Mixture Poisson exponential–inverse Gaussian regression model

Abstract

In this paper a mixed Poisson regression model for count data is introduced. This model is derived by mixing the Poisson distribution with the one–parameter continuous exponential–inverse Gaussian distribution. The obtained probability mass function is over-dispersed and unimodal with modal value located at zero. Estimation is performed by maximum likelihood. As an application, the demand for health services among people 65 and over is examined using this regression model since empirical evidence has suggested that the over–dispersion and a large portion of non–users are common features of medical care utilization data.