Details

Autor(en) / Beteiligte

• Qian, Longxia
• Wang, Xiaojun
• Liu, Nanjun

Titel

Parameter Estimation for a Mixed Copula Based on Renyi Entropy: A Case Study of Annual Precipitation

Ist Teil von

• Mathematical geosciences, 2023-11, Vol.55 (8), p.1169-1188

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Multivariate frequency analysis is essential for hydraulic design and water resource management. Copulas have been widely utilized for frequency analysis. However, it is difficult to estimate the parameters of copulas when a real-valued or discrete marginal probability density function (PDF) is unavailable. Employing the matrix-based Renyi's α -order entropy functional, a new estimation method (mutual information estimation, MIE) for the parameters of a bivariate mixed copula is derived by investigating the relationship between Shannon’s entropy of the mixed copula and mutual information. MIE requires only the value of mutual information that can be directly estimated from two precipitation sequences without marginal and joint PDF estimation. Based on the annual precipitation sequences at four pairs of neighbouring counties in Qingyang City, four experiments are performed to test the effectiveness of MIE and compared with maximum likelihood estimation (MLE), which requires accurate marginal PDF estimation. All the experiments show that the performance of MIE is even better than that of MLE in three pairs of counties. MIE performs nearly as well as MLE in Huachi and Heshui Counties. Moreover, the mixed copula by MIE is applied to predict the encounter probability of rich–poor precipitation for four pairs of counties. The results show that the values of synchronous probability are much greater than those of asynchronous probability for all four pairs of counties and that the synchronous probability varies from 0.60 to 0.68. Renyi's α -order entropy functional-based derivation contributes to a new method for multivariate frequency analysis of hydrology.