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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2021, Vol. 38 ›› Issue (2): 271-281.doi: 10.3969/j.issn.1005-3085.2021.02.010

• • 上一篇    下一篇

Extropy和累积剩余熵度量的偏单调性（英）

濮明月1,   邱国新1,2   

  1. 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
  • 收稿日期:2018-11-01 接受日期:2019-12-06 出版日期:2021-04-15 发布日期:2022-11-08
  • 通讯作者: 邱国新 E-mail: qiugx02@ustc.edu.cn
  • 基金资助:
    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).

Partial Monotonicities of Extropy and Cumulative Residual Entropy Measure of Uncertainty

PU Ming-yue1,   QIU Guo-xin1,2   

  1. 1- School of Accounting and Finance, Xinhua University of Anhui, Hefei 230088
    2- School of Management, University of Science and Technology of China, Hefei 230026
  • Received:2018-11-01 Accepted:2019-12-06 Online:2021-04-15 Published:2022-11-08
  • Contact: G. Qiu. E-mail address: qiugx02@ustc.edu.cn
  • Supported by:
    The Natural Science Foundation of Anhui Province (1908085MG236); the Natural Science Foundation of Universities in Anhui Province (KJ2018A0590); the Program of Statistics Team in Anhui Province (2017jxtd046).

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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．

关键词: 累积剩余熵, 熵, extropy, 对数凹, 偏单调性

Abstract: 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.

Key words: cumulative residual entropy, entropy, extropy, log-concavity, partially monotonicity

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