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BOUNDS ON EXTROPY WITH VARIATIONAL DISTANCE CONSTRAINT

Published online by Cambridge University Press:  06 April 2018

Jianping Yang ,
Wanwan Xia  and
Taizhong Hu
Jianping Yang
Affiliation:
Department of Mathematical Sciences, School of Science, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, People's Republic of China, E-mail: yangjp@zstu.edu.cn
Wanwan Xia
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei Anhui 230026, People's Republic of China, E-mails: xiaww@mail.ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei Anhui 230026, People's Republic of China, E-mails: xiaww@mail.ustc.edu.cn; thu@ustc.edu.cn
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Abstract

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].

Keywords

confidence intervalentropyextropyextropy estimationmajorizationvariational distance
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 33 , Issue 2 , April 2019 , pp. 186 - 204
Copyright
Copyright © Cambridge University Press 2018 

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