Journal ArticleDOI
A measure of discrimination between past lifetime distributions
TLDR
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.About:
This article is published in Statistics & Probability Letters.The article was published on 2004-04-01. It has received 80 citations till now. The article focuses on the topics: Measure (mathematics).read more
Citations
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On weighted residual and past entropies
TL;DR: 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.
Journal ArticleDOI
Information Measures in Perspective
TL;DR: This work presents information‐theoretic methodologies for a set of problems in probability and statistics using Shannon entropy and Kullback–Leibler information as the unifying notion.
Journal ArticleDOI
Dynamic generalized information measures
TL;DR: It is shown that dynamic Renyi entropy uniquely determines distributions that have monotone densities, which leads to a Maximum Dynamic Entropy of order [alpha] formulation and characterizations of some well-known lifetime models.
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Kullback–Leibler divergence: A quantile approach
TL;DR: A quantile based definition of the Kullback–Leibler divergence is introduced and the quantile versions of Kull back–Leiberler divergence for residual and past lifetime random variables are proposed.
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Some properties of past entropy and their applications
Asok K. Nanda,Prasanta Paul +1 more
TL;DR: In this paper, a measure of uncertainty in past lifetime distribution has been proposed by Di Crescenzo and Longobardi (J Appl Probab 39:434-440, 2002).
References
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Journal ArticleDOI
Modeling failure time data by lehman alternatives
TL;DR: In this paper, the authors proposed to model failure time data by F*(f) = [F(t)]θ where F(t) is the baseline distribution function and θ is a positive real number.
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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.