Related papers: Information theory and generalized statistics
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
In R\'enyi's representation for exponential order statistics, we replace the iid exponential sequence with any iid sequence, and call the resulting order statistic generalized R\'enyi statistic. We prove that by randomly reordering the…
Introducing the generalized, non-extensive statistics proposed by Tsallis[1988], into the standard s-wave pairing BCS theory of superconductivity in 2D yields a reasonable description of many of the main properties of high temperature…
An analytical expression of probability density function (PDF) of velocity fluctuation is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the R\'{e}nyi entropy). It is revealed that the derived…
In this paper have written the results of the information analysis of structures. The obtained information estimation (IE) are based on an entropy measure of C. Shannon. Obtained IE is univalent both for the non-isomorphic and for the…
We propose a statistical framework to quantify location and co-location associations of economic activities using information-theoretic measures. We relate the resulting measures to existing measures of revealed comparative advantage,…
This article proposes a link between statistics and the theory of Dirichlet forms used to compute errors. The error calculus based on Dirichlet forms is an extension of classical Gauss' approach to error propagation. The aim of this paper…
We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
Numerous entropy-type characteristics (functionals) generalizing R\'enyi entropy are widely used in mathematical statistics, physics, information theory, and signal processing for characterizing uncertainty in probability distributions and…
We present a theoretical framework that extends classical information theory to finite and structured systems by redefining redundancy as a fundamental property of information organization rather than inefficiency. In this framework,…
Assessing fit in common factor models solely through the lens of mean and covariance structures, as is commonly done with conventional goodness-of-fit (GOF) assessments, may overlook critical aspects of misfit, potentially leading to…
In this paper, we will study the large scale structure formation using the gravitational partition function. We will assertively argue that the system of gravitating galaxies can be analyzed using the Tsallis statistical mechanics. The…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
Large-scale astrophysical systems are non-extensive due to their long-range force of gravity. Here we show an approach toward the statistical mechanics of such self-gravitating systems (SGS). This is a generalization of the standard…
Information theory is an excellent framework for analyzing Earth system data because it allows us to characterize uncertainty and redundancy, and is universally interpretable. However, accurately estimating information content is…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
We address the problem of the foundation of generalized ensembles in statistical physics. The approach is based on Boltzmann's concept of orthodes. These are the statistical ensembles that satisfy the heat theorem, according to which the…
When engagement with a randomized trial is driven by factors that affect the outcome or when trial engagement directly affects the outcome independent of treatment, the average treatment effect among trial participants is unlikely to…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…