Count data prediction is widely used in various domains, including transportation, marketing, and telecommunications. These datasets often exhibit diverse dispersion levels, ranging from overdispersion to equidispersion and underdispersion. The Conway-Maxwell-Poisson (COM-Poisson) distribution provides a flexible framework for modeling such data, encompassing Poisson, Bernoulli, and Geometric distributions within the exponential family. However, its predictive application is limited by computational complexity and the lack of closed-form expressions for the mean and variance. This chapter explores key extensions of the COM-Poisson regression model, including parametric and nonparametric approaches such as additive models, model-based recursive partitioning trees, and gradient boosting. The effectiveness of these methods is demonstrated in R software through a real-world case study on bike-sharing demand in Washington, DC.