In optical non-linear processes, rogue waves can be observed, which can be mathematically described by heavy-tailed distributions. These distributions are special since 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. Our work provides 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, nano-optics, atomic, solid-state processes, and optomechanics.

在光学非线性过程中，可以观察到流氓波，这可以用重尾分布在数学上描述。这些分布是特殊的，因为记录极高强度的概率显着高于指数分布，后者在统计和量子光学中最常见。我们的工作提供了有关重尾分布的通用统计工具包的实用概述，并提出了处理非线性光学特定问题的方法。我们仔细研究了超连续谱的产生，在那里已经观察到了流氓波。我们建议对 Hill 估计器进行修改，以处理检测器饱和度以及通过明亮挤压真空抽吸过程引入的校正。