  We provide theoretical and experimental evidence of statistical outliers in
random laser emission that are not accounted for by the, now established,
power-law tailed (L\'evy) distribution. Such outliers manifest themselves as
single, large isolated spikes over an otherwise smooth background. A
statistical test convincingly shows that their probability is larger than the
one extrapolated from lower-intensity events. To compare with experimental
data, we introduced the anomaly parameter that allows for an identification of
such rare events from experimental spectral measurements and that agrees as
well with the simulations of our Monte Carlo model. A possible interpretation
in terms of Black Swans or Dragon Kings, large events having a different
generation mechanism from their peers, is discussed.
