ABSTRACT
This chapter provides a definition of Generalized Additive Models for Location Scale, and Shape (GAMLSS). It also provides an introduction to different types of distributions within GAMLSS and in particular: continuous, discrete, and mixed distributions. The chapter introduces all the available distributions within the current implementation of GAMLSS. GAMLSS are distributional regression models where the response variable can have any distribution and all the parameters of the distribution can depend on explanatory variables. The explicit GAMLSS family distributions are subdivided into several distinct types according to the type of random variable modeled as a response. Beta inflated distributions are useful for modeling a proportion response variable on the interval 0 to 1, including 0 or 1 or both.
