We consider the statistics of pulsar binaries with white dwarf companions ( NS - WD ) .
Using the statistical analysis method developed by Kim et al .
( 2003 ) we calculate the Galactic coalescence rate of NS - WD binaries due to gravitational-wave emission .
We find that the most likely values for the total Galactic coalescence rate ( { \cal R } _ { tot } ) of NS - WD binaries lie in the range 0.2–10 Myr ^ { -1 } depending on different assumed pulsar population models .
For our reference model , we obtain { \cal R } _ { tot } = 4.11 _ { -2.56 } ^ { +5.25 } Myr ^ { -1 } at a 68 % statistical confidence level .
These rate estimates are not corrected for pulsar beaming and as such they are found to be about a factor of 20 smaller than the Galactic coalescence rate estimates for double neutron star systems .
Based on our rate estimates , we calculate the gravitational-wave background due to coalescing NS - WD binaries out to extragalactic distances within the frequency band of the Laser Interferometer Space Antenna .
We find the contribution from NS - WD binaries to the gravitational-wave background to be negligible .