含零值水文序列频率的计算原理与应用

Principle and Application of Hydrological Series Frequency Analysis with Zero Values

研究含零值水文序列频率的计算方法。应用条件概率和全概率公式,推导了含零值水文序列频率的计算公式,两种方法的频率计算公式一致。同时,文中也给出了经验频率和理论频率计算方法及其相应的计算步骤。通过3个含零值水文序列的实例计算,表明文中的计算公式可以灵活地选用目前常用的频率分布,借助现有的统计计算函数包,不难获得相应设计频率的设计水文值。文中含零值水文序列频率的计算具有严格的数学基础,以期为含零值水文序列频率的计算提供理论基础。

The principle and application of hydrological series frequency analysis with zero values were presented. Employing condi- tional probability and total probability theories, this paper obtained the formulas of hydrological series frequency analysis with zero values, which indicates that the formulas are the same by these two methods. The empirical frequency and theoretical frequency and corresponding procedures were given. Three cases of hydrological series frequency analysis with zero values were used to illus- trate these methods. The results show that the formulas can be fitted by arbitrary common distributions, using the statistical compu- tation functions, the design hydrological values of the design frequency are easy to obtain. It also indicates that the formulas in this paper can provide some basic theories for hydrological series frequency analysis with zero values.