  In optical non-linear processes rogue waves can be observed, which can be
mathematically described by heavy-tailed distributions. These distributions are
special due to the fact that the probability of registering extremely high
intensities is significantly higher than for the exponential distribution,
which is most commonly observed in statistical and quantum optics. The current
manuscript gives a practical overview of the generic statistics toolkit
concerning heavy-tailed distributions and proposes methods to deal with issues
specific to non-linear optics. We take a closer look at supercontinuum
generation, where rogue waves were already observed. We propose modifications
to the Hill estimator to deal with detector saturation as well as corrections
introduced by pumping the process by bright squeezed vacuum. The suggested
methodology facilitates statistically reliable observation of heavy-tailed
distribution in non-linear optics, nanooptics, atomic, solid-state processes
and optomechanics.
