ABSTRACT
This chapter provides explanation for different distributions for a binomial type response variable within the Generalized Additive Models for Location Scale, and Shape (GAMLSS) family. It also provides how these distributions model overdispersion, underdispersion, and an excess or shortage of zeros. The special characteristic of any binomial type distribution is the fact that the binomial denominator appears in all probability functions. The data are the number of mice having alveolar-bronchiolar adenomas out of the total numbers of mice in 23 independent groups. The beta binomial is the best-fitting model. The fitted probabilities are increasing almost linearly with the number of examinations passed, while the worm plot indicates an adequate.
