Estimation of heavy tails in optical non-linear processes

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