极值波高Weibull分布的参数估计方法对比分析

Comparative analysis on the parameter estimation methods of Weibull distribution of extreme wave heights

介绍了三参数威布尔分布及其4种参数估计方法:极大似然估计法、相关系数优化法、灰色估计法和概率权重矩法。利用蒙特卡罗法对以上参数估计方法进行不同样本尺度的模拟,通过偏差、标准差和均方误差对比分析各种方法的特点、精度和适用性。运用上述方法结合涠洲站34a实测年极值波高,推算涠洲岛的设计波高,从相关系数、均方根误差和Q统计值分析各种方法的差异及优劣性。结果表明,小样本情况下各估计法的差别较大,而大样本时差别较小,极大似然估计法能较好拟合各种大小的样本,相关系数优化法次之;选取合适的经验频率会提高参数估计精度;各种参数估计方法计算而得的设计波高相差不大,其中极大似然估计法的精度最高。

This paper discusses four parameter estimation methods （MLE, CCM, GM and PWM） of three-parameter Weibull distribution. Monte Carlo method was used to simulate the parameter estimation results for different sample lengths. And their characteristics, accuracy and applicability based on the deviation, standard deviation and MSE were analyzed. The design wave heights of sea waters near the Weizhou Island were calculated by methods mentioned above based on 34- year annual maximum wave heights and their differences were discussed by correlation coefficient, RMSE and Q statistic. The results showed that the parameter difference was much larger in small samples than in large samples. The MLE method could better fit the various sizes of samples, followed by the CCM. Choosing appropriate empirical frequency could enhance the estimation accuracy. The design wave heights calculated by different methods were close, and the MLE method had the best estimation accuracy.