Related papers: The Conway-Maxwell-Poisson distribution: distribut…
We show that for all $\psi$-mixing shifts distributions of the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of all points are close either to Poisson or to compound Poisson distributions. We also describe…
Bayesian models that can handle both over and under dispersed counts are rare in the literature, perhaps because full probability distributions for dispersed counts are rather difficult to construct. This note takes a first look at Bayesian…
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…
Renyi's "thinning" operation on a discrete random variable is a natural discrete analog of the scaling operation for continuous random variables. The properties of thinning are investigated in an information-theoretic context, especially in…
In this paper, we have investigated the nature of emission distribution of the Maxwell Chern Simon (MCS) Theory in the 2+1 dimension. The distribution of the topologically massive quanta seems to be Poissonian in nature just like the…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
This paper introduces constrained mixtures for continuous distributions, characterized by a mixture of distributions where each distribution has a shape similar to the base distribution and disjoint domains. This new concept is used to…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
There is given a characterization of the geometric distribution by the independence of linear forms with random coefficients. The result is a discrete analog of the corresponding theorem on exponential distribution. The property of linear…
By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…
In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
We investigate sets of random variables that can be arranged sequentially such that a given variable only depends conditionally on its immediate predecessor. For such sets, we show that the full joint probability distribution may be…
Approximating complex probability distributions, such as Bayesian posterior distributions, is of central interest in many applications. We study the expressivity of geometric Gaussian approximations. These consist of approximations by…
This Ph.D. thesis concerns the version of the classical coupon collector's problem, when a collector samples with replacement a set of $n\ge 2$ distinct coupons so that at each time any one of the $n$ coupons is drawn with the same…
In this paper, we propose a discrete circular distribution obtained by extending the wrapped Poisson distribution. This new distribution, the Invariant Wrapped Poisson (IWP), enjoys numerous advantages: simple tractable density,…
Statistical inference on the mean of a Poisson distribution is a fundamentally important problem with modern applications in, e.g., particle physics. The discreteness of the Poisson distribution makes this problem surprisingly challenging,…
In a Cox model, the partial likelihood, as the product of a series of conditional probabilities, is used to estimate the regression coefficients. In practice, those conditional probabilities are approximated by risk score ratios based on a…