Related papers: $\alpha$-divergence derived as the generalized rat…

For two families of beta distributions, we show that the generalized Stieltjes transforms of their elements may be written as elementary functions (powers and fractions) of the Stieltjes transform of the Wigner distribution. In particular,…

Factorial series played a major role in Stirling's classic book "Methodus Differentialis" (1730), but now only a few specialists still use them. This article wants to show that this neglect is unjustified, and that factorial series are…

We obtain error rates for large deviations of sums of i.i.d. random variables in, a particular case, of the domain of a non-symmetric infinite mean $\alpha=1$-stable law. The focus of this work is on the method of proof via analytic…

From a new class of q-deformed coherent states we introduce a generalization of the Euler probability distribution for which the main statistical parameters are obtained explicitly. As application, we discuss the corresponding photon…

The question of the convergence of generalized formal power series (with complex power exponents) solutions of $q$-difference equations is studied in the situation where the small divisors phenomenon arises; a sufficient condition of…

We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…

Inspired by the $k$-inversion statistic for LLT polynomials, we define a $k$-inversion number and $k$-descent set for words. Using these, we define a new statistic on words, called the $k$-major index, that interpolates between the major…

We studied the thermodynamic quantities and the probability distribution, expressing the probability distribution as a function of the energy, in the canonical ensemble within the framework of the Tsallis statistics, which is characterized…

A completely new strategy to calculate parton distribution functions on the lattice has recently been proposed. In this method, lattice calculable observables, called quasi distributions, are related to normal distributions. The quasi…

This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…

We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using…

In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837--851.] to construct q-difference equations with seven variables, which generalize…

A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…

What happens when a continuously evolving stochastic process is interrupted with large changes at random intervals $\tau$ distributed as a power-law $\sim \tau^{-(1+\alpha)};\alpha>0$? Modeling the stochastic process by diffusion and the…

We derive and study quasicanonical Gibbs distribution function which is characterized by the thermostat with finite number of particles (quasithermostat). We show that this naturally leads to Tsallis nonextensive statistics and…

The Tsallis entropy, which possesses non-extensive property, is derived from the first principle employing the non-extensive Hamiltonian or the $q$-deformed Hamiltonian with the canonical ensemble assumption in statistical mechanics. Here,…

Based on the $\kappa$-deformed functions ($\kappa$-exponential and $\kappa$-logarithm) and associated multiplication operation ($\kappa$-product) introduced by Kaniadakis (Phys. Rev. E \textbf{66} (2002) 056125), we present another…

We consider Kemp's q-analogue of the binomial distribution. Several convergence results involving the classical binomial, the Heine, the discrete normal, and the Poisson distribution are established. Some of them are q-analogues of…

The $\alpha$-stable distributions introduced by L\'evy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study…

Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…