广义极值分布序列经验概率的计算

Plotting position formula for general extreme value distribution

【目的】研究并建立广义极值分布无偏经验概率计算公式,为广义极值分布经验概率的计算提供支持。【方法】应用次序统计量原理,推导广义极值分布无偏经验概率计算公式,采用统计试验方法将推导的公式与现有的经验频率公式进行对比,对其进行检验,最后以陕北地区12个水文测站的年最大洪峰流量系列为例进行模型应用。【结果】推导出了便于工程设计应用的广义极值分布经验概率计算公式GEVQG。统计试验和实例应用表明:推导的公式GEVQG和现有经验频率公式Cunnane公式的相对误差和偏差均较小,并且对研究区的拟合效果良好。【结论】推导的计算公式GEVQG和Cunnane公式均可以作为广义极值分布经验概率计算的优选公式,为工程水文经验概率计算提供了新的选择。

【Objective】This study developed the unbiased plotting position formula for general extreme value（GEV）distribution.【Method】Based on the theory of order statistics,this paper developed an unbiased plotting position formula for the GEV distribution.The statistical testing was used to compare the developed formula and other existing formulas.At last,the parameters of annual maximum floods peak flow series of twelve stations in Northern Shaanxi were estimated.【Result】This paper developed a practical and convenient plotting position formula for the GEV distribution.The case study and statistical testing showed that the developed formula and Cunnane formula had small error and bias as well as good fitness in the study area.【Conclusion】The developed formula and Cunnane formula can be used as better methods for the GEV distribution,which provides new choice for empirical probability calculation in hydrology engineering.