Box-Cox正态分布及其在降雨极值分析中的应用

Box-Cox Normal Distribution and Its Application in Rainfall Extreme Value

Box-Cox变换和正态分布有机结合构建新的Box-Cox正态分布,可以用来研究降水极值分布拟合问题,采用极大似然估计方法估计Box-CoX正态分布的参数,并基于1951-2010年河北省21个气象站逐日降水观测资料,拟合逐年日最大降水量序列,借助K-S与A-D方法进行拟合优度的比较,结果表明BoX-Cox正态分布能适应不同站点的降雨极值分布的拟合,且大部分优于降雨极值分布拟合中常用的广义极值(GEV)分布、Weibull分布、Gamma分布,因而对掌握降雨极值分布规律,分析降水极值重现期、时空特征和变化趋势具有重要意义。

In this paper, a new Box-Cox normal distribution is used to study the goodness-of-fit of the extreme rainfall distribution, and the method of maximum likelihood is applied to estimate parameters in the Box-Cox normal distribution. For the dataset of rainfall daily observations on 21 sites from 1951 to 2010 in Hebei Province, the comparisons with the generalized extreme value distribution, Weibull distribution and Gamma distributions, which is useful in the goodness-of-fit of the extreme rainfall distribution, are made by the K-S distance as well as the A-D distance. It is shown that the goodness- of-fit is suitable for different sites and better overall based on Box-Cox normal distribution. Therefore, we can analyze the return periods, time and spatial feature as well as the trend of extreme rainfall more efficiently by using Box-Cox normal distribution fit.