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The sampling of the position in the SNR and pulsar distribution is done in cylindrical coordinates. The current approach misses a$r$ term for the radial componet. The differential number of sampled positions should be given by $dN = f(R, z) dV = f(R, z) \ R dR\ dZ \ d\phi$ .
Additionaly the PR reduces the amount computation by skipping the normalisation of the curves. For the MC-rejection sampling only the knowleadge of the overall maximum is needed (once calculated) and not a normalized curve.