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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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Theoretical Aspects on Measures of Directed Information with Simulations
TL;DR: This work presents, study and provides simulations for measures of directed information, which quantify the information with emphasis on specific parts (or events) of their probability distribution, without losing the whole information of the less significant parts and at the same time by concentrating on the Information of the parts the authors care about the most.
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On bounds of some dynamic information divergence measures
S. Madhavan Sunoj,M. N. Linu +1 more
TL;DR: Certain bounds are obtained for some dynamic information divergences measures viz.
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Some Results on DDCRE Class of Life Distributions
TL;DR: In this paper, Navarro et al. define the decreasing dynamic cumulative residual entropy (DDCRE) class of life distributions, some properties of the DDCRE class are studied.
Dissertation
Some properties of reciprocal coordinate subtangent in the context of stochastic modelling
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On shift-dependent generalized entropies for doubly truncated random variable
Rajesh Moharana,Suchandan Kayal +1 more
TL;DR: Recently, Das as discussed by the authors studied the importance of weighted generalized entropy for one-sided truncation problems in survival study, where data are usually truncated and showed that weighted entropy can be used for survival study.
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.