Related papers: When Is the Conway-Maxwell-Poisson Distribution In…

The object of this paper is to introduce and study the concept of quasi-geometric infinite divisibility for distributions on $\bf R_+$. These distributions arise as mixing distributions of (discrete) geometric infinitely divisible Poisson…

We state some inequalities for m-divisible and infinite divisible characteristic functions. Basing on them we propose a statistical test for a distribution to be infinitely divisible. Keywords: infinite divisible distributions; statistical…

A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn,…

We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional…

We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely…

In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…

We consider the notion of the matrix (tensor) distribution of a measurable function of several variables. On the one hand, it is an invariant of this function with respect to a certain group of transformations of variables; on the other…

We prove that symmetric Meixner distributions, whose probability densities are proportional to $|\Gamma(t+ix)|^2$, are freely infinitely divisible for $0<t\leq\frac{1}{2}$. The case $t=\frac{1}{2}$ corresponds to the law of L\'evy's…

In simple -- but selected -- quantum systems, the probability distribution determined by the ground state wave function is infinitely divisible. Like all simple quantum systems, the Euclidean temporal extension leads to a system that…

We prove for Gibbs-Markov maps that the number of visits to a sequence of shrinking sets with bounded cylindrical lengths converges in distribution to a Poisson law. Applying to continued fractions, this result extends Doeblin's Poisson…

Let $Z$ be a standard normal random variable (r.v.). It is shown that the distribution of the r.v. $\ln|Z|$ is infinitely divisible; equivalently, the standard normal distribution considered as the distribution on the multiplicative group…

We show that large critical multi-type Galton-Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analoguous to Kesten's infinite monotype Galton-Watson tree. This is proven when we…

The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…

The Mallows distribution is a non-uniform distribution, first introduced over permutations to study non-ranked data, in which permutations are weighted according to their length. It can be generalized to any Coxeter group, and we study the…

Recently, many classes of infinitely divisible distributions on R^d have been characterized in several ways. Among others, the first way is to use Levy measures, the second one is to use transformations of Levy measures, and the third one…

We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…

In this note we prove that, for infinitely divisible laws, convergence of the fourth moment to 3 is sufficient to ensure convergence in law to the Gaussian distribution. Our results include infinitely divisible measures with respect to…