  We present a statistical study of the glitch population and the behaviour of
the glitch activity across the known population of neutron stars. An unbiased
glitch database was put together based on systematic searches of radio timing
data of 898 rotation-powered pulsars obtained with the Jodrell Bank and Parkes
observatories. Glitches identified in similar searches of 5 magnetars were also
included. The database contains 384 glitches found in the rotation of 141 of
these neutron stars. We confirm that the glitch size distribution is at least
bimodal, with one sharp peak at approximately $20\, \rm{\mu\,Hz}$, which we
call large glitches, and a broader distribution of smaller glitches. We also
explored how the glitch activity $\dot{\nu}_{\rm{g}}$, defined as the mean
frequency increment per unit of time due to glitches, correlates with the spin
frequency $\nu$, spin-down rate $|\dot{\nu}|$, and various combinations of
these, such as energy loss rate, magnetic field, and spin-down age. It is found
that the activity is insensitive to the magnetic field and that it correlates
strongly with the energy loss rate, though magnetars deviate from the trend
defined by the rotation-powered pulsars. However, we find that a constant ratio
$\dot\nu_{\rm{g}}/|\dot\nu| = 0.010 \pm 0.001$ is consistent with the behaviour
of all rotation-powered pulsars and magnetars. This relation is dominated by
large glitches, which occur at a rate directly proportional to $|\dot{\nu}|$.
The only exception are the rotation-powered pulsars with the highest values of
$|\dot{\nu}|$, such as the Crab pulsar and PSR B0540$-$69, which exhibit a much
smaller glitch activity, intrinsically different from each other and from the
rest of the population. The activity due to small glitches also shows an
increasing trend with $|\dot\nu|$, but this relation is biased by selection
effects.
