污染正态分布的熵估算

Entropy estimation of contaminated normal distribution

针对污染分布密度函数特性,研究污染正态分布常用2种模型密度函数的近似推演。采用Kullback-Leibler距离研究2种模型概率密度函数的差异性,导出污染正态分布的主体分布概率密度函数、均值漂移模型下和方差扩大模型下总体分布概率密度函数之间的Kullback-Leibler距离表达式。研究结果表明:在主体分布为标准正态分布时,2种模型的概率密度函数差异与均值平移参数λ和方差膨胀因子α密切相关,呈非线性正比关系;污染分布密度函数不一致必将导致熵估算出现很大差异;导出污染正态分布熵估算的关键不在于选取概率密度函数,而在于寻求一种适合熵值运算规律的方案。

The probability density function（PDF）feature of contaminated normal distribution was investigated.The Kullback-Leibler distance was suggested to measure PDF difference between mean shift model and variance inflation model.Three Kullback-Leibler distance formulas about contaminated normal basis distribution PDF,mean shift model PDF and variance inflation model PDF were deduced.A numerical simulation was performed to analyze the difference of the two kinds of models.The results show that the PDF difference of two kinds of models is related to mean shift parameterλand the variance inflation factorαclosely when the main distribution is standard normal distribution and the relationship is nonlinear proportional.Two kinds of general models PDF can not be used to estimate contaminated normal distribution entropy and entropy coefficient.An approximate formula is suggested for entropy estimation of contaminated normal distribution.