parametric estimation methods for bivariate copula in rainfall application

Abstract

This study focuses on the parametric methods: maximum likelihood (ML), inference function of margins (IFM), and adaptive maximization by parts (AMBP) in estimating copula dependence parameter. Their performance is compared through simulation and empirical studies. For the empirical study, 44 years of daily rainfall data of Station Kuala Krai and Station Ulu Sekor were used. The correlation of the two stations is statistically significant at 0.4137. The results from the simulation study show that when the sample size is small (n <1000) for correlation level less than 0.80, IFM has the best performance. While, when the sample size is large (n ≥ 1000) for any correlation level, AMBP has the best performance. The results from the empirical study also show that AMBP has the best performance when the sample size is large. Thus, in order to estimate a precise Copula dependence parameter, it can be concluded that for parametric approaches, IFM is preferred for small sample size and has correlation level less than 0.80 and AMBP is preferred for larger sample size and for any correlation level. The results obtained in this study highlight the importance of estimating the dependence structure of the hydrological data. By using the fitted copula, the Malaysian Meteorological Department will be able to generate hydrological events for a system performance analysis such as flood and drought control system.