Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data

This study aims to model the joint probability distribution of periodic hydrologic data using meta-elliptical copulas. Monthly precipitation data from a gauging station (410120) in Texas, US, was used to illustrate parameter estimation and goodness-of-fit for univariate drought distributions using chi-square test, Kolmogorov–Smirnov test, Cramer-von Mises statistic, Anderson-Darling statistic, modified weighted Watson statistic, and Liao and Shimokawa statistic. Pearson’s classical correlation coefficient r _n , Spearman’s ρ _n, Kendall’s τ, Chi-Plots, and K-Plots were employed to assess the dependence of drought variables. Several meta-elliptical copulas and Gumbel-Hougaard, Ali-Mikhail-Haq, Frank and Clayton copulas were tested to determine the best-fit copula. Based on the root mean square error and the Akaike information criterion, meta-Gaussian and t copulas gave a better fit. A bootstrap version based on Rosenblatt’s transformation was employed to test the goodness-of-fit for meta-Gaussian and t copulas. It was found that none of meta-Gaussian and t copulas considered could be rejected at the given significance level. The meta-Gaussian copula was employed to model the dependence, and these results were found satisfactory.