Pair-copula decomposition constructions for multivariate hydrological drought frequency analysis

Pair-copula is a new method for higher dimensional copulas construction. Based on the principle of pair-copula decomposition, An example of applying the copula to multivariate hydrological drought frequency was given. Monthly average flow data from Zhuang tou gauging station in Weihe Basin, China, was used to illustrate these methods. Chi-square test, Kolmogorov-Smirnov test, Cramer-von Mises statistic, Anderson-Darling statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic were employed to test goodness-of-fit for these univariate distribution. Pearson´s classical correlation coefficient r_n, Spearman´s ρ_n, Kendall´s τ, Chi-Plots, and K-Plots were used to assess the dependence of drought variables. According to three different permuting ways of drought variables, twelve copulas were used to model the joint probability distributions. A three dimensional probability distribution formula was derived. Based on the Root Mean Square Error (RMSE), the Akaike Information Criterion (AIC) and Bayesian Information Criterial (BIC), the best fitting copula was selected. A bootstrap version based on Rosenblatt´s transformation was employed to test the goodness-of-fit of the copula. Comparing with 12 copulas, the Frank copula under D-V-P structure has the best fitting for joint probability distribution of hydrological drought distribution. The results indicated pair-copula decomposition is a feasible way to model multivariate frequency analysis.