Pseudo-Poisson Distributions with Concomitant Variables

It has been argued in Arnold and Manjunath (2021) that the bivariate pseudo-Poisson distribution will be the model of choice for bivariate data with one equidispersed marginal and the other marginal over-dispersed. This is due to its simple structure, straightforward parameter estimation and fast computation. In the current note, we introduce the effects of concomitant variables on the bivariate pseudo-Poisson parameters and explore the distributional and inferential aspects of the augmented models. We also include a small simulation study and an example of application to real-life data.