  A hardening of the proton and helium fluxes is observed above a few hundreds
of GeV/nuc. The distribution of local sources of primary cosmic rays has been
suggested as a potential solution to this puzzling behavior. Some authors even
claim that a single source is responsible for the observed anomalies. But how
probable these explanations are? To answer that question, our current
description of cosmic ray Galactic propagation needs to be replaced by the
Myriad model. In the former approach, sources of protons and helium nuclei are
treated as a jelly continuously spread over space and time. A more accurate
description is provided by the Myriad model where sources are considered as
point-like events. This leads to a probabilistic derivation of the fluxes of
primary species, and opens the possibility that larger-than-average values may
be observed at the Earth. For a long time though, a major obstacle has been the
infinite variance associated to the probability distribution function which the
fluxes follow. Several suggestions have been made to cure this problem but none
is entirely satisfactory. We go a step further here and solve the infinite
variance problem of the Myriad model by making use of the generalized central
limit theorem. We find that primary fluxes are distributed according to a
stable law with heavy tail, well-known to financial analysts. The probability
that the proton and helium anomalies are sourced by local SNR can then be
calculated. The p-values associated to the CREAM measurements turn out to be
small, unless somewhat unrealistic propagation parameters are assumed.
