Author
Received April
Bio: Received April is an academic researcher. The author has contributed to research in topics: Differential entropy & Residual. The author has an hindex of 1, co-authored 1 publications receiving 84 citations.
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01 Sep 2006
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.
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, 62B10
84 citations
Cited by
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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.
225 citations
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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.
Abstract: Recently, cumulative residual entropy (CRE) has been found to be a new measure of information that parallels Shannon's entropy (see Rao et al. [Cumulative residual entropy: A new measure of information, IEEE Trans. Inform. Theory. 50(6) (2004), pp. 1220–1228] and Asadi and Zohrevand [On the dynamic cumulative residual entropy, J. Stat. Plann. Inference 137 (2007), pp. 1931–1941]). Motivated by this finding, in this paper, we introduce a generalized measure of it, namely cumulative residual Renyi's entropy, and study its properties. We also examine it in relation to some applied problems such as weighted and equilibrium models. Finally, we extend this measure into the bivariate set-up and prove certain characterizing relationships to identify different bivariate lifetime models.
64 citations
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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.
Abstract: In analogy with the weighted Shannon entropy proposed by Belis and Guiasu (1968) and Guiasu (1986), we introduce a new information measure called weighted cumulative residual entropy (WCRE). This is based on the cumulative residual entropy (CRE), which is introduced by Rao et al. (2004). This new information measure is “length-biased” shift dependent that assigns larger weights to larger values of random variable. The properties of WCRE and a formula relating WCRE and weighted Shannon entropy are given. Related studies of reliability theory is covered. Our results include inequalities and various bounds to the WCRE. Conditional WCRE and some of its properties are discussed. The empirical WCRE is proposed to estimate this new information measure. Finally, strong consistency and central limit theorem are provided.
45 citations
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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.
41 citations
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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.
39 citations