常见分布的最大Kullback-Leibler距离  

Maximum Kullback-Leibler Distance of Some Conventional Distributions

作　　者：蔡择林[1] 李开灿[1] 

机构地区：[1]湖北师范学院数学系,湖北黄石435002

出　　处：《武汉大学学报（理学版）》2007年第5期513-517,共5页Journal of Wuhan University:Natural Science Edition

基　　金：湖北省优秀创新团队项目;湖北省教育厅重点项目(D200622001)

摘　　要：在Kullback-Leibler距离的基础上,定义了两个概率分布之间的最大Kullback-Leibler距离,证明了这个距离具有欧式距离的对称性,三角不等式性等分析性质,依照该定义,计算了两个不同的二项分布,两个不同的正态分布等一些常见分布之间的最大Kullback-Leibler距离.还定义了多元最大Kullback-Leibler距离,并且计算两个矩阵Γ分布的Kullback-Leibler距离.另外在Kullback-Leibler距离下,还得到了一种正态分布逼近指数分布的条件.Based on the distance of Kullback-Leibler, this paper give the exact definition of the maximum Kullback-Leibler distance between two different distribution functions and prove that this one has analytic properties such as symmetry, triangle inequality which is the same as the Euclidean distance. By the definition, the maximum Kullback-Leibler distance between some conventional distributions, such as two different binomial distributions, two different normal distributions are obtianed. Farther, for multivariable distribution,this paper give the definition of the Kullback-Leibler distance, and to derive the Kullback- Leibler distance for two different matrix Г-distribution. On the other hand, the conditions that a normal distribution approximate to a exponetial distribution is obtained under Kullback-Leibler distance.

关 键 词：密度函数 Kullback-Leibler距离 矩阵Γ分布 

分 类 号：O212[理学—概率论与数理统计]