  Plastino, Rocca and Pennini [Phys. Rev. E \textbf{94} (2016) 012145] recently
stated that the R\'enyi entropy is not suitable for thermodynamics by using
functional calculus, since it leads to anomalous results unlike the Tsallis
entropy. We first show that the Tsallis entropy also leads to such anomalous
behaviours if one adopts the same functional calculus approach. Second, we note
that one of the Lagrange multipliers is set in an \textit{ad-hoc} manner in the
functional calculus approach of Plastino, Rocca and Pennini. Finally, the
explanation for these anomalous behaviours is provided by observing that the
generalized distributions obtained by Plastino, Rocca and Pennini does not
yield the ordinary canonical partition function in the appropriate limit and
therefore cannot be considered as genuine generalized distributions.
