Rare events in a log-Weibull scenario - Application to earthquake magnitude data

We discuss the pertinency of the log-Weibull model in the statistical under standing of energy release for earthquake magnitude data. This model has ma ny interesting features, the most remarkable of which being: depending on t he value alpha > 0 of the deformation index of the source; it may present t ails ranging from moderately heavy (alpha < 1) to very heavy (with tail ind ex zero as alpha > 1): through hyperbolic (power law) for the critical valu e a = 1. Under this model (fur which a precise tail study is supplied); the occurrence of power laws appears as a critical phenomenon: this reinforces the current tread predicting that some departure from the ideal (strictly scaling fractal) model may be ubiquitous. Raving applied an affine transfor mation in the logarithmic scale, quantile estimation and the Kolmogorov-Smi rnov statistics are used to fit the log-Weibull distribution to a realizati on of all iid sample. This enables to decide whether the upper tail of the phenomenon under study is light/heavy/very heavy. A comparative study of re corded French and Japanese earthquake magnitudes suggests that they exhibit comparable tail behaviour; albeit with different centrality and dispersion parameters.