ABSTRACT
This chapter discusses the fitting multimodal distributions to data or for fitting latent class models. Finite mixture distributions are fitted within Generalized additive models for location scale and shape (GAMLSS) using the expectation-maximization (EM) algorithm. Specific mixed distributions are explicitly available in the gamlss.dist package, for example the zero adjusted gamma, the zero adjusted inverse Gaussian and the zero-and-one inflated beta. The function for fitting finite mixtures with no parameters in common is gamlssMX() in the gamlss.mx package. The function for fitting finite mixtures with parameters in common is gamlssNP(), of the package gamlss.mx, with argument mixture="np". The function gamlssMX() follows a similar approach to that adopted by F. Leisch and B. Grun and Leisch. Both gamlssMX() and gamlssNP() functions estimate the finite mixture model with a fixed number of components using the EM algorithm in a likelihood-based framework.
