ABSTRACT
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.
Editor A. Castellarin Associate editor I. Prosdocimi
Editor A. Castellarin Associate editor I. Prosdocimi
Acknowledgements
I thank the Associate Editor and the three reviewers for their constructive comments and suggestions that significantly improved the content and quality of the manuscript. Also, I acknowledge the motivational and always fruitful discussions on the broader topic of stochastics with my NTUA colleagues, Panagiotis Kossieris, Andreas Efstratiadis, Demetris Koutsoyiannis and Christos Makropoulos.
Data and software availability
The analysis, simulations, and visualization were performed in R language (R Core Team Citation2017). The source code for the anySim R package (Tsoukalas et al. Citation2020) is available at the GitHub repository: https://github.com/itsoukal/anySim. The source code for the bBextremes R package (introduced in this work) is available at the GitHub repository: https://github.com/itsoukal/bBextremes. Also, all the figures/plots presented herein were produced via ggplot2 R package (Wickham Citation2016).
Supplementary material
Supplemental data for this article can be accessed here
Notes
1 The simulations were performed using the anySim R package (Tsoukalas et al. Citation2020), which is capable of simulating Nataf-based (i.e. Gaussian copula) processes with any marginal distribution (with finite variance) and (valid; i.e. positive definite) correlation structure (temporal, spatial or combination of them).
2 The distribution fitting was performed using the lmom R package (Hosking Citation2019). In particular, for the distribution we employed the pelp function which, as described, provides “Parameter estimation for a general distribution by the method of Lmoments.” It is noted that for computational efficiency, and optimization-related reasons, in the case of distribution (as well as for other models comprising a scale and multiple shape parameters), the argument type should be set to “s” (for more details see p. 37 of the package manual).