Extropy 和累积剩余熵度量的偏单调性  

Partial Monotonicities of Extropy and Cumulative Residual Entropy Measure of Uncertainty

作　　者：濮明月 邱国新 PU Ming-yue;QIU Guo-xin(School of Accounting and Finance,Xinhua University of Anhui,Hefei 230088;School of Management,University of Science and Technology of China,Hefei 230026)

机构地区：[1]安徽新华学院财会与金融学院,合肥230088 [2]中国科学技术大学管理学院,合肥230026

出　　处：《工程数学学报》2021年第2期271-281,共11页Chinese Journal of Engineering Mathematics

基　　金：安徽省自然科学基金(1908085MG236);安徽省高校自然科学基金(KJ2018A0590);安徽省教育厅统计学教学团队项目基金(2017jxtd046)。

摘　　要：不确定性是与信息多少紧密相关的一个概念,在诸如通讯理论、概率论、统计等一系列领域均有广泛应用.假定已知的信息是随机变量的取值位于一个区间,直观的观察应是该随机变量的不确定性将随着区间长度的减少而减少.但实际上,此结论并不是总成立.给定随机变量的取值区间,本文获得了extropy以及累积剩余熵关于给定取值区间偏单调的充分条件.在随机变量独立同分布,且密度函数是对数凹的条件下,证明了随机变量差的extropy也关于给定取值区间偏单调.Uncertainty is closely related to amount of information and has been extensively studied in a variety of scientific fields including communication theory,probability theory and statistics.Given the information that the outcome of a random variable is in an interval,the uncertainty is expected to reduce when the interval shrinks.However,this conclusion is not always true.In this paper,we present the conditions under which the conditional extropy/cumulative residual entropy is a partially monotonic function of interval.Similar result is obtained for extropy of convolution of two independent and identically distributed random variables if their probability density functions are log-concave.

关 键 词：累积剩余熵 熵 extropy 对数凹 偏单调性 

分 类 号：O212.1[理学—概率论与数理统计]