> Is Figure 8 an unconditional empirical CDF of inter-arrival times?
My understanding is that it's the inter-arrival times after some cleaning and resampling. If I've understood correctly, when they resampled the data, they did so uniformly between the neighbours of the points they omitted, which would actually make the data appear more like an exponential distribution.
> Especially considering its purpose. Maybe it would have been more accurate to say "there's a mixture of two Poissons: the bulk and the network disruption".
Could be. Could also follow a power law or a phase type distribution.
> But this isn't physics. We want to know how useful the approximation is, and whether there is a similarly tractable one with better predictive power.
It's worse, it's math :-) I take your point though, it all comes down to what you're trying to do. If inter-arrival times did follow an exponential distribution with parameter $\lambda$, then we'd have finite variance and I'd be pretty confident that I could build a performant predictive model. The presence of a heavy right tail makes me think otherwise.