  The production of artificial light curves with known statistical and
variability properties is of great importance in astrophysics. Consolidating
the confidence levels during cross-correlation studies, understanding the
artefacts induced by sampling irregularities, establishing detection limits for
future observatories are just some of the applications of simulated data sets.
Currently, the widely used methodology of amplitude and phase randomisation is
able to produce artificial light curves which have a given underlying power
spectral density (PSD) but which are strictly Gaussian distributed. This
restriction is a significant limitation, since the majority of the light curves
e.g. active galactic nuclei, X-ray binaries, gamma-ray bursts show strong
deviations from Gaussianity exhibiting `burst-like' events in their light
curves yielding long-tailed probability distribution functions (PDFs). In this
study we propose a simple method which is able to precisely reproduce light
curves which match both the PSD and the PDF of either an observed light curve
or a theoretical model. The PDF can be representative of either the parent
distribution or the actual distribution of the observed data, depending on the
study to be conducted for a given source. The final artificial light curves
contain all of the statistical and variability properties of the observed
source or theoretical model i.e. same PDF and PSD, respectively. Within the
framework of Reproducible Research, the code, together with the illustrative
example used in this manuscript, are both made publicly available in the form
of an interactive Mathematica notebook.
