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Entropy-based derivation of generalized distributions for hydrometeorological frequency analysis
Journal of Hydrology ( IF 6.4 ) Pub Date : 2018-02-01 , DOI: 10.1016/j.jhydrol.2017.12.066
Lu Chen , Vijay P. Singh

Abstract Frequency analysis of hydrometeorological and hydrological extremes is needed for the design of hydraulic and civil infrastructure facilities as well as water resources management. A multitude of distributions have been employed for frequency analysis of these extremes. However, no single distribution has been accepted as a global standard. Employing the entropy theory, this study derived five generalized distributions for frequency analysis that used different kinds of information encoded as constraints. These distributions were the generalized gamma (GG), the generalized beta distribution of the second kind (GB2), and the Halphen type A distribution (Hal-A), Halphen type B distribution (Hal-B) and Halphen type inverse B distribution (Hal-IB), among which the GG and GB2 distribution were previously derived by Papalexiou and Koutsoyiannis (2012) and the Halphen family was first derived using entropy theory in this paper. The entropy theory allowed to estimate parameters of the distributions in terms of the constraints used for their derivation. The distributions were tested using extreme daily and hourly rainfall data. Results show that the root mean square error (RMSE) values were very small, which indicated that the five generalized distributions fitted the extreme rainfall data well. Among them, according to the Akaike information criterion (AIC) values, generally the GB2 and Halphen family gave a better fit. Therefore, those general distributions are one of the best choices for frequency analysis. The entropy-based derivation led to a new way for frequency analysis of hydrometeorological extremes.

中文翻译:

用于水文气象频率分析的广义分布的基于熵的推导

摘要 水文气象和水文极端事件的频率分析是水利和民用基础设施设计以及水资源管理所需要的。许多分布已被用于这些极端的频率分析。然而,没有一个单一的发行版被接受为全球标准。本研究采用熵理论,推导出五种广义分布用于频率分析,这些分布使用不同种类的信息作为约束编码。这些分布是广义 gamma (GG)、第二类广义 beta 分布 (GB2) 和 Halphen A 型分布 (Hal-A)、Halphen B 型分布 (Hal-B) 和 Halphen 型逆 B 分布 (哈尔-IB), 其中GG和GB2分布先前由Papalexiou和Koutsoyiannis(2012)推导出,Halphen家族在本文中首次使用熵理论推导出。熵理论允许根据用于推导的约束来估计分布的参数。使用极端的每日和每小时降雨数据对分布进行了测试。结果表明,均方根误差(RMSE)值很小,这表明五种广义分布与极端降雨数据拟合良好。其中,根据 Akaike 信息准则(AIC)值,一般 GB2 和 Halphen 家族给出了更好的拟合。因此,这些一般分布是频率分析的最佳选择之一。
更新日期:2018-02-01
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