Building flexible regression models: including the Birnbaum-Saunders distribution in the gamlss package

Abstract

Generalized additive models for location, scale and shape (GAMLSS) are a very flexible statistical modeling framework, being an important generalization of the well-known generalized linear models and generalized additive models. Their main advantage is that any probability distribution (that does not necessarily belong to the exponential family) can be considered to model the response variable and different regression structures can be fitted in each of its parameters. Currently, there are more than 100 distributions that are already implemented in the gamlss package in R software. Nevertheless, researchers can implement different distributions if they are not yet available, e.g., the Birnbaum-Saunders (BS) distribution, which is widely used in fatigue studies. In this paper we make available all codes regarding the inclusion of the BS distribution in the gamlss package, and then present a simple application related to air quality data for illustration purposes