  We test statistically the hypothesis that radio pulsar glitches result from
an avalanche process, in which angular momentum is transferred erratically from
the flywheel-like superfluid in the star to the slowly decelerating, solid
crust via spatially connected chains of local, impulsive, threshold-activated
events, so that the system fluctuates around a self-organised critical state.
Analysis of the glitch population (currently 285 events from 101 pulsars)
demonstrates that the size distribution in individual pulsars is consistent
with being scale invariant, as expected for an avalanche process. The
waiting-time distribution is consistent with being exponential in seven out of
nine pulsars where it can be measured reliably, after adjusting for
observational limits on the minimum waiting time, as for a constant-rate
Poisson process. PSR J0537$-$6910 and PSR J0835$-$4510 are the exceptions;
their waiting-time distributions show evidence of quasiperiodicity. In each
object, stationarity requires that the rate $\lambda$ equals $- \epsilon
\dot{\nu} / <\Delta\nu>$, where $\dot{\nu}$ is the angular acceleration of the
crust, $<\Delta\nu>$ is the mean glitch size, and $\epsilon\dot{\nu}$ is the
relative angular acceleration of the crust and superfluid. There is no evidence
that $\lambda$ changes monotonically with spin-down age. The rate distribution
itself is fitted reasonably well by an exponential for $\lambda \geq 0.25 {\rm
yr^{-1}}$. For $\lambda < 0.25 {\rm yr^{-1}}$, its exact form is unknown; the
exponential overestimates the number of glitching pulsars observed at low
$\lambda$, where the limited total observation time exercises a selection bias.
