极端降水广义帕累托分布参数的Pickands自助矩估计研究

Study on Pickands bootstrap moment estimation of generalized Pareto distribution parameters of extreme precipitations

广义帕累托分布(GPD)是描述超门限峰值(POT)序列较好的概率分布模型,但确定门限值是使用该模型最棘手的问题。为此,提出了一种广义帕累托分布参数的Pickands自助矩估计方法。首先,运用Pickands自助估计算法对广义帕累托分布的形状参数和最佳超门限峰值个数进行估计,进而计算出门限值;然后,结合矩估计法得到广义帕累托分布的尺度参数。将该方法应用于北京日降水序列,并与相同门限值时的线性矩估计结果进行了比较。结果表明,Pickands自助矩估计可以得到比较好的广义帕累托分布和广义极值分布的参数,由此估计的广义帕累托分布的分位数和北京极端降水超门限峰值的相关系数可达0.997以上,而两者的标准差和最大偏差最小,明显优于线性矩估计结果。

The generalized Pareto distribution （GPD） is a good probability distribution model to describe peak-over-threshold （POT） series, but the determination of its threshold is a great challenge in practical application. To solve this problem, we herein describe a Pickands bootstrap moment method for estimation of the GPD parameters. The method is used to estimate the shape parameter of GPD and the optimum number of POT and calculate the threshold, then the scale parameter is obtained with the moment estimation method. This new method is applied to the daily precipitation series of the Beijing meteorological station and its results are compared with those estimated by the linear moment estimation method using the same threshold. The comparison shows that it has a good ability of parameter estimation for GDP and generalized extreme value （GEV）. From the fitting of the GDP quantiles and POT series, their correlation coefficients are up to 0.997 or more while their standard deviation and maximum deviation are the lowest. These results indicate that the Pickands bootstrap moment estimation method is obviously superior to the linear moment estimation.