GAMLSS - A distributional regression approach

The Generalized Additive Models for Location, Scale and Shape (GAMLSS) introduced almost 20 year ago by Rigby and Stasinopoulos (2005), are a very general framework for univariate regression. Their novelty arise from the fact that all the parameters of the assumed parametric distribution of the response (target) can be modelled as functions of the explanatory variables (features). This allows modelling a response variable with high skewness or kurtosis. The assumed distribution can be any theoretical distribution as described by Rigby et al. (2019). There are different ways for modelling all the distribution parameters using explanatory variables. These include linear terms, smoothing terms and any sensible machine learning technique like neural networks, LASSO, principal component regression etc., see Stasinopoulos et al. (2017). There are also different ways of fitting the model which includes the classical (using penalized likelihood), the Bayesian using MCMC, or boosting, see Stasinopoulos et al. (2024).