  Determining whether the flux distribution of an Astrophysical source is a
Gaussian or a log-normal, provides key insight into the nature of its
variability. For lightcurves of moderate length ($< 10^3$), a useful first
analysis is to test the Gaussianity of the flux and logarithm of the flux, by
estimating the skewness and applying the Anderson-Darling (AD) method. We
perform extensive simulations of lightcurves with different lengths,
variability, Gaussian measurement errors and power spectrum index $\beta$ (i.e.
$P(f) \propto f^{-\beta}$), to provide a prescriptionand guidelines for
reliable use of these two tests. We present empirical fits for the expected
standard deviation of skewness and tabulated AD test critical values for $\beta
= 0.5$ and $1.0$, which differ from the values given in the literature which
are for white noise ($\beta = 0$). Moreover, we show that for white noise, for
most practical situations, these tests are meaningless, since binning in time
alters the flux distribution. For $\beta \gtrsim 1.5$, the skewness variance
does not decrease with length and hence the tests are not reliable. Thus, such
tests can be applied only to systems with $\beta\gtrsim 0.5$ and $\beta
\lesssim 1.0$. As an example of the prescription given in this work, we
reconfirm that the Fermi data of the blazar, 3FGL\,J0730.2-1141, shows that its
$\gamma$ ray flux is consistent with a log-normal distribution and not with a
Gaussian one.
