Related papers: On some compound distributions with Borel summands

A new class of Poisson algebras, the class of {\em generalized Weyl Poisson algebras}, is introduced. It can be seen as Poisson algebra analogue of generalized Weyl algebras or as giving a Poisson structure to (certain) generalized Weyl…

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial…

This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…

The binomial, the negative binomial, the Poisson, the compound Poisson and the Erlang distribution do all admit integral representations with respect to its (continuous) parameter. We use the Margulis-Russo type formulas for Bernoulli and…

In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

Multivariate Poisson processes have many important applications in Insurance, Finance, and many other areas of Applied Probability. In this paper we study the backward simulation approach to modelling multivariate Poisson processes and…

Clusters traverse a gas and collide with gas particles. The gas particles are adsorbed and the clusters become hosts. If the clusters are size selected, the number of guests will be Poisson distributed. We review this by showcasing four…

Motivated by the need, in some Bayesian likelihood free inference problems, of imputing a multivariate counting distribution based on its vector of means and variance-covariance matrix, we define a generic multivariate discrete…

Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov's multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a…

We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…

The claim experience of the past is a very important information to calculate the fair price of an insurance contract. In a lot of European countries for instance the prices for motor car insurance depend on the number of claims the driver…

The aim of this paper is to study the mixture of the Riesz distribution on symmetric matrices with respect to the multivariate Poisson distribution. We show, in particular, that this distribution is related to the modified Bessel function…

The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator…

Generalizing earlier works of Delbaen & Haezendonck [5] as well as of [18] and [16] for given compound mixed renewal process S under a probability measure P, we characterize all those probability measures Q on the domain of P such that Q…

We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…

Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these…

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…

One may consider three types of statistical inference: Bayesian, frequentist, and group invariance-based. The focus here is on the last method. We consider the Poisson and binomial distributions in detail to illustrate a group invariance…

We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…