  The statistics of edge-localised plasma instabilities (ELMs) in toroidal
magnetically confined fusion plasmas are considered. From first principles,
standard experimentally motivated assumptions are shown to determine a specific
probability distribution for the waiting times between ELMs: the Weibull
distribution. This is confirmed empirically by a statistically rigorous
comparison with a large data set from the Joint European Torus (JET). The
successful characterisation of ELM waiting times enables future work to
progress in various ways. Here we present a quantitative classification of ELM
types, complementary to phenomenological approaches. It also informs us about
the nature of ELMing processes, such as whether they are random or
deterministic.
