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Extropy: Characterizations and dynamic versions

Part of: Survival analysis and censored data Parametric inference

Published online by Cambridge University Press:  02 June 2023

Abdolsaeed Toomaj ,
Majid Hashempour  and
Narayanaswamy Balakrishnan
Abdolsaeed Toomaj*
Affiliation:
Gonbad Kavous University
Majid Hashempour*
Affiliation:
University of Hormozgan
Narayanaswamy Balakrishnan*
Affiliation:
McMaster University
*
*Postal address: Faculty of Basic Sciences and Engineering, Department of Mathematics and Statistics, Gonbad Kavous University, Gonbad Kavous, Iran. Emails: ab.toomaj@gonbad.ac.ir, ab.toomaj@gmail.com
**Postal address: Department of Statistics, Faculty of Basic Sciences, University of Hormozgan, Bandar Abbas, Iran. Email: ma.hashempour@hormozgan.ac.ir
***Postal address: Department of Mathematics and Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada. Email: bala@mcmaster.ca
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Abstract

Several information measures have been proposed and studied in the literature. One such measure is extropy, a complementary dual function of entropy. Its meaning and related aging notions have not yet been studied in great detail. In this paper, we first illustrate that extropy information ranks the uniformity of a wide array of absolutely continuous families. We then discuss several theoretical merits of extropy. We also provide a closed-form expression of it for finite mixture distributions. Finally, the dynamic versions of extropy are also discussed, specifically the residual extropy and past extropy measures.

Keywords

Shannon’s entropyextropyKullback–Leibler informationrelative extropydynamic extropymixture distribution

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 62F10: Point estimation

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 4 , December 2023 , pp. 1333 - 1351
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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