Approximation of the distribution of excesses through a generalized probability-weighted moments method

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Modeling jointly low, moderate, and heavy rainfall intensities without a threshold selection (2016, methodology): “Having s empirical moments and s theoretical moments (depending on s unknown parameters), we can pursue a method-of-moments by equating these quantities and solving the resulting system of equations [e.g., Diebolt et al., 2008, 2007].”
Extreme Value Analysis: an Introduction (2013, background): “To overcome these drawbacks, generalized probability weighted moment estimates have been proposed by Diebolt et al. (2007) for the parameters of the GDP distribution that exist for γ < 2 and are asymptotically normal for γ ∈ ] − 1 , 3 / 2 [ .”