On a weighted Poisson distribution and its associated regression model

Count data emerge naturally within the biomedical and economic sciences, in engineering and in industrial applications. The benchmark Poisson distribution is seldom an appropriate statistical model for counts but none of the more flexible distributions available are universally accepted as an alternative. Among such flexible models, the class of weighted Poisson distributions has recently been studied in theoretical investigations but their application is still incipient. This article investigates a particular weighted Poisson model, providing the associated statistical tools for analyzing count data. We make comparisons with other flexible models using public available datasets. For the weighted Poisson model under investigation, we have developed estimation by maximum likelihood and method of moments, random number generation, visual tools for univariate analysis and finally, regression modeling. Results indicate that weighted Poisson distributions are very flexible and capable of modeling count responses in different scenarios.