Related papers: Degenerate zero-truncated Poisson random variables
Compound Poisson distributions and signed compound Poisson measures are used for approximation of the Markov binomial distribution. The upper and lower bound estimates are obtained for the total variation, local and Wasserstein norms. In a…
We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission…
Given a set of independent Poisson random variables with common mean, we study the distribution of their maximum and obtain an accurate asymptotic formula to locate the most probable value of the maximum. We verify our analytic results with…
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of…
In this paper we introduce the zero-adjusted Birnbaum-Saunders regression model. This new model generalizes at least seven Birnbaum-Saunders regression models. The idea of this modeling is mixing a degenerate distribution at zero with a…
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
A 2022 paper arXiv:2009.10305v4 introduced the notion of true positive and negative skewness for continuous random variables via Fr\'echet $p$-means. In this work, we find novel criteria for true skewness, establish true skewness for the…
Two degenerate Poisson structures of the same rank possess a recursion operator if and only if their characteristic distributions coincide.
It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate…
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this…
We overview results on the topic of Poisson approximation that are missed in existing surveys. The topic of Poisson approximation to the distribution of a sum of integer-valued random variables is presented as well. We do not restrict…
Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…
Motivated by the properties of the descent polynomials, which enumerate permutations of $S_n$ with a fixed descent set, we define descent polynomials for labeled rooted trees. We give recursive and explicit formulas for these polynomials…
We obtain new closed-form formulas for the moments and absolute moments of the variance-gamma distribution. We thus deduce new formulas for the moments and absolute moments of the product of two correlated zero mean normal random variables.
This paper establishes the optimal sub-Gaussian variance proxy for truncated Gaussian and truncated exponential random variables. The proofs rely on first characterizing the optimal variance proxy as the unique solution to a set of two…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
Power series distributions form a useful subclass of one-parameter discrete exponential families suitable for modeling count data. A zero-inflated power series distribution is a mixture of a power series distribution and a degenerate…
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
This paper presents foundational theoretical results on distributed parameter estimation for undirected probabilistic graphical models. It introduces a general condition on composite likelihood decompositions of these models which…
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution.