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A Generalized Measure of Cumulative Residual Entropy
Version 1
: Received: 24 February 2022 / Approved: 25 February 2022 / Online: 25 February 2022 (04:44:39 CET)
A peer-reviewed article of this Preprint also exists.
Kattumannil, S.K.; Sreedevi, E.P.; Balakrishnan, N. A Generalized Measure of Cumulative Residual Entropy. Entropy 2022, 24, 444. Kattumannil, S.K.; Sreedevi, E.P.; Balakrishnan, N. A Generalized Measure of Cumulative Residual Entropy. Entropy 2022, 24, 444.
Abstract
In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of the generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss generating function approach using which we derive different entropy measures. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.
Keywords
cumulative entropy; cumulative residual entropy; extropy; gini mean difference; tsallis entropy; weighted cumulative residual entropy
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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