Related papers: Generalised exponential families and associated en…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…
The {\lambda}-exponential family has recently been proposed to generalize the exponential family. While the exponential family is well-understood and widely used, this it not the case of the {\lambda}-exponential family. However, many…
Exponential families comprise a broad class of statistical models and parametric families like normal distributions, binomial distributions, gamma distributions or exponential distributions. Thereby the formal representation of its…
Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
Generalized entropies are studied as Lyapunov functions for the Master equation (Markov chains). Three basic properties of these Lyapunov functions are taken into consideration: universality (independence of the kinetic coefficients),…
The notion of generalised exponential family is considered in the restricted context of nonextensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown…
We propose a number of concepts and properties related to `weighted' statistical inference where the observed data are classified in accordance with a `value' of a sample string. The motivation comes from the concepts of weighted…
Similar to the generalized extreme value (GEV) family, the generalized extreme value distributions under power normalization are introduced by Roudsari (1999) and Barakat et al. (2013). In this article, we study the asymptotic behavior of…
Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…
For statistical systems that violate one of the four Shannon-Khinchin axioms, entropy takes a more general form than the Boltzmann-Gibbs entropy. The framework of superstatistics allows one to formulate a maximum entropy principle with…
Exponential families encompass the distributions central to modern machine learning -- softmax, Gaussians, and Boltzmann distributions -- and underlie the theory of variational inference, entropy-regularized reinforcement learning, and…
In this paper we propose a method for proving some exponential inequalities based on power series expansion and analysis of derivations of the corresponding functions. Our approach provides a simple proof and generates a new class of…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
The present paper studies a large class of temperature dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized…
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
Recently, G.~Yanev obtained a characterization of the exponential family of distributions in terms of a functional equation for certain mixture densities. The purpose of this note is twofold: we extend Yanev's theorem by relaxing a…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
This paper generalises the exponential family GLM to allow arbitrary distributions for the response variable. This is achieved by combining the model-assisted regression approach from survey sampling with the GLM scoring algorithm, weighted…