Frequency analysis of droughts using the Plackett copula and parameter estimation by genetic algorithm |
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| Authors: | Songbai Song Vijay P Singh |
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| Institution: | (1) College of Water Resources and Architecture Engineering, Northwest A & F University, Yangling, Shaanxi, 712100, China;(2) Department of Biological and Agricultural Engineering, Texas A & M University, College Station, TX 77843, USA;(3) Department of Civil and Environmental Engineering, Texas A & M University, College Station, TX 77843, USA |
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| Abstract: | This study aims to model the joint probability distribution of drought duration, severity and inter-arrival time using a trivariate
Plackett copula. The drought duration and inter-arrival time each follow the Weibull distribution and the drought severity
follows the gamma distribution. Parameters of these univariate distributions are estimated using the method of moments (MOM),
maximum likelihood method (MLM), probability weighted moments (PWM), and a genetic algorithm (GA); whereas parameters of the
bivariate and trivariate Plackett copulas are estimated using the log-pseudolikelihood function method (LPLF) and GA. Streamflow
data from three gaging stations, Zhuangtou, Taian and Tianyang, located in the Wei River basin, China, are employed to test
the trivariate Plackett copula. The results show that the Plackett copula is capable of yielding bivariate and trivariate
probability distributions of correlated drought variables. |
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