Related papers: Bounds for some entropies and special functions
Analysis of low-degree polynomial algorithms is a powerful, newly-popular method for predicting computational thresholds in hypothesis testing problems. One limitation of current techniques for this analysis is their restriction to…
For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and P\'olya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution…
The equilibrium distributions of probabilities providing maximality of Renyi and Tsallis entropies are rederived. New S-forms of them are found which are normalised with corresponding entropies in contrast to the usual Z-forms normalised…
Shannon entropy for discrete distributions is a fundamental and widely used concept, but its continuous analogue, known as differential entropy, lacks essential properties such as positivity and compatibility with the discrete case. In this…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
The Shannon-Khinchin axioms for the ordinary information entropy are generalized in a natural way to the nonextensive systems based on the concept of nonextensive conditional entropy, and a complete proof of the uniqueness theorem for the…
Starting with the additivity condition for Lyapunov functions of master equation, we derive a one-parametric family of entropy functions which may be appropriate for a description of certain effects of finiteness of statistical systems, in…
The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…
We demonstrate that dual entropy expressions of the Tsallis type apply naturally to statistical-mechanical systems that experience an exceptional contraction of their configuration space. The entropic index $\alpha>1$ describes the…
We calculate explicit formulae for the Shannon entropies of several families of tailored random graph ensembles for which no such formulae were as yet available, in leading orders in the system size. These include bipartite graph ensembles…
We derive an asymptotic lower bound on the Shannon entropy $H$ of sums of $N$ arbitrary iid discrete random variables. The derived bound $H \geq \frac{r(X)}{2}\log(N) + {\it cst}$ is given in terms of the incommensurability rank $r(X)$ of…
Quite general, analytical (both exact and approximate) forms for discrete probability distributions (PD's) that maximize Tsallis entropy for a fixed variance are here investigated. They apply, for instance, in a wide variety of scenarios in…
The requirement that an entropy function be composable is key: it means that the entropy of a compound system can be calculated in terms of the entropy of its independent components. We prove that, under mild regularity assumptions, the…
The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an…
Gauss' law of error is generalized in Tsallis statistics such as multifractal systems, in which Tsallis entropy plays an essential role instead of Shannon entropy. For the generalization, we apply the new multiplication operation determined…
Coincidence probabilities, which yield Renyi entropies, are investigated in a generalized Gaussian model, which includes interparticle correlations
Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when…
Sufficient conditions are developed, under which the compound Poisson distribution has maximal entropy within a natural class of probability measures on the nonnegative integers. Recently, one of the authors [O. Johnson, {\em Stoch. Proc.…
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…
By developing the entropy theory of random walks on equivalence relations and analyzing the asymptotic geometry of horospheric products we describe the Poisson boundary for random walks on random horospheric products of trees.