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On Weighted Residual and Past Entropies
TLDR
In this paper, a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables is introduced.Abstract:
We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables This allows us to introduce the notions of "weighted residual entropy" and "weighted past entropy", that are suitable to describe dynamic information of random lifetimes, in analogy with the entropies of residual and past lifetimes introduced in [9] and [6], respectively The obtained results include their behaviors under monotonic transformationsread more
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A Note on Double Truncated (Interval) Weighted Cumulative Entropies
Salimeh Yasaei Sekeh,Salimeh Yasaei Sekeh,Gholam Reza Mohtashami Borzadaran,Abdolhamid Rezaei Roknabadi +3 more
TL;DR: Referring properties of doubly truncated (interval) cumulative residual and past entropy, several bounds and properties in terms of the weighted cumulative entropy is proposed.
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Weighted Cumulative Residual (Past) Inaccuracy For Minimum (Maximum) of Order Statistics
TL;DR: In this article, a measure of weighted cumulative residual inaccuracy between survival function of the first-order statistic and parent survival function was proposed, and the reliability properties and characterization results such as relationships with other functions, bounds, stochastic ordering and effect of linear transformation were obtained.
Posted Content
Weighted Fractional Generalized Cumulative Past Entropy
TL;DR: In this article, the weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support is introduced. But the proposed measure is not suitable for the proportional reversed hazard rate models.
On the weighted dynamic cumulative residual entropy and dynamic cumulative past entropy with applications: A survey
Fikri Akdeniz,H. Altan Çabuk +1 more
TL;DR: The main measure of the uncertainty contained in random variable X is the Shannon entropy H(X) = −E(log(f(X)), and weighted residual entropy and weighted cumulative residual entropy are discussed.
References
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A mathematical theory of communication
TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
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Entropy-based measure of uncertainty in past lifetime distributions
TL;DR: A dual characterization of life distributions that is based on entropy applied to the past lifetime is analyzed, including its connection with the residual entropy, the relation between its increasing nature and the DRFR property, and the effect of monotonic transformations on it.
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New partial ordering of survival functions based on the notion of uncertainty
Nader Ebrahimi,Franco Pellerey +1 more
TL;DR: A new partial ordering among life distributions in terms of their uncertainties is introduced, and the notion of a ‘better system' is introduced based on this ordering and various existing orderings.
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Some results on residual entropy function
TL;DR: The authors proposed the Shannon residual entropy as a dynamic measure of uncertainty and used it to define a stochastic order and two classes of distributions, DURL and IURL, and obtained new results on this function and corrected some mistakes in preceding literature.
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A measure of discrimination between past lifetime distributions
TL;DR: In this article, a measure of discrepancy between past-life distributions is proposed, based on Kullback-Leibler discrimination information and of discrimination information introduced by Ebrahimi and Kirmani.