We use Monte Carlo methods to simulate the galactic gamma-ray pulsar p
opulation using a Compton-induced pair cascade model for gamma-ray pro
duction from pulsars. We compare the distance, period, magnetic field,
age, and gamma-ray flux distributions of the simulated pulsars with t
hose of the seven known gamma-ray pulsars and find that this model can
reproduce the observed trends given a pulsar cap size between 3 and 4
times larger than the nominal polar cap size. Polar caps of this size
are suggested by braking index measurements and can be explained by t
he presence of an equatorial disk in the pulsar magnetosphere. The int
egrated flux from all pulsars below the EGRET point source threshold i
s calculated and found to contribute to the diffuse galactic gamma-ray
flux at the 5%-10% level.