Related papers: On the Maximum and Minimum of a Multivariate Poiss…
The distribution of the sum of dependent risks is a crucial aspect in actuarial sciences, risk management and in many branches of applied probability. In this paper, we obtain analytic expressions for the probability density function (pdf)…
In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This…
In this paper, we first study the Poisson reductions of controlled Hamiltonian (CH) system and symmetric CH system by controllability distributions. These reductions are the extension of Poisson reductions by distribution for Poisson…
Bimodal truncated count distributions are frequently observed in aggregate survey data and in user ratings when respondents are mixed in their opinion. They also arise in censored count data, where the highest category might create an…
In this paper, we investigate the cumulative distribution function (CDF) of the aggregate interference in carrier sensing multiple access/collision avoidance (CSMA/CA) networks measured at an arbitrary time and position. We assume that…
Multivariate Poisson distributions have numerous applications. Fast computation of these distributions, holding constant a fixed set of linear combinations of these variables, has been explored by Sontag and Zeilberger. This elaborates on…
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…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. For $k=1$ it is the standard Poisson distribution. Our main result is a proof that for sufficiently small values of the rate parameter $\lambda$,…
A three-parameter discrete distribution is developed to describe the multiplicity distributions observed in total- and limited phase space volumes in different collision processes. The probability law is obtained by the Poisson transform of…
Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…
This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…
In this paper, an alternative mixed Poisson distribution is proposed by amalgamating Poisson distribution and a modification of the Quasi Lindley distribution. Some fundamental structural properties of the new distribution, namely the shape…
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…
We introduce a novel class of bivariate common-shock discrete phase-type (CDPH) distributions to describe dependencies in loss modeling, with an emphasis on those induced by common shocks. By constructing two jointly evolving terminating…
In this note we discuss additional properties of mixed Poisson distributions. We discuss the convergence of mixed Poisson distributions to its mixing distribution for the scaling parameter tending to infinity. Moreover, we obtain a central…
In this letter, we derive new lower bounds on the cumulative distribution function (CDF) of the contact distance in the Poisson Hole Process (PHP) for two cases: (i) reference point is selected uniformly at random from $\mathbb{R}^2$…
Many application domains such as ecology or genomics have to deal with multivariate non Gaussian observations. A typical example is the joint observation of the respective abundances of a set of species in a series of sites, aiming to…
The statistical characterization of the sum of random variables (RVs) are useful for investigating the performance of wireless communication systems. We derive exact closed-form expressions for the probability density function (PDF) and…
A technique is presented to evaluate the performance of a wireless link with a multi-antenna linear Minimum-Mean-Square Error (MMSE) receiver in the presence of interferers distributed according to non-homogeneous Poisson processes or…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…