交互熵法在洪水频率分布参数估计中的应用研究

An Application of Cross Entropy Method to the Parameter Estimation in Flood Frequency Analysis

摘要: 本文研究基于分位数对约束下的交互熵进行洪水频率分布参数估计方法。以加拿大Feather河和陕北地区张村驿站年最大洪峰流量序列为例，选取Gumbel和Gamma分布，基于最小交互熵原理，进行年最大洪峰流量序列分布参数估计，并根据估计参数推求洪峰流量频率曲线图。与矩法和极大似然法所求熵值比较，结果表明：交互熵法获得最小熵值，频率点距拟合亦取得满意效果。因此，在考虑分位数对约束的条件下，交互熵法能有效的估计分布参数，且较矩法和极大似然法优越。

Abstract: This paper studies on the application of fractile constrained cross-entropy to the estimation of dis- tribution parameters in flood frequency analysis. Based on the principle of minimum cross-entropy, two annual maximum flood peak series respectively in Feather River in Canada and Zhangcunyi Station in north- ern Shaanxi province with Gumbel distribution and Gamma distribution were employed to the parameter estimation of the four distribution functions. Four frequency curves with the estimated parameters were also plotted. Then, comparing the calculated cross-entropy values with those that are derived by traditional methods- MOM and MLM, it turned out that: by using cross entropy method, we got the minimum cross entropy values. The plotted theoretical frequency curves fit well with the empirical frequency curves. So, we can conclude that the quantile constrained cross-entropy method has the considerable merit in the flood frequency parameter estimation and is superior to the traditional methods-MOM and MLM.