Related papers: Entropy Moments Characterization of Statistical Di…
Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy…
A method is introduced for the verification of nonclassicality in terms of moments of nonclassicality quasiprobability distributions. The latter are easily obtained from experimental data and will be denoted as nonclassicality moments.…
Here we present an analytic approximation for the entropy of floating-point numbers, along with bounds on the error of this approximation. It is well-known that the differential entropy is tightly linked to the discrete entropy of a…
The concepts of variability and uncertainty, both epistemic and alleatory, came from experience and coexist with different connotations. Therefore this article attempts to express their relation by analytic means firstly setting sights on…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…
Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed. Here we propose a general method of moments approach that can be used to fit a…
We deal with a generalized statistical description of nonequilibrium complex systems based on least biased distributions given some prior information. A maximum entropy principle is introduced that allows for the determination of the…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
The distribution of frequency counts of distinct words by length in a language's vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that…
Inferring models, predicting the future, and estimating the entropy rate of discrete-time, discrete-event processes is well-worn ground. However, a much broader class of discrete-event processes operates in continuous-time. Here, we provide…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is…
We suggest an extension of the standard concept of statistical ensembles. Namely, we introduce a class of ensembles with extensive quantities fluctuating according to an externally given distribution. As an example the influence of energy…
Alternative definitions are given of basic concepts of generalized thermostatistics. In particular, generalizations of Shannon's entropy, of the Boltzmann-Gibbs distribution, and of relative entropy are considered. Particular choices made…
In statistical analysis, quantifying uncertainties through measures such as entropy, extropy, varentropy, and varextropy is of fundamental importance for understanding distribution functions. This paper investigates several properties of…