Related papers: Conditional Probabilities of Multivariate Poisson …
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…
Multivariate Gaussian distributions enjoy Gaussian conditional distributions that makes conditioning easy: conditioning boils down to implementing analytical formulae for conditional means and covariances. For more general distributions,…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to obtain, although a few cases have been solved and upper/lower…
This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where $\pm \x$ are equivalent), for…
Physical and mathematical applications of fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we…
We study properties of the (generalized) Dickman distribution with two parameters and the stationary solution of the Ornstein-Uhlenbeck stochastic differential equation driven by a Poisson process. In particular, we show that the marginal…
A modification of the Skellam and Poisson distributions is proposed for subsystems when the constraints imposed by the charge conservation law in the complete system are taken into account. Such distributions can be applied, for example,…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new…
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families…
Gibbs-type random probability measures and the exchangeable random partitions they induce represent an important framework both from a theoretical and applied point of view. In the present paper, motivated by species sampling problems, we…
Investigations of complexity of sequences lead to important applications such as effective data compression, testing of randomness, discriminating between information sources and many others. In this paper we establish formulas describing…
We propose a multivariate probability distribution that models a linear correlation between binary and continuous variables. The proposed distribution is a natural extension of the previously developed multivariate binary distribution. As…
This work defines and investigates the properties of the Max-U-Exp distribution. The method of moments is applied in order to estimate its parameters. Then, by using the previous general theory about Mixed Poisson processes, developed by…
Karlin and Altschul in their statistical analysis for multiple high-scoring segments in molecular sequences introduced a distribution function which gives the probability there are at least r distinct and consistently ordered segment pairs…
Let X_1,...., X_n be a collection of iid discrete random variables, and Y_1,..., Y_m a set of noisy observations of such variables. Assume each observation Y_a to be a random function of some a random subset of the X_i's, and consider the…
We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the…
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…
Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…