Statistical properties of cosmic ray fluxes and anisotropy predictions

Spectral anomalies detected by the PAMELA and CREAM experiments could be due to the presence of nearby and young cosmic ray sources. This can be studied in the myriad model, in which cosmic rays diffuse from point-like instantaneous sources located randomly throughout the Galaxy. The computation of erros bars associated to the flux (and anisotropy) turns out not to be as straightforward as it seems in the myriad model, as the standard deviation is infinite when computed for the most general statistical ensemble. The goals of this poster is to describe a method to associate error bars to the flux measurements which has a clear statistical meaning. We show that the quantiles (68% confidence levels, for instance) of the flux distribution are well-defined, even though the standard deviation is infinite. We also use the fact that local sources have known positions and ages to reduce the statistical ensemble from which random sources are drawn in the myriad model. In this context, we also discuss the status of the spectral features observed in the proton flux by CREAM and PAMELA.