  Studies of the Galactic population of radio pulsars have shown that their
luminosity distribution appears to be log-normal in form. We investigate some
of the consequences that occur when one applies this functional form to
populations of pulsars in globular clusters. We use Bayesian methods to explore
constraints on the mean and standard deviation of the luminosity function, as
well as the total number of pulsars, given an observed sample of pulsars down
to some limiting flux density, accounting for measurements of flux densities of
individual pulsars as well as diffuse emission from the direction of the
cluster. We apply our analysis to Terzan 5, 47 Tucanae and M 28, and
demonstrate, under reasonable assumptions, that the number of potentially
observable pulsars should be within 95% credible intervals of
$147^{+112}_{-65}$, $83^{+54}_{-35}$ and $100^{+91}_{-52}$, respectively.
Beaming considerations would increase the true population size by approximately
a factor of two. Using non-informative priors, however, the constraints are not
tight due to the paucity and quality of flux density measurements. Future
cluster pulsar discoveries and improved flux density measurements would allow
this method to be used to more accurately constrain the luminosity function,
and to compare the luminosity function between different clusters.
