  Measurements of cosmic ray fluxes by the PAMELA and CREAM experiments show
unexpected spectral features between 200 GeV and 100 TeV. They 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. To test this hypothesis, one
must compute the flux due to a catalog of local sources, but also the error
bars associated to this quantity. This turns out not to be as straightforward
as it seems, as the standard deviation is infinite when computed for the most
general statistical ensemble. The goals of this paper are to provide a method
to associate error bars to the flux measurements which has a clear statistical
meaning, and to explore the relation between the myriad model and the more
usual source model based on a continuous distribution. To this end, we show
that the quantiles of the flux distribution are well-defined, even though the
standard deviation is infinite. They can be used to compute 68% confidence
levels, for instance. 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. We present a method to evaluate meaningful error
bars for the flux obtained 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.
