  The orbital sampling effect (OSE) appears in phase-folded transit light
curves of extrasolar planets with moons. Analytical OSE models have hitherto
neglected stellar limb darkening and non-zero transit impact parameters and
assumed that the moon is on a circular, co-planar orbit around the planet.
Here, we present an analytical OSE model for eccentric moon orbits, which we
implement in a numerical simulator with stellar limb darkening that allows for
arbitrary transit impact parameters. We also describe and publicly release a
fully numerical OSE simulator (PyOSE) that can model arbitrary inclinations of
the transiting moon orbit. Both our analytical solution for the OSE and PyOSE
can be used to search for exomoons in long-term stellar light curves such as
those by Kepler and the upcoming PLATO mission. Our updated OSE model offers an
independent method for the verification of possible future exomoon claims via
transit timing variations and transit duration variations. Photometrically
quiet K and M dwarf stars are particularly promising targets for an exomoon
discovery using the OSE.
