The source of radiation surely makes a difference. Directing the sensor at a small point source makes clustering higher than if pointing it up into space [0] a

The source of radiation surely makes a difference. Directing the sensor at a small point source makes clustering higher than if pointing it up into space [0] and receiving the "planar wave" background radiation of the Universe. I took a while to figure this out when measuring the audio clicks and crackles from fire. I expect similar statistics to apply on a nuclear level (physicists please correct me). Within small, local sources common effects can be linked to common instigators. In other words events beget events. So a local variation in some variable sets off a bunch of related things [1]. As you sum this over an ever larger number of suitably decoupled sources, the central limit theorem starts to apply and what was bad uniform/even distribution becomes good Gaussian. In practice you need more than the theoretical >12 sources, but once you approach a few hundred uncorrelated sources the bell curve gets pretty good. [0] probably assume the sky/space is an infinite number of sources all at very large distances. [1] In the (dangerous) limit imagine a near critical mass of Uranium emitting bursts of chain cascades.