一类由概率分布生成的新度量  

A CLASS OF NEW METRICS GENERATED BY PROBABILITY DISTRIBUTIONS

作　　者：卢国祥[1] 沈世镒[1] 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《系统科学与数学》2009年第4期451-459,共9页Journal of Systems Science and Mathematical Sciences

基　　金：天津市科技发展计划(043185111-17)项目资助.

摘　　要：主要得到了一类由概率分布生成的新度量.以信息理论中的重要概念一相对熵为基础,对前人文章中的重要结论进行推广,通过利用改进的初等方法在离散的可测空间中得到了这类新度量,并且证明了得到的新度量成立的充要条件.由此再将这类新度量推广到连续的可测空间中,得到了同样的结果.最后讨论了新度量的最值问题.In this paper, a class of new metrics generated by probability distributions is introduced. The new metrics, based on the important concept of relative entropy, are the generalization of the existing conclusions. Using the improved elementary method, the new metrics are obtained in a discrete measurable space. The sufficient and necessary conditions for the new merics to hold are given. The new metrics is then generalized to a continuous measurable space. Finally, the maxima and minima of the new metrics are discussed.

关 键 词：相对熵 度量 三角不等式. 

分 类 号：O211.3[理学—概率论与数理统计] TP311.5[理学—数学]