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An Entropy-Based Generalized Gamma Distribution for Flood Frequency Analysis
Open AccessArticle

Generalized Beta Distribution of the Second Kind for Flood Frequency Analysis

by Lu Chen 1,* and Vijay P. Singh 2
College of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, China
Department of Biological and Agricultural Engineering & Zachry Department of Civil Engineering, Texas A&M University, College Station, TX 77843, USA
Author to whom correspondence should be addressed.
Academic Editor: Kevin H. Knuth
Entropy 2017, 19(6), 254;
Received: 18 April 2017 / Revised: 18 May 2017 / Accepted: 26 May 2017 / Published: 12 June 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
Estimation of flood magnitude for a given recurrence interval T (T-year flood) at a specific location is needed for design of hydraulic and civil infrastructure facilities. A key step in the estimation or flood frequency analysis (FFA) is the selection of a suitable distribution. More than one distribution is often found to be adequate for FFA on a given watershed and choosing the best one is often less than objective. In this study, the generalized beta distribution of the second kind (GB2) was introduced for FFA. The principle of maximum entropy (POME) method was proposed to estimate the GB2 parameters. The performance of GB2 distribution was evaluated using flood data from gauging stations on the Colorado River, USA. Frequency estimates from the GB2 distribution were also compared with those of commonly used distributions. Also, the evolution of frequency distribution along the stream from upstream to downstream was investigated. It concludes that the GB2 is appealing for FFA, since it has four parameters and includes some well-known distributions. Results of case study demonstrate that the parameters estimated by POME method are found reasonable. According to the RMSD and AIC values, the performance of the GB2 distribution is better than that of the widely used distributions in hydrology. When using different distributions for FFA, significant different design flood values are obtained. For a given return period, the design flood value of the downstream gauging stations is larger than that of the upstream gauging station. In addition, there is an evolution of distribution. Along the Yampa River, the distribution for FFA changes from the four-parameter GB2 distribution to the three-parameter Burr XII distribution. View Full-Text
Keywords: entropy theory; principle of maximum entropy (POME); GB2 distribution; flood frequency analysis entropy theory; principle of maximum entropy (POME); GB2 distribution; flood frequency analysis
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Chen, L.; Singh, V.P. Generalized Beta Distribution of the Second Kind for Flood Frequency Analysis. Entropy 2017, 19, 254.

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