ABSTRACT
This chapter provides explanation for: a general introduction to mixed distributions and in particular, explicit and generated zero-adjusted distributions defined on the interval, explicit and generated inflated distributions defined on [0, 1], and generalized Tobit model providing mixed distributions defined on any interval. A mixed distribution is a mixture of two components: a continuous distribution and a discrete distribution. There are two types of mixed distributions in GAMLSS: zero-adjusted distributions, and inflated distributions. The chapter defines a zero-adjusted distribution and describes several ways of fitting a zero-adjusted response variable within the GAMLSS framework. There are two explicitly defined zero-adjusted distributions in gamlss.dist: the zero-adjusted gamma, and the zero-adjusted inverse Gaussian.
