  In a recent paper [\textit{M. Cristelli, A. Zaccaria and L. Pietronero, Phys.
Rev. E 85, 066108 (2012)}], Cristelli \textit{et al.} analysed relation between
skewness and kurtosis for complex dynamical systems and identified two
power-law regimes of non-Gaussianity, one of which scales with an exponent of 2
and the other is with $4/3$. Finally the authors concluded that the observed
relation is a universal fact in complex dynamical systems. Here, we test the
proposed universal relation between skewness and kurtosis with large number of
synthetic data and show that in fact it is not universal and originates only
due to the small number of data points in the data sets considered. The
proposed relation is tested using two different non-Gaussian distributions,
namely $q$-Gaussian and Levy distributions. We clearly show that this relation
disappears for sufficiently large data sets provided that the second moment of
the distribution is finite. We find that, contrary to the claims of Cristelli
\textit{et al.} regarding a power-law scaling regime, kurtosis saturates to a
single value, which is of course different from the Gaussian case ($K=3$), as
the number of data is increased. On the other hand, if the second moment of the
distribution is infinite, then the kurtosis seems to never converge to a single
value. The converged kurtosis value for the finite second moment distributions
and the number of data points needed to reach this value depend on the
deviation of the original distribution from the Gaussian case. We also argue
that the use of kurtosis to compare distributions to decide which one deviates
from the Gaussian more can lead to incorrect results even for finite second
moment distributions for small data sets, whereas it is totally misleading for
infinite second moment distributions where the difference depends on $N$ for
all finite $N$.
