East-Azarbaijan province, Iran. The performance of OBM was compared with two conventional methods, namely, method of moments and inference function for margins. The results illustrate the supremacy of the OBM to estimate the copula parameters compared to the other considered methods.