The tales that the distribution tails of non-Gaussian autocorrelated processes tell: efficient methods for the estimation of the k-length block-maxima distribution

The focal point of this work is the estimation of the distribution of maxima without the use of classic extreme value theory and asymptotic properties, which may not be ideal for hydrological processes. The problem is revisited from the perspective of non-asymptotic conditions, and regards the so-called exact distribution of block-maxima of finite-sized k-length blocks. First, we review existing non-asymptotic approaches/models, and introduce an alternative and fast model. Next, through simulations and comparisons (using asymptotic and non-asymptotic models), involving intermittent processes (e.g. rainfall), we highlight the capability of non-asymptotic approaches to model the distribution of maxima with reduced uncertainty and variability. Finally, we discuss an alternative use of such models that concerns the theoretical estimation of the multi-scale probability of obtaining a zero value. This is a useful finding when the scope is the multi-scale modelling of intermittent hydrological processes (e.g. intensity-duration-frequency models). The work also provides step-by-step recipes and an R package.

Automated summary

The focus of this study is to estimate the distribution of maxima using non-asymptotic approaches, as classic extreme value theory and asymptotic properties may not be suitable for hydrological processes. The study revisits the problem from a non-asymptotic perspective and introduces a fast alternative model. Through simulations and comparisons, the study demonstrates that non-asymptotic approaches can model the distribution of maxima with reduced uncertainty and variability, particularly for intermittent processes like rainfall. The study also discusses the theoretical estimation of the multi-scale probability of obtaining a zero value and provides step-by-step recipes and an R package.