  (Abridged) We infer the velocity distribution of radio pulsars by modelling
their birth, evolution, and detection in large-scale 0.4 GHz pulsar surveys,
and by comparing model distributions of measurable pulsar properties with
survey data using a likelihood function. We test models that characterize a
population's birth rate, luminosity, shutoff of radio emission, birth
locations, and birth velocities. We infer that the radio beam luminosity (i) is
comparable to the energy flux of relativistic particles in models for
spin-driven magnetospheres, signifying that radio emission losses reach nearly
100% for the oldest pulsars; and (ii) scales approximately as sqrt(Edot) which,
in magnetosphere models, is proportional to the voltage drop available for
acceleration of particles. We find that a two-component velocity distribution
with characteristic velocities of 90 km/s and 500 km/s is greatly preferred to
any one-component distribution. We explore some consequences of the preferred
birth velocity distribution: (i) roughly 50% of pulsars in the solar
neighborhood will escape the Galaxy, while ~15% have velocities greater than
1000 km/s; (ii) an important low-velocity population exists that increases the
fraction of neutron stars retained by globular clusters and is consistent with
the number of old objects that accrete from the interstellar medium; (iii)
under standard assumptions for supernova remnant expansion and pulsar
spin-down, ~10% of pulsars younger than 20 kyr will appear to lie outside of
their host remnants. Finally, we comment on the ramifications of our birth
velocity distribution for binary survival and the population of inspiraling
binary neutron stars relevant to some GRB models and potential sources for
LIGO.
