About occurrences process for POT analysis

The paper focuses on the occurrences process about POT (Peaks over a Threshold) and, in particular, on the influence of the selected occurrences distribution (Poisson, Binomial or Negative Binomial) for the successive analysis. In this context, exponential distribution is considered for the magnitude of peak values, and the differences in terms of quantile estimation of annual maxima (AM) are discussed. The theoretical obtained results, valid for any kind of variable (rainfall, flood, temperature, and so on), highlight that assuming Binomial or Negative Binomial counting functions provides results (in terms of AM distribution) which are very close to Poisson-based ones. Consequently, Poisson can be preferred with respect to other counting distributions, even when its hypothesis can be statistically rejected for the observed time series of interest.