Introduction

This chapter is an introduction to the book on double generalized linear models under classic and Bayesian frameworks. These models include the class of generalized linear models as special cases. The family of double generalized linear models is a unified class of models, where appropriate functions of the mean and dispersion parameters follow linear regression structures that are linear combinations of the explanatory variables. A central topic in the framework of DGLMs is count overdispersion regression models, specifically those associated with the Poisson and binomial distributions. This section presents an introduction to generalized linear models, heteroscedastic normal linear regression models, double generalized linear models, overdispersion linear regression models, and nonlinear regression models, including datasets related to the applications developed in each of the chapters. These datasets were obtained from well-known papers.