水文频率分析中参数估计最大熵法的梅林变换推导

Mellin transform derivation of maximum entropy for parameter estimation in hydrologic frequency analysis

针对水文频率分析中最大熵法估计概率分布参数求解问题,探讨了用最大信息熵原理推导概率分布参数估计最大熵法的数学特性,分析了该方法与梅林变换之间的关系。从梅林变换出发,对各种水文频率分布参数估计的最大熵法进行了推导,说明了推导的具体步骤。用梅林变换推导最大熵法的过程更为简单、易懂。

Principle of maximum entropy( POME) is a method for estimating the parameters of probability distribution. The paper discussed the method that used the maximum entropy principle to infer the mathematical properties of estimation parameters of probability distribution of POME. The relationships between POME and Mellin transform were analyzed. From Mellin transform,it derived POME of estimation parameters of 13 kinds of hydrological frequency distribution curve and illustrated the specific steps of derivation. The process of inferring POME by Mellin transform is simpler and easier to be understood.