A New Estimation Method for Copula Parameters for Multivariate Hydrological Frequency Analysis With Small Sample Sizes

Multivariate hydrological frequency analysis is important when designing hydraulic and civil infrastructures. However, hydrologic data scarcity and insufficiency are common. By studying the relationship between copula entropy and total correlation estimated by the matrix-based Renyi's α-order entropy functional, a new estimation method (total correlation estimation, TCE) for parameters of the Gumbel-Hougaard copula and Clayton copula was proposed when the sample size was equal to or less than 30. A total of 11,802 simulations were performed to evaluate the performance of TCE for sample sizes ranging from 30 to 5, and were compared with traditional estimation methods that require a large amount of data. As for the Gumbel-Hougaard copula, the performance of TCE is satisfactory regardless of sample size, while the traditional methods perform poorly when the sample size is equal to or less than 20. For the Clayton copula, TCE is reliable and robust and performs well if the sample size is greater than 10, while the traditional methods are unreliable when the sample size is less than 25. Also, TCE is applied to construct the joint distributions of annual runoff and sediment discharge in the Xiliugou River, China. The method based on Renyi's α-order entropy functional provides a new way for multivariate hydrological frequency analysis with small sample sizes.