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About 245 papers for “extropy”

extropy, n.

Oxford University Press eBooks · 2023

Cited by 0

Renyi extropy

Jia‐Li Liu, Fuyuan Xiao · Communication in Statistics- Theory and Methods · 2021

Renyi entropy is a generalization of Shannon entropy, which plays an important role in information theory. Recently, a new concept called extropy has been developed, which is the dual complement of entropy. This paper proposes Renyi extropy, maximum Renyi extropy and conditional Renyi extropy. When the parameter q of Renyi extropy tends to 1, Renyi extropy degenerates to extropy. When the probability is uniformly distributed, Renyi extropy takes the maximum value, and the maximum Renyi extropy is equal to the maximum extropy.

Cited by 11

On general weighted cumulative residual extropy and general weighted negative cumulative extropy

Santosh Kumar Chaudhary, Nitin Gupta, Pradeep Kumar Sahu · Statistics · 2023

In this paper, we define general weighted cumulative residual extropy (GWCRJ) and general weighted negative cumulative extropy (GWNCJ). We obtain its simple estimators for complete and right censored data. We obtain some results on GWCREJ and GWNCJ. We establish its connection to reliability theory and coherent systems. We also propose empirical estimators of weighted negative cumulative extropy (WNCJ).

Cited by 4

Extropy: Complementary Dual of Entropy

Lad, Frank, Sanfilippo, Giuseppe, Agrò, Gianna · arXiv (Cornell University) · 2011

This article provides a completion to theories of information based on entropy, resolving a longstanding question in its axiomatization as proposed by Shannon and pursued by Jaynes. We show that Shannon's entropy function has a complementary dual function which we call "extropy." The entropy and the extropy of a binary distribution are identical. However, the measure bifurcates into a pair of distinct measures for any quantity that is not merely an event indicator. As with entropy, the maximum extropy distribution is also the uniform distribution, and both measures are invariant with respect to permutations of their mass functions. However, they behave quite differently in their assessments of the refinement of a distribution, the axiom which concerned Shannon and Jaynes. Their duality is specified via the relationship among the entropies and extropies of course and fine partitions. We also analyze the extropy function for densities, showing that relative extropy constitutes a dual to the Kullback-Leibler divergence, widely recognized as the continuous entropy measure. These results are unified within the general structure of Bregman divergences. In this context they identify half the $L_2$ metric as the extropic dual to the entropic directed distance. We describe a statistical application to the scoring of sequential forecast distributions which provoked the discovery.

Cited by 1Open access

Wavelet eXtropy of fractal signals

Julio César Ramírez Pacheco · Revista Mexicana de Física E · 2025

Recently, the concept of eXtropy was proposed as a complementary dual of Shannon entropy. This article extends the standard time-domain eXtropy concept to the time-scale domain and then obtains a closed-form expression for this wavelet eXtropy for fractal signals of parameter α. A didactic study of the wavelet eXtropy of fractal signals reveals that this infomation-theory quantifier increases for short-memory fractal signals, is maximum for white noise (α = 0) and decreases for long-memory fractal processes. Compared to the standard wavelet entropy, wavelet eXtropy performs similar, however has lower variability for stationary fractal signals and higher variability for nonstationary ones. Moreover, the computation of fractality based eXtropy planes allows to highlight further properties and also potential applications for the analysis/estimation of fractals. .

Cited by 0Open access

Extropy - 1990 Issue Forbidden Cover

Extropy Institute · Bulletin of Miscellaneous Information (Royal Gardens Kew) · 1990

Extropy: Journal of Transhumanist Thought covers the full range of advanced, emerging, and future technologies, and their impact and implications for both the present and the future. Extropy emphasizes finding solutions to problems of the human condition, as well proactively considering potential unwanted side-effects of new technologies. Not all solutions will be fully formed, with some Extropy content aiming to form a clear understanding of the issues.

Cited by 0

On the estimation of extropy

Hadi Alızadeh Noughabi, Jalil Jarrahiferiz · Journal of nonparametric statistics · 2018

Recently, Lad, Sanfilippo, and Agro [(2015), ‘Extropy: Complementary Dual of Entropy’, Statistical Science, 30, 40–58.] showed the measure of entropy has a complementary dual, which is termed extropy. The present article introduces some estimators of the extropy of a continuous random variable. Properties of the proposed estimators are stated, and comparisons are made with Qiu and Jia’s estimators [(2018a), ‘Extropy Estimators with Applications in Testing uniformity’, Journal of Nonparametric Statistics, 30, 182–196]. The results indicate that the proposed estimators have a smaller mean squared error than competing estimators. A real example is presented and analysed.

Cited by 44

Extropy: Characterizations and dynamic versions

Abdolsaeed Toomaj, Majid Hashempour‎, N. Balakrishnan · Journal of Applied Probability · 2023

Abstract Several information measures have been proposed and studied in the literature. One such measure is extropy, a complementary dual function of entropy. Its meaning and related aging notions have not yet been studied in great detail. In this paper, we first illustrate that extropy information ranks the uniformity of a wide array of absolutely continuous families. We then discuss several theoretical merits of extropy. We also provide a closed-form expression of it for finite mixture distributions. Finally, the dynamic versions of extropy are also discussed, specifically the residual extropy and past extropy measures.

Cited by 10Open access

Past Extropy of 𝑘-Records

E. I. Abdul Sathar, Jitto Jose · Stochastics and Quality Control · 2020

Abstract Recently, A. S. Krishnan, S. M. Sunoj and N. U. Nair [Some reliability properties of extropy for residual and past lifetime random variables, J. Korean Stat. Soc. 2020, 10.1007/s42952-019-00023-x] introduced past extropy for measuring uncertainty contained in past lifetime of random variables. In the present study, we focus on the past extropy of k -records. The motivation for considering past extropy of k -records has been discussed in detail. We have also illustrated the merit of considering past extropy of k -records over past extropy of classical records and past extropy of original random sample using two real life data sets. Some important properties of past extropy of k -records are discussed in this work. We have expressed past extropy of k -records using past extropy of k -records arising from uniform distribution. The work proposes a simple estimator for past extropy of k -records as well.

Cited by 16

General Weighted Cumulative Past Extropy

Kumar Sahu, Pradeep, Gupta, Nitin · Revstat-statistical Journal · 2023

In this paper, we study some properties and characterization of the general weighted cumulative past extropy (n-WCPJ). Many results including some bounds, inequalities, and effects of linear transformations are obtained. We study the characterization of n-WCPJ based on the largest order statistics. Conditional WCPJ and some of its properties are discussed.

Cited by 0Open access

Residual extropy of k-record values

Jose, Jitto, Abdul Sathar, E.I. · RePEc: Research Papers in Economics

Recently, extropy was defined as an alternative measure of uncertainity to that of entropy. But in measuring uncertainity about remaining lifetime of a component entropy was not much useful and hence residual entropy was formulated. Analogous to residual entropy, residual extropy was defined and used to study about the uncertainity of remaining life of a unit. In this paper, we defined the residual extropy of k-records arising from any continuous distribution in terms of residual extropy of k-records arising from uniform distribution. We also obtain lower bound for residual extropy of upper and lower k-records arising from any continuous probability distribution. Further, we discuss the monotone property of residual extropy of both upper and lower k-records.

Cited by 0

A CONCISE INTRODUCTION OF THE EXTROPY

Veronika Poór · RePEc: Research Papers in Economics · 2005

The Clausian introduction of entropy is based on an unnecessary restriction, namely that diminishing circle integral leads to a unique state variable.Eliminating that restriction a family of entropy-like function is introduced.After we have chosen one, called extropy, which has better properties as the well known entropy.

Cited by 0Open access

Residual Inaccuracy Extropy and its properties

Majid Hashempour‎, Abdolsaeed Toomaj, Mohammad Reza Kazemi · Mathematica Slovaca · 2024

Abstract In this paper, we introduce a novel concept of a dynamic residual inaccuracy measure based on extropy. We extend the traditional residual inaccuracy measure to its dynamic version, which allows us to measure the discrepancy between two residual life distributions. We study the properties of the proposed measure, including its discrimination principle and the proportional hazard rate model. We also investigate a characterization problem related to the extropy inaccuracy measure and propose some alternative expressions of the dynamic residual measure of inaccuracy. Furthermore, we establish upper and lower bounds and some inequalities concerning dynamic residual inaccuracy measures based on extropy. We demonstrate that the defined measure of inaccuracy is invariant under scale but not under location transformation. The given findings have important implications for statistical inference, estimation, and modeling. The proposed extropy-based dynamic residual inaccuracy measure provides a powerful tool for quantifying the discrepancy between two residual life distributions over time. At the end of the paper, we provide two non-parametric estimators for the proposed extropy measure of inaccuracy for both the non-censored (complete sample) and the right-censored scheme. The performances of these estimators are compared numerically based on their bias and MSE.

Cited by 3

Excess Lifetime Extropy of Order Statistics

Mansour Shrahili, Mohamed Kayid · Axioms · 2023

This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution.

Cited by 10Open access

Extropy, Transhumanism Affirmation, and Human+AI

Natasha Vita-More · 2026

This chapter argues that Human+AI foresight is essential to the future of Transhumanism, which has long served as a critical philosophy of progress. As Artificial Intelligence, human enhancement technologies, and the longevity industry advance, public concerns about the future of human existence intensify. Yet Transhumanism is increasingly misrepresented – its principles misattributed, its values misunderstood. Such distortions undermine the philosophy’s coherence and erode epistemic integrity by spreading poorly grounded beliefs. This chapter defends extropy as the foundation of Transhumanism. It identifies core misconceptions about Transhumanism over the past few decades and proposes that a renewed focus on Human+AI – not merely as a tool, but as a co-evolutionary paradigm – is the most urgent and ethically grounded trajectory for advancing humanity’s future.

Cited by 0

On negative cumulative extropy with applications

Saeid Tahmasebi, Abdolsaeed Toomaj · Communication in Statistics- Theory and Methods · 2020

Recently, an alternative measure of uncertainty termed by extropy was proposed by Lad et al. Accordingly, a cumulative residual extropy is also introduced by replacing the survival function in place of the density function in the extropy. In this paper, we define negative cumulative extropy (NCEX) measure of information and study several properties of this concept. We then elaborate the NCEX of coherent system’s lifetime when lifetimes of components are dependent and identically distributed. We also consider the conditional negative cumulative extropy and discuss some its properties. Finally, we propose the estimator of this measure using empirical approach and study it as a risk measure and large sample properties of this estimator.

Cited by 46