  Time series analysis allows for the determination of the Power Spectral
Density (PSD) and Probability Density Function (PDF) for astrophysical sources.
The former of these illustrates the distribution of power at various
timescales, typically taking a power-law form, while the latter characterises
the distribution of the underlying stochastic physical processes, with Gaussian
and lognormal functional forms both physically motivated. In this paper, we use
artificial time series generated using the prescription of Timmer & Koenig to
investigate connections between the PDF and PSD. PDFs calculated for these
artificial light curves are less likely to be well described by a Gaussian
functional form for steep (<-1) PSD spectral indices due to weak
non-stationarity. Using the Fermi LAT monthly light curve of the blazar
PKS2155-304 as an example, we prescribe and calculate a false positive rate
which indicates how likely the PDF is to be attributed an incorrect functional
form. Here, we generate large numbers of artificial light curves with
intrinsically normally distributed PDFs and with statistical properties
consistent with observations. These are used to evaluate the probabilities that
either Gaussian or lognormal functional forms better describe the PDF. We use
this prescription to show that PKS2155-304 requires a high prior probability of
having a normally distributed PDF, P(G) >= 0.82, for the calculated PDF to
prefer a Gaussian functional form over a lognormal. We present possible choices
of prior and evaluate the probability that PKS2155-304 has a lognormally
distributed PDF for each.
