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Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…
Consider a second-order elliptic operator $L$ in the half-plane $\mathbb R \times (0, \infty)$ with coefficients depending only on the second coordinate. The Poisson kernel for $L$ is used in the representation of positive $L$-harmonic…
In this paper, we consider a fractional Poisson random field (FPRF) on positive plane. It is defined as a process whose one dimensional distribution is the solution of a system of fractional partial differential equations. A time-changed…
A partition polynomial is a refinement of the partition number p(n) whose coefficients count some special partition statistic. Just as partition numbers have useful asymptotics so do partition polynomials. In fact, their asymptotics…
In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful…
A family of consistent tests, derived from a characterization of the probability generating function, is proposed for assessing Poissonity against a wide class of count distributions, which includes some of the most frequently adopted…
This paper introduces the notion of probabilistic zero bounds for random polynomials. It presents new results regarding the probabilistic bounds of random polynomials whose coefficients are independently and identically distributed as…
We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…
Regression models for limited continuous dependent variables having a non-negligible probability of attaining exactly their limits are presented. The models differ in the number of parameters and in their flexibility. Fractional data being…
This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…
We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution where the three parameters (the number of trials, the probability of…
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…
Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference).…
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…
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's…
We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for…
We present some correlated fractional counting processes on a finite time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional…
A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common…
Permutation tests are amongst the most commonly used statistical tools in modern genomic research, a process by which p-values are attached to a test statistic by randomly permuting the sample or gene labels. Yet permutation p-values…
The two-parameter Poisson--Dirichlet distribution is a probability distribution on the totality of positive decreasing sequences with sum 1 and hence considered to govern masses of a random discrete distribution. A characterization of the…