  The paper that is commented by Touchette contains a computational study which
opens the door to a desirable generalization of the standard large deviation
theory (applicable to a set of $N$ nearly independent random variables) to
systems belonging to a special, though ubiquitous, class of strong
correlations. It focuses on three inter-related aspects, namely (i) we exhibit
strong numerical indications which suggest that the standard exponential
probability law is asymptotically replaced by a power-law as its dominant term
for large $N$; (ii) the subdominant term appears to be consistent with the
$q$-exponential behavior typical of systems following $q$-statistics, thus
reinforcing the thermodynamically extensive entropic nature of the exponent of
the $q$-exponential, basically $N$ times the $q$-generalized rate function;
(iii) the class of strong correlations that we have focused on corresponds to
attractors in the sense of the Central Limit Theorem which are $Q$-Gaussian
distributions (in principle $1 < Q < 3$), which relevantly differ from
(symmetric) L\'evy distributions, with the unique exception of Cauchy-Lorentz
distributions (which correspond to $Q = 2$), where they coincide, as well
known. In his Comment, Touchette has agreeably discussed point (i), but,
unfortunately, points (ii) and (iii) have, as we detail here, visibly escaped
to his analysis. Consequently, his conclusion claiming the absence of special
connection with $q$-exponentials is unjustified.
