Extending Generalized Additive Models for extreme value modeling: a software review

The terms distributional regression and Generalized Additive Model for Location, Scale and Shape both indicate a class of broad statistical models which allow for the modeling of a given response variable as a flexible function of some predictors. These models extend traditional regression models by allowing the response variable to follow any distribution indexed by one or more parameters. These parameters are then allowed to vary as unknown functions of the predictors: these functions are typically estimated using basis expansions. The analysis of extremes has proven to be an interesting area of application for distributional regression: there is for example an interest in assessing whether climate and other anthropogenic changes are having an impact on the measured records of some environmental extremes. These type of data is typically assumed to follow some highly skewed distribution which does not belong to the exponential family. Furthermore, there is little prior knowledge on the type of shape that the impacts of climate change could have on extremes: it is therefore preferable to allow for the relationship to be derived from observations. In this work, I provide a brief overview of distributional regression, extreme value statistic and of some off-the-shelf implementations available in the \texttt{R} statistical software for the estimation of distributional regression models for extremes.