  The Parkes 20 cm Multibeam pulsar surveys have discovered nearly half of the
known pulsars and revealed many distant pulsars with high dispersion measures.
Using a sample of 1,301 pulsars from these surveys, we have explored the
spatial distribution and birth rate of normal pulsars. The pulsar distances
used to calculate the pulsar surface density are estimated from the YMW16
electron-density model. When estimating the impact of the Galactic background
radiation on our survey, we projected pulsars in the Galaxy onto the Galactic
plane, assuming that the flux density distribution of pulsars is uniform in all
directions, and utilized the most up-to-date background temperature map. We
also used an up-to-date version of the ATNF Pulsar Catalogue to model the
distribution of pulsar flux densities at 1400 MHz. We derive an improved radial
distribution for the pulsar surface density projected on to the Galactic plane,
which has a maximum value at $\sim$4 kpc from the Galactic Centre. We also
derive the local surface density and birthrate of pulsars, obtaining 47 $\pm$ 5
$\mathrm{kpc^{-2}}$ and $\sim$ 4.7 $\pm$ 0.5 $\mathrm{kpc^{-2}\ Myr^{-1}}$,
respectively. For the total number of potentially detectable pulsars in the
Galaxy, we obtain (1.1 $\pm$ 0.2) $\times$ $10^{4}$ and (1.1 $\pm$ 0.2)
$\times$ $10^{5}$ before and after applying the TM98 beaming correction model.
The radial distribution function is used to estimate the proportion of pulsars
in each spiral arm and the Galactic centre.
