用Mellin变换推导几种分布参数估计的最大熵法

Derivation of POME for Estimation Parameters of Several Distributions Using Mellin Tranform

鉴于最大信息熵原理推导水文频率分布参数估计的最大熵法(POME)通过泛函分析及Lagrange乘子法推演过程相当繁琐复杂的问题,探讨了Mellin变换在指数Γ分布、广义Pareto分布和二参数对数正态分布等参数估计POME中的应用,采用Mellin变换代替Lagrange乘子法推导了其统计分布参数估计的POME。结果表明,相比Lagrange乘子法,Mellin变换推导过程更为快捷、简单、直接,可作为推导统计分布参数估计POME的一种有效方法。

The inference process of functional analysis and Lagrange multiplier method based the principle of maximum information entropy is quite complex for estimation parameters of hydrological frequency analysis with the POME method. This paper studies the POME for estimation parameters of exponential--gamma distribution, general Pareto distribution and two-parameters log normal distribution based on Mellin transform. And then Lagrange multiplier method is replaced by the Mellin transform to deduce POME for estimation parameters. The results show that the Mellin transform is faster, simpler and more direct in derivation process than Lagrange multiplier method. Therefore, Mellin transform is an effective method for deriving the POME of statistical parameter distribution.