Non-asymptotic distributions of water extremes: Superlative or superfluous?

Abstract. Non-asymptotic (𝒩𝒜) probability distributions of block maxima (BM) have been proposed as an alternative to asymptotic distributions of BM derived by classic extreme value theory (EVT). Their advantage should be the inclusion of moderate quantiles as well as extremes in the inference procedures. This would increase the amount of used information and reduce the uncertainty characterizing the inference based on short samples of BM or peaks over high threshold.  In this study, we show that 𝒩𝒜 distributions of BM suffer from two main drawbacks that make them of little usefulness for practical applications. Firstly, unlike classic EVT distributions, 𝒩𝒜 models of BM imply the preliminary definition of their conditional parent distributions, which explicitly appears in their expression. However, when such conditional parent distributions are known or estimated also the unconditional parent distribution is readily available, and the corresponding 𝒩𝒜 distribution of BM is no longer needed, as it is just an approximation of the upper tail of the parent. Secondly, when declustering procedures are used to remove autocorrelation characterizing hydro-climatic records, 𝒩𝒜 distributions of BM devised for independent data are strongly biased even if the original process exhibits low/moderate autocorrelation. On the other hand, 𝒩𝒜 distributions of BM accounting for autocorrelation are less biased but still of little practical usefulness. Such conclusions are supported by theoretical arguments, Monte Carlo simulations, and re-analysis of sea level data.