极值波高Weibull分布参数的贝叶斯估计

Bayesian estimation of Weibull distribution parameter for extreme wave height

为了研究波浪的分布规律,常常采用统计方法选择合适的分布函数以及参数估计方法进行计算分析。利用Weibull分布对极值波高进行统计分析,选取贝叶斯方法和最大似然法分别估计其中的未知参数,从对样本的拟合效果和设计波高计算两个角度来评价这两种不同思想的估计方法效果。利用广西涠洲岛和白龙尾测站6组年极值波高资料进行案例分析。结果表明:两种方法均表现出对样本良好的拟合效果,Jeffreys先验下的贝叶斯估算结果的离差平方和总体小于最大似然法,计算得到的50 a一遇和100 a一遇设计波高比最大似然法略大。先验信息能保证样本不足时计算结果的可靠性,在无先验信息时,贝叶斯方法结合Jeffreys先验能很好地应用于极值波高的统计分析。

In order to study the distribution law of waves,statistical methods are often used to select appropriate distribution functions and parameter estimation methods for analysis.In this paper,Weibull distribution was used for statistical analysis of wave height,and Bayesian method and maximum likelihood method were selected to estimate the unknown parameters respectively.Then the estimation effect of two methods was evaluated from the perspectives of samples fitting and the design wave height calculation.A case study was carried out by using the data of annual extreme wave height of Weizhou Island and Bailongwei Station in Guangxi.The results showed that both two methods had good fitting effect on samples.The sum of square residuals calculated by Bayesian estimation based on Jeffreys prior was less than that of the maximum likelihood method,and the design wave height of 50-year frequency and 100-year frequency wave height obtained by Bayesian estimation based on Jeffreys prior was larger than that of maximum likelihood method.The prior information can ensure the reliability of the calculation results when the sample was insufficient.When there was no prior information,the Bayesian method based on the Jeffreys prior can be applied to the statistical analysis of the extreme wave height.