广义极值分布参数估计方法比较研究

Comparative Study on Parameter Estimation Methods of Generalized Extreme Value Distribution

摘要: 研究广义极值分布参数估计的普通矩法、普通概率权重矩法和高阶概率权重矩法。以黔北地区五家院子和江滨水文站年最大洪峰流量序列为例，选用广义极值分布，应用普通矩法、普通概率权重矩和高阶概率权重矩进行参数估计，并对各方法的拟合效果和参数估计结果进行分析比较。结果表明：与普通矩法和普通概率权重矩法相比，高阶概率权重矩法能更好的拟合洪水序列的高尾部分洪水值，可以进行洪水频率分布的参数估计。蒙特卡洛试验表明：高阶概率权重矩法计算出的不同重现期洪水设计值的SE、Bias和RMSE较小，与常用的矩法、普通概率权重矩法相比，高阶概率权重矩法具有较高的精度。

Abstract: Research on parameter estimation of Generalized Extreme Value distribution based on the moment, the probability weighted moment and the higher probability weighted moments. The two examples of Wujia Yuanzi and Jiang Bin stations annual maximum flow series were analyzed by the three parameter esti-mation methods of GEV distribution, which included the moment estimation, the probability weighted moment estimation and the higher probability weighted moment estimation. The results indicate that using the higher PWMs to fit the large flood values are much better than the moment and the probability weighted moment, and we can use it to estimate the parameters of the flood frequency distribution. The Monte Carlo experiments indicate that the SE, Bias and RMSE in the design floods of different return pe-riods which based on the higher probability weighted moments are smaller and the PWMs have higher accuracy than the moment and the probability weighted moment.