On the Analysis of Recurrence Characteristics at Variable Actions

The paper is devoted to some methodological problems raised by the analysis of hazards due to variable actions having implications for the risk of damage to structures. The basic recurrence model used is that of Poissonian stochastic processes. The techniques of calibration of specific recurrence characteristics are discussed, adopting a critical point of view versus statistical analyses relying exclusively on data like annual maxima. The adoption of some types of distributions is critically discussed, from the point of view of their compatibility with the Poissonian model referred to. Only the Gumbel and Fréchet distributions are accepted as adequate for the purpose adopted. Starting from their common properties an unbounded family of distributions is proposed. This family makes it possible to adopt calibrations providing an approximation of unlimited closeness to observation samples. The case of a pluri-dimensional characterization of the randomness of observation data is then tackled, considering as an illustrative case the directional statistical analysis of sequences of wind events. Some specific expressions are proposed for the directional analysis, leading to a good approximation of observation samples. A case study relying on the expressions is then presented.