Modelos aditivos generalizados para locação, escala e forma: análise histórica e a proposição de novas distribuições zero-ajustadas

Abstract

From the perspective of the class of regression models, which dates back to the 19th century, the aim is to understand how a set of predictor variables influences or explains one or more response variables. Within this class of univariate regression models, we can trace a historical line that begins with linear models (LM), followed by generalized linear models (GLM), gene- ralized additive models (GAM), and finally, generalized additive models for location, scale, and shape (GAMLSS), also currently known as distributional regression models. GAMLSS can be considered the most flexible regression models available in the literature, given their versatility in modeling responses with different characteristics, such as strong asymmetry, varying degrees of kurtosis, or excess zeros. This study aimed to construct continuous distributions with an extra probability of zero occurrence (zero–adjusted) using generalized additive models for location, scale, and shape (GAMLSS). To achieve the main objective, two stages were outlined. The first stage presents an article that discusses the historical evolution of GAMLSS, from their origins, highlighting their main contributions and innovations in various fields of knowledge. The se- cond stage presents an article that seeks to contribute to the advancement of data modeling with GAMLSS, focusing on positive continuous responses with excess zeros, developing new zero– adjusted distributions. Two distributions belonging to the Box–Cox family were proposed: the Zero–Adjusted Box–Cox Cole and Green (zBCCG) and the Zero–Adjusted Box–Cox Power Exponential (zBCPE). Simulation studies showed that the maximum likelihood estimators for the parameters of the zBCCG and zBCPE distributions provide consistent results for different sample sizes and scenarios, including symmetric, positively and negatively skewed distributi- ons, as well as platykurtic and leptokurtic scenarios. For the analyzed case study, the zBCPE distribution demonstrated greater flexibility and better statistical performance compared to the zBCCG. Thus, it can be concluded that GAMLSS models have a significant impact on vari- ous fields of knowledge, as evidenced by the growing scientific production, in addition to their recognized flexibility in modeling data with complex characteristics.