  In light of recent and probably upcoming observations of very high energy
astroparticles, such as those reported by the IceCube collaboration, we
readdress the energy loss mechanism by Lorentz violating particles. We
analytically show that Cohen-Glashow's formula for energy loss is connected
with a Poisson distribution for the number of decays, whose large fluctuations
prevent placing bounds on Lorentz invariance violations. However, this model
ignores the sharp change in the decay width after each process. We propose
replacing Poisson statistics with a new distribution that takes this into
account. We study the average final energy and its fluctuations according to
the new statistics, contrasting it with Cohen-Glashow's result, and discussing
the reliability of energy loss mechanisms to constrain violations of Lorentz
invariance.
