Related papers: A note on mixed Poisson distributions
We completely characterize $\Delta$- and local subexponentialities of positive-half compound Poisson distributions and extend the characterization on two-sided distributions. Moreover, $\Delta$-subexponentiality of infinitely divisible…
We consider the estimation of the mixing distribution of a normal distribution where both the shift and scale are unobserved random variables. We argue that in general, the model is not identifiable. We give an elegant non-constructive…
Consider generalized adapted stochastic integrals with respect to independently scattered random measures with second moments. We use a decoupling technique, known as the "principle of conditioning", to study their stable convergence…
A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…
We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
The Poisson probability distribution is frequently encountered in physical science measurements. In spite of the simplicity and familiarity of this distribution, there is considerable confusion among physicists concerning the description of…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
The hypergeometric distributions have many important applications, but they have not had sufficient attention in information theory. Hypergeometric distributions can be approximated by binomial distributions or Poisson distributions. In…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
We develop a new tool, the time inhomogeneous Poisson equation in the whole space and with a terminal condition at infinity, to study the asymptotic behavior of the non-autonomous multi-scale stochastic system with irregular coefficients,…
Subordinators are infinitely divisible distributions on the positive half-line. They are often used as mixing distributions in Poisson mixtures. We show that appropriately scaled Poisson mixtures can approximate the mixing subordinator and…
It is well known that, under broad assumptions, the time-scaled point process of exceedances of a high level by a stationary sequence converges to a compound Poisson process as the level grows. The purpose of this note is to demonstrate…
Results of numerical procedure of constructing confidence intervals for parameter of the Poisson distribution of signal events in the presence of background events with known value of parameter of Poisson distribution are presented. It is…
One aspect of Poisson approximation is that the support of the random variable of interest is often finite while the support of the Poisson distribution is not. In this paper we will remedy this by examining truncated negative binomial (of…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
We consider random rectangles in $\mathbb{R}^2$ that are distributed according to a Poisson random measure, i.e., independently and uniformly scattered in the plane. The distributions of the length and the width of the rectangles are…
An essential character for a distribution to play a central role in the limit theory is infinite divisibility. In this note, we prove that the Conway-Maxwell-Poisson (CMP) distribution is infinitely divisible iff it is the Poisson or…