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This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time…

Methodology · Statistics 2026-01-13 Suchismita Das , Akul Ameya , Cahyani Karunia Putri

By replacing linear averaging in Shannon entropy with Kolmogorov-Nagumo average (KN-averages) or quasilinear mean and further imposing the additivity constraint, R\'{e}nyi proposed the first formal generalization of Shannon entropy. Using…

Information Theory · Computer Science 2007-07-13 Ambedkar Dukkipati , M. Narasimha Murty , Shalabh Bhatnagar

This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with invariant measure. A space equipped with a measure and a metric…

Dynamical Systems · Mathematics 2023-11-27 A. M. Vershik , G. A. Veprev , P. B. Zatitskii

Different notions of entropy play a fundamental role in the classical theory of dynamical systems. Unlike many other concepts used to analyze autonomous dynamics, both measure-theoretic and topological entropy can be extended quite…

Dynamical Systems · Mathematics 2017-08-03 Christoph Kawan

The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…

Information Theory · Computer Science 2021-05-26 Andrew Feutrill , Matthew Roughan

Following [1], the aim of this paper is to analyze the relative weighted entropy involving the central moments weight functions. We compare the standard relative entropy with the weighted case in two particular forms of Gaussian…

Information Theory · Computer Science 2015-06-23 Salimeh Yasaei Sekeh , Adriano Polpo

Stochastic thermodynamics extends classical thermodynamics to small systems in contact with one or more heat baths. It can account for the effects of thermal fluctuations and describe systems far from thermodynamic equilibrium. A basic…

Statistical Mechanics · Physics 2018-01-04 Momčilo Gavrilov , Raphaël Chétrite , John Bechhoefer

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

Information Theory · Computer Science 2024-05-07 Mokshay Madiman , Prasad Tetali

We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…

Dynamical Systems · Mathematics 2016-11-26 Christoph Kawan

In recent decades, several definitions of new entropy measures have been proposed, which expands the range of applications for this important tool. The present work focuses on the extension of the classical Shannon entropy to the hyperbolic…

We introduce a method for quantifying the inherent unpredictability of a continuous-valued time series via an extension of the differential Shannon entropy rate. Our extension, the specific entropy rate, quantifies the amount of predictive…

Machine Learning · Computer Science 2016-06-09 David Darmon

The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…

Information Theory · Computer Science 2017-05-01 Maciej Skorski

In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…

Data Analysis, Statistics and Probability · Physics 2016-05-20 György Steinbrecher , Giorgio Sonnino

Thermodynamic uncertainty relations reveal a fundamental trade-off between the precision of a trajectory observable and entropy production, where the uncertainty of the observable is quantified by its variance. In information theory,…

Statistical Mechanics · Physics 2025-11-25 Yoshihiko Hasegawa , Tomohiro Nishiyama

We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing…

Statistics Theory · Mathematics 2025-07-24 Angelika Silbernagel , Christian Weiß

In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed…

Statistical Mechanics · Physics 2011-06-08 P. Maynar , E. Trizac

We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…

Statistical Mechanics · Physics 2009-11-11 Israel Klich , Gil Refael , Alessandro Silva

In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…

Risk Management · Quantitative Finance 2025-08-15 Xiangyu Han , Yijun Hu , Ran Wang , Linxiao Wei

In this work, we establish a connection between the cumulative residual entropy and the Gini mean difference (GMD). Some relationships between the extropy and the GMD, and the truncated GMD and dynamic versions of the cumulative extropy are…

Statistics Theory · Mathematics 2022-08-29 Sudheesh Kattumannil , Sreedevi E. P , N. Balakrishnan

Recently, weighted cumulative residual Tsallis entropy has been introduced in the literature as a generalization of weighted cumulative residual entropy. We study some new properties of weighted cumulative residual Tsallis entropy measure.…

Statistics Theory · Mathematics 2026-02-02 Siddhartha Chakraborty , Asok K. Nanda