  This work presents two distinct approaches to estimating the exponent related
to the distribution of optical rogue waves observed in supercontinuum generated
in a single-mode fiber, that is, to quantifying the rogueness. The first is a
generalization of the well-known Hill estimator, and the second relies on
estimating all parameters of a multi-parameter model. We show that the model
shows a good correspondence with experimental data, and that the two estimating
approaches provide consistent results, which are significantly more accurate
than those obtained with earlier methods of estimation. Furthermore,
alternative visualization through the tail function revealed the presence of
pump depletion as well as detector saturation leading to the breakdown of
power-law behavior for the largest observations. We characterized this
breakdown via a combination of an exponential and a generalized Pareto
distribution. Additionally, we have uncovered a weak memory effect in the data,
which can be attributed to changes of the refractive index in the single-mode
fiber.
