Tail classification using non-linear regression on model plots

Selecting an appropriate statistical model is a crucial initial step in various statistical analyses, particularly when estimating extreme values. Empirical plots, such as Pareto, log-normal, and Weibull plots, serve as valuable tools for visualising the data and identifying patterns that can suggest a suitable model. Focusing on probability plots, we apply non-linear regression so as to enable the visualisation of extreme data in terms of their compatibility with widely accepted tail models. We further develop asymptotic theory for the non-linearity parameter, which, in turn, allows us to formalise classification procedures to distinguish between specific sets of tail models. The finite sample behaviour is investigated with simulations and illustrated on real data comprised of weekly maxima of hourly precipitation measures at different weather stations in France.