This study presents several extensions of the most familiar models for count data, the Poisson and negative binomial models. We develop an encompassing model for two well-known variants of the negative binomial model (the NB1 and NB2 forms). We then analyze some alternative approaches to the standard log gamma model for introducing heterogeneity into the loglinear conditional means for these mo...

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g. matched pairs experiments, twin or family data), bivariate correlated frailty models were suggested, where the frailties were constructed using independent additive components. The purpose of this paper is to des...

A class of bivariate integer-valued time series models was constructed via copula theory. Each follows a Markov chain with the serial dependence captured using copula-based transition probabilities from Poisson and zero-inflated (ZIP) margins. The theory also used again to capture between two either Gaussian or “t-copula” functions. Such method provides flexible structure that allows for positi...

the interaction of radiation with cells and tissues has a random nature. therefore, understanding the random nature of cell killing that is determined by poisson distribution statistics is an essential point in education of radiation biology. radbiostat is a newly developed educational matlab-based software designed for computer-assisted learning of the target theory in radiation biology. altho...

We consider an extension of the Poisson Hail model where the service speed is either zero or infinity at each point of the Euclidean space. We use and develop tools pertaining to sub-additive ergodic theory in order to establish shape theorems for the growth of the ice-heap under light tail assumptions on the hailstone characteristics. The asymptotic shape depends on the statistics of the hails...

This article is concerned with the analysis of correlated count data, a class of model in which the correlation between the counts is presented by correlated unobserved heterogeneity components. A Hierarchical Bayesian analysis is used for estimation of the parameters. A Gibbs sampling algorithm is suggested for find posterior densities of parameters. The proposed method is applied to IVF data ...

The distributions of the run occurrences for a sequence of independent and identically distributed (i.i.d.) experiments are usually obtained by combinatorial methods (see Balakrishnan and Koutras (2002, Chapter 5)) and the resulting formulae are often very tedious, while the distributions for non i.i.d. experiments are generally intractable. It is therefore of practical interest to find a suita...

We present “Trivariate Reduction Extension” (TREx) — an exact algorithm for fast generation of bivariate Poisson random vectors. Like the NORTA procedure, TREx has two phases: a preprocessing phase when the required algorithm parameters are identified, and a generation phase when the parameters identified during the preprocessing phase are used to generate the desired Poisson vector. We prove t...