Gumbel分布参数估计及在水位资料分析中应用  

The Estimates of the Parameters of Gumbel Distribution and Their Application to the Analysis of the Water Level Data

作　　者：罗纯[1] 王筑娟[1] 

机构地区：[1]上海应用技术学院数理教学部,上海200235

出　　处：《应用概率统计》2005年第2期169-175,共7页Chinese Journal of Applied Probability and Statistics

基　　金：上海应用技术学院科学技术发展基金资助项目(QJ2004-10).

摘　　要：本文利用Gumbel分布拟合某条河流三个观测站的历年最高水位资料.我们用分位数法、极大似然法、概率加权矩法对Gumbel分布中的参数进行估计,不仅从理论上而且利用蒙特卡洛方法讨论了三种估计方法的统计性质,并给出了三个观测站处的T年一遇的最高水位数据.我们认为极大似然法给出的估计量在各个方面都有好的且稳定的表现.The current paper fits and analysis, by means of type I extreme value distribution, the historical data, which is constituted of the highest water levels in calendar years in three survey stations of certain river, so as to predict the highest water level in the future. While the procedures of quartiles, maximum-likelihood and probability weighted moments, are engaged to estimate the parameters involved in Gumbel distributions, the statistical behaviors of these three estimate procedures are compared not only theoretically in terms of so-called large sample theory but also in finite sample simulation by Monte-Carlo processes. After got the estimators of the parameters from the data in hand, the curves of the predicted highest water levels in T years in the three survey stations of certain river, which may be used by the government, are presented at the last section of this paper.

关 键 词：Gumbel分布 参数估计 分位数估计 极大似然估计 概率加权矩估计 蒙特卡洛方法 

分 类 号：O212.1[理学—概率论与数理统计]