This paper aims to model integer valued time series with possible negative values and either positive or negative correlations by introducing the Poisson difference integer valued autoregressive model of order one. This model has Poisson difference marginal distribution and is defined by a new operator called the extended binomial thinning operator. It includes previous integer valued autoregre...

In this paper, a new bivariate negative binomial regression (BNBR) model allowing any type of correlation is defined and studied. The marginal means of the bivariate model are functions of the explanatory variables. The parameters of the bivariate regression model are estimated by using the maximum likelihood method. Some test statistics including goodness-of-fit are discussed. Two numerical da...

This paper is concerned with the estimation of the regression coe cients for a count data model when one of the explanatory variables is subject to hete roscedastic measurement error The observed values W are related to the true regressor X by the additive error model W X U The errors U are assumed to be normally distributed with zero mean but heteroscedastic variances which are known or can be...

In this paper, we apply and compare two generalized estimating equation approaches to the analysis of car breakdowns data in Mauritius. Number of breakdowns experienced by a machinery is a highly under-dispersed count random variable and its value can be attributed to the factors related to the mechanical input and output of that machinery. Analyzing such under-dispersed count observation as a ...

Transportation origin-destination analysis is investigated through the use of Poisson mixtures by introducing covariate-based models which incorporate different transport modelling phases and also allow for direct probabilistic inference on link traffic based on Bayesian predictions. Emphasis is placed on the Poisson-inverse Gaussian model as an alternative to the commonly used Poisson-gamma an...

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications ...

We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are in general required for deriving the marginal models, we obtain the multivariate negati...

Real-life count data are frequently characterized by overdispersion and excess zeros. Zero-inflated count models provide a parsimonious yet powerful way to model this type of situation. Such models assume that the data are a mixture of two separate data generation processes: one generates only zeros, and the other is either a Poisson or a negative binomial data-generating process. The result of...

In this article, a new kind of stationary zero-inflated Pegram’s operator based integer-valued time series process of order p with Poisson marginal or ZIPPAR(p) is constructed for modelling a count time series consisting a large number of zeros compared to standard Poisson time series processes. Estimates of the model parameters are studied using three methods, namely Yule-Walker, conditional l...