  In a recent Brief Report [Phys. Rev. E 79 (2009) 057201], Grassberger
re-investigates probability densities of sums of iterates of the logistic map
near the critical point and claims that his simulation results are inconsistent
with previous results obtained by us [U. Tirnakli et al., Phys. Rev. E 75
(2007) 040106(R) and Phys Rev. E 79 (2009) 056209]. In this comment we point
out several errors in Grassberger's paper. We clarify that Grassberger's
numerical simulations were mainly performed in a parameter region that was
explicitly excluded in our 2009 paper and that his number of iterations is
insufficient for the region chosen. We also show that, contrary to what is
claimed by the author, (i) Levy distributions are irrelevant for this problem,
and that (ii) the probability distributions of sums that focus on transients
are unlikely to be universal.
