Information Divergence and the Generalized Normal Distribution:A Study on Symmetricity  

作　　者：Thomas L.Toulias Christos P.Kitsos 

机构地区：[1]Department of Electrical and Electronics Engineering,University of West Attica,Campus 1,Egaleo,12243 Athens,Greece [2]Department of Informatics and Computer Engineering,University of West Attica,Campus 1,Egaleo,12243 Athens,Greece

出　　处：《Communications in Mathematics and Statistics》2021年第4期439-465,共27页数学与统计通讯（英文）

摘　　要：This paper investigates and discusses the use of information divergence,through the widely used Kullback–Leibler(KL)divergence,under the multivariate(generalized)γ-order normal distribution(γ-GND).The behavior of the KL divergence,as far as its symmetricity is concerned,is studied by calculating the divergence of γ-GND over the Student’s multivariate t-distribution and vice versa.Certain special cases are also given and discussed.Furthermore,three symmetrized forms of the KL divergence,i.e.,the Jeffreys distance,the geometric-KL as well as the harmonic-KL distances,are computed between two members of the γ-GND family,while the corresponding differences between those information distances are also discussed.

关 键 词：Kullback-Leibler divergence Jeffreys distance Resistor-average distance Multivariateγ-order normal distribution Multivariate Student’s t-distribution Multivariate Laplace distribution 

分 类 号：O17[理学—数学]