A review of the CTP distribution: a comparison with other over- and underdispersed count data models

The complex triparametric Pearson (CTP) distribution is a flexible model belonging to the Gaussian hypergeometric family that can account for over- and underdispersion. However, despite its good properties, not much attention has been paid to it. So, we revive the CTP comparing it with some well-known distributions that cope with overdispersion (negative binomial, generalized Poisson and univariate generalized Waring) as well as underdispersion (Conway–Maxwell–Poisson (CMP) and hyper-Poisson (HP)). We make a simulation study that reveals the performance of the CTP and shows that it has its own space among count data models. In this sense, we also explore some overdispersed datasets which seem to be more appropriately modelled by the CTP than by other usual models. Moreover, we include two underdispersed examples to illustrate that the CTP can provide similar fits to the CMP or HP (sometimes even more accurate) without the computational problems of these models.