GNGTS 2013 - Atti del 32° Convegno Nazionale

If, in the i-th model the (10) where e s and e z are the realizations of the Bernoulli variable defined above at two generic s-th and z-th sites. In this case, the standard deviation of the random variable N* is (11) When S is relatively large, the Lyapunov variant of the Central Limit Theorem (e.g., Gnedenko, 1976) implies that (12) Eq. (12) allows us to evaluate whether a potential disagreement between the experimental value N * and the “forecast” µ i ( N ) is statistically significant, thus making the H i PSHA computational model “not confirmed” by the set of S observations. An application in the frame of the DPC-INGV-S2 project. In the following, an example will be presented of the approach described above in the frame of the DPC-INGV-S2 research project. Aims of a task of this project was the comparative evaluation of performances relative to a number of PSHA procedures proposed in the last 20 years for the Italian area. In particular, in the frame of the S2 project, a repository of PSHA results was built (https://sites.google.com/ site/ingvdpc2012progettos2/deliverables/d1-1), that includes both time-dependent and time independent estimates. For all the considered models, the same exposure time of 30 years was considered. In the case of time-dependent models, the time interval 1 Jan 2010 – 31 Dec 2029 was considered. Furthermore, since in most cases the PSHA outcome is provided in the form of a PGA value, this parameter only has been considered for scoring. An important problem arises since PSHA outcomes here considered where provided in the form of PGA values characterized Fig. 1 – Position of the 72 accelerometric sites considered for empirical testing (white diamonds). 12 GNGTS 2013 S essione 2.1