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Marginalized models are in great demand by most researchers in the life sciences particularly in clinical trials, epidemiology, health-economics, surveys and many others since they allow generalization of inference to the entire population…

Stable distributions are of fundamental importance in probability theory, yet their absolute continuity makes them unsuitable for modeling count data. A discrete analog of strict stability has been previously proposed by replacing scaling…

In reinsurance, Poisson and Negative binomial distributions are employed for modeling frequency. However, the incomplete data regarding reported incurred claims above a priority level presents challenges in estimation. This paper focuses on…

We consider the analysis of count data in which the observed frequency of zero counts is unusually large, typically with respect to the Poisson distribution. We focus on two alternative modelling approaches: Over-Dispersion (OD) models, and…

We propose two novel ways of introducing dependence among Poisson counts through the use of latent variables in a three levels hierarchical model. Marginal distributions of the random variables of interest are Poisson with strict…

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…

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an…

A flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and negative binomial model, as well as to more general models accounting for excess zeros that…

We introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The…

Abundance data are used in ecology for species monitoring and conservation. These count data often display several specific characteristics like numerous missing data, high variance, and a high proportion of zeros, particularly when…

It will be recalled that the classical bivariate normal distributions have normal marginals and normal conditionals. It is natural to ask whether a similar phenomenon can be encountered involving Poisson marginals and conditionals.…

In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson…

We propose a statistical model for networks of event count sequences built on a cascade structure. We assume that each event triggers successor events, whose counts follow additive probability distributions; the ensemble of counts is given…

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…

Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…

The analysis of multivariate discrete data is crucial in various scientific research areas, such as epidemiology, the social sciences, genomics, and environmental studies. As the availability of such data increases, developing robust…

Many of the data, particularly in medicine and disease mapping are count. Indeed, the under or overdispersion problem in count data distrusts the performance of the classical Poisson model. For taking into account this problem, in this…

A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…

Relational data characterized by directed edges with count measurements are common in social science. Most existing methods either assume the count edges are derived from continuous random variables or model the edge dependency by…

The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…