广义误差分布熵系数与最小相对熵的研究  

Research on Entroy Coefficient and Minimum Relative Entroy of Generalized Error Distribution

作　　者：苑慧芳 赵学超 吕长青 YUAN Huifang;ZHAO Xuechao;L Changqing(Department of Mathematics and Statistics,Zaozhuang University,Zaozhuang 277160,China)

机构地区：[1]枣庄学院数学与统计学院,山东枣庄277160

出　　处：《枣庄学院学报》2023年第2期36-42,共7页Journal of Zaozhuang University

基　　金：山东自然科学基金(ZR2021MA094);山东省本科教学改革研究项目面上项目(M2020051)。

摘　　要：为直观描述分布尾部特征及两分布之间的差异程度,基于Kulllback-Leibler距离研究广义误差分布熵系数的变动情况,从另一角度说明正态分布满足最大熵原理,尾部特征极不明显,且推导出两个广义误差分布之间的最小相对熵及性质,克服了相对熵的非对称性质,并且确定了不同参数的变动范围对应的最小相对熵形式。In order to intuitively describe the tail characteristics of the distribution and the degree of difference between the two distributions,this paper studies the change of the entropy coefficient of the generalized error distribution based on Kullback-Leibler distance.From another perspective,it shows that the normal distribution meets the maximum entropy principle,and the tail characteristics are very inconspicuous.The minimum relative entropy and properties between the two generalized error distributions are derived,which overcomes the asymmetric nature of the relative entropy.The minimum relative entropy corresponding to the variation range of different parameters is determined.

关 键 词：广义误差分布 熵系数 对称性 最小相对熵 

分 类 号：O212.1[理学—概率论与数理统计]