Open Access
On weighted residual and past entropies
Antonio Di Crescenzo,Maria Longobardi,Received April +2 more
- Vol. 64, Iss: 2, pp 255-266
TLDR
In this article, a shift-biased information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables, is considered. And the notions of weighted residual entropy and weighted past entropy are introduced to describe dynamic information of random lifetimes.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 transformations. AMS Classification: 62N05, 62B10read more
Citations
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Journal ArticleDOI
On cumulative entropies
TL;DR: The cumulative entropy is introduced and studied, which is a new measure of information alternative to the classical differential entropy and is particularly suitable to describe the information in problems related to ageing properties of reliability theory based on the past and on the inactivity times.
Journal ArticleDOI
Dynamic cumulative residual Renyi's entropy
S. M. Sunoj,M. N. Linu +1 more
TL;DR: This paper introduces a generalized measure of cumulative residual Renyi's entropy, and extends this measure into the bivariate set-up and proves certain characterizing relationships to identify different bivariate lifetime models.
Journal ArticleDOI
On weighted cumulative residual entropy
TL;DR: The empirical WCRE is proposed to estimate this new information measure called weighted cumulative residual entropy (WCRE), which is “length-biased” shift dependent that assigns larger weights to larger values of random variable.
Journal ArticleDOI
On weighted interval entropy
F. Misagh,Gholamhossein Yari +1 more
TL;DR: This paper studies the weighted differential information measure for two-sided truncated random variables, a generalization of recent dynamic weighted entropy measures, and obtains its upper and lower bounds.
Journal ArticleDOI
Quantile based entropy function in past lifetime
TL;DR: In this article, the authors introduced a quantile version of the entropy function in past lifetime and studied its properties, and proved characterizations theorems for some well known quantile lifetime distributions.
References
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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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TL;DR: A Quantitative-Qualitative Measure of Information in Cybernetic Systems equal to the sum of the information supplied by each event separately, taking into account the two basis concepts of probability and utility.
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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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.