Abstract:
The variance of Shannon information related to the random variable XX, which is called varentropy, is a measurement that indicates, how the information content of XX is scattered around its entropy and explains its various applications in information theory, computer sciences, and statistics. In this paper, we introduce a new generalized varentropy based on the Tsallis entropy and also obtain some results and bounds for it. We compare the varentropy with the Tsallis varentropy. Moreover, we explain the Tsallis varentropy of the order statistics and analyse this concept in residual (past) lifetime distributions and then introduce two new classes of distributions by them.
Citation:
S. Maadani, G. Mohtashami Borzadaran, A. Rezaei Roknabadi, “A new generalized varentropy and its properties”, Ural Math. J., 6:1 (2020), 114–129
\Bibitem{MaaMohRez20}
\by S.~Maadani, G.~Mohtashami Borzadaran, A.~Rezaei Roknabadi
\paper A new generalized varentropy and its properties
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 1
\pages 114--129
\mathnet{http://mi.mathnet.ru/umj115}
\crossref{https://doi.org/10.15826/umj.2020.1.009}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4128764}
\zmath{https://zbmath.org/?q=an:1450.62006}
\elib{https://elibrary.ru/item.asp?id=43793628}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85088991360}
Linking options:
https://www.mathnet.ru/eng/umj115
https://www.mathnet.ru/eng/umj/v6/i1/p114
This publication is cited in the following 2 articles:
Shital Saha, Suchandan Kayal, “Weighted past and paired dynamic varentropy measures, their properties, usefulness and inferences”, Journal of Statistical Computation and Simulation, 2025, 1
Luai Al-Labadi, Mohammed Hamlili, Anna Ly, “Bayesian Estimation of Variance-Based Information Measures and Their Application to Testing Uniformity”, Axioms, 12:9 (2023), 887
Citation in format AMSBIB
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